[
    {
        "id": 1,
        "task_id": 248,
        "test_case_id": 1,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "1 2 2 1\n",
        "output": "6\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 2,
        "task_id": 248,
        "test_case_id": 2,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "1 1 1 2\n",
        "output": "31\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 3,
        "task_id": 248,
        "test_case_id": 3,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "2 12 3 1\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 4,
        "task_id": 248,
        "test_case_id": 4,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "4 6 2 1\n",
        "output": "3\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 5,
        "task_id": 248,
        "test_case_id": 5,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "4 6 2 2\n",
        "output": "122\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 6,
        "task_id": 248,
        "test_case_id": 6,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "6 4 2 2\n",
        "output": "435\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 7,
        "task_id": 248,
        "test_case_id": 7,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "10 1 3 3\n",
        "output": "112812\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 8,
        "task_id": 248,
        "test_case_id": 8,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "5 3 1 1\n",
        "output": "8\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 9,
        "task_id": 248,
        "test_case_id": 9,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "50 22 5 5\n",
        "output": "876439301\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 10,
        "task_id": 248,
        "test_case_id": 10,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "6 20 1 1\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 11,
        "task_id": 248,
        "test_case_id": 11,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "42 42 2 3\n",
        "output": "6937\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 12,
        "task_id": 248,
        "test_case_id": 12,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "42 42 3 2\n",
        "output": "1085\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 13,
        "task_id": 248,
        "test_case_id": 13,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "45 54 4 5\n",
        "output": "433203628\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 14,
        "task_id": 248,
        "test_case_id": 14,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "6 5 4 3\n",
        "output": "282051\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 15,
        "task_id": 248,
        "test_case_id": 15,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "42 42 42 42\n",
        "output": "284470145\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 16,
        "task_id": 248,
        "test_case_id": 16,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "1 100 42 42\n",
        "output": "58785421\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 17,
        "task_id": 248,
        "test_case_id": 17,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "1 100 1000 100\n",
        "output": "542673827\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 18,
        "task_id": 248,
        "test_case_id": 18,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "1 1 1000 100\n",
        "output": "922257788\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 19,
        "task_id": 248,
        "test_case_id": 19,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "100 100 1000 100\n",
        "output": "922257788\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 20,
        "task_id": 248,
        "test_case_id": 20,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "1 8 1 4\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 21,
        "task_id": 248,
        "test_case_id": 21,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "9 4 5 2\n",
        "output": "11045\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 22,
        "task_id": 248,
        "test_case_id": 22,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "2 6 6 2\n",
        "output": "8015\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 23,
        "task_id": 248,
        "test_case_id": 23,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "7 8 5 9\n",
        "output": "860378382\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 24,
        "task_id": 248,
        "test_case_id": 24,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "3 7 8 6\n",
        "output": "510324293\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 25,
        "task_id": 248,
        "test_case_id": 25,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "69 69 803 81\n",
        "output": "74925054\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 26,
        "task_id": 248,
        "test_case_id": 26,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "67 67 871 88\n",
        "output": "123371511\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 27,
        "task_id": 248,
        "test_case_id": 27,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "71 71 891 31\n",
        "output": "790044038\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 28,
        "task_id": 248,
        "test_case_id": 28,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "49 49 631 34\n",
        "output": "764129060\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 29,
        "task_id": 248,
        "test_case_id": 29,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "83 83 770 49\n",
        "output": "761730117\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 30,
        "task_id": 248,
        "test_case_id": 30,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "49 49 163 15\n",
        "output": "458364105\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 31,
        "task_id": 248,
        "test_case_id": 31,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "38 38 701 74\n",
        "output": "496603581\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 32,
        "task_id": 248,
        "test_case_id": 32,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "65 65 803 79\n",
        "output": "253679300\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 33,
        "task_id": 248,
        "test_case_id": 33,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "56 56 725 64\n",
        "output": "338598412\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 34,
        "task_id": 248,
        "test_case_id": 34,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "70 70 176 56\n",
        "output": "990579000\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 35,
        "task_id": 248,
        "test_case_id": 35,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "32 32 44 79\n",
        "output": "20803934\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 36,
        "task_id": 248,
        "test_case_id": 36,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "35 35 353 21\n",
        "output": "149936279\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 37,
        "task_id": 248,
        "test_case_id": 37,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "57 57 896 52\n",
        "output": "271910130\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 38,
        "task_id": 248,
        "test_case_id": 38,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "86 86 373 19\n",
        "output": "940701970\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 39,
        "task_id": 248,
        "test_case_id": 39,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "27 27 296 97\n",
        "output": "394599845\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 40,
        "task_id": 248,
        "test_case_id": 40,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "60 60 86 51\n",
        "output": "277883413\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 41,
        "task_id": 248,
        "test_case_id": 41,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "40 40 955 95\n",
        "output": "600387428\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 42,
        "task_id": 248,
        "test_case_id": 42,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "34 34 706 59\n",
        "output": "274236101\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 43,
        "task_id": 248,
        "test_case_id": 43,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "74 74 791 51\n",
        "output": "367968499\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 44,
        "task_id": 248,
        "test_case_id": 44,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "69 69 443 53\n",
        "output": "385620893\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 45,
        "task_id": 248,
        "test_case_id": 45,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "59 19 370 48\n",
        "output": "125206836\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 46,
        "task_id": 248,
        "test_case_id": 46,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "78 82 511 33\n",
        "output": "375900871\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 47,
        "task_id": 248,
        "test_case_id": 47,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "66 90 805 16\n",
        "output": "593436252\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 48,
        "task_id": 248,
        "test_case_id": 48,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "60 61 772 19\n",
        "output": "931528755\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 49,
        "task_id": 248,
        "test_case_id": 49,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "81 13 607 21\n",
        "output": "762608093\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 50,
        "task_id": 248,
        "test_case_id": 50,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "35 79 128 21\n",
        "output": "177972209\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 51,
        "task_id": 248,
        "test_case_id": 51,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "93 25 958 20\n",
        "output": "873170266\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 52,
        "task_id": 248,
        "test_case_id": 52,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "44 85 206 80\n",
        "output": "170080402\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 53,
        "task_id": 248,
        "test_case_id": 53,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "79 99 506 18\n",
        "output": "486170430\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 54,
        "task_id": 248,
        "test_case_id": 54,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "97 22 29 8\n",
        "output": "471632954\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 55,
        "task_id": 248,
        "test_case_id": 55,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "14 47 184 49\n",
        "output": "726421144\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 56,
        "task_id": 248,
        "test_case_id": 56,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "74 33 868 5\n",
        "output": "826980486\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 57,
        "task_id": 248,
        "test_case_id": 57,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "53 79 823 11\n",
        "output": "526626321\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 58,
        "task_id": 248,
        "test_case_id": 58,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "99 99 913 42\n",
        "output": "446683872\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 59,
        "task_id": 248,
        "test_case_id": 59,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "52 34 89 41\n",
        "output": "905639400\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 60,
        "task_id": 248,
        "test_case_id": 60,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "87 100 200 80\n",
        "output": "913761305\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 61,
        "task_id": 248,
        "test_case_id": 61,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "40 94 510 53\n",
        "output": "233079261\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 62,
        "task_id": 248,
        "test_case_id": 62,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "2 56 438 41\n",
        "output": "500592304\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 63,
        "task_id": 248,
        "test_case_id": 63,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "6 68 958 41\n",
        "output": "719351710\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 64,
        "task_id": 248,
        "test_case_id": 64,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "44 80 814 26\n",
        "output": "414148151\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 65,
        "task_id": 248,
        "test_case_id": 65,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "100 1 1000 100\n",
        "output": "603336175\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 66,
        "task_id": 248,
        "test_case_id": 66,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "1 3 1000 100\n",
        "output": "604187087\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 67,
        "task_id": 248,
        "test_case_id": 67,
        "question": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.\n\nMemory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.\n\n\n-----Input-----\n\nThe first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.\n\n\n-----Output-----\n\nPrint the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.\n\n\n-----Examples-----\nInput\n1 2 2 1\n\nOutput\n6\n\nInput\n1 1 1 2\n\nOutput\n31\n\nInput\n2 12 3 1\n\nOutput\n0\n\n\n\n-----Note-----\n\nIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.",
        "solutions": "[\"mod=10**9+7\\nf=[0]*500000\\n\\ndef POW(a,b):\\n\\tif(b==0):\\n\\t\\treturn 1\\n\\tif(b&1):\\n\\t\\treturn POW(a,b//2)**2*a%mod\\n\\telse:\\n\\t\\treturn POW(a,b//2)**2\\n\\ndef C(n,m):\\n\\tif(m>n):\\n\\t\\treturn 0\\n\\tt=f[n]*POW(f[m],mod-2)%mod*POW(f[n-m],mod-2)%mod\\n\\treturn t\\n\\n\\nf[0]=1\\nfor i in range(1,500000):\\n\\tf[i]=f[i-1]*i%mod\\na,b,k,t=list(map(int,input().split(' ')))\\n\\nans=0\\nfor i in range(0,2*t+1):\\n\\tt1=POW(-1,i)*C(2*t,i)%mod\\n\\tt2=(C(210000+2*k*t-a+b+2*t-1-(2*k+1)*i+1,2*t)-C(1+2*k*t-a+b+2*t-1-(2*k+1)*i,2*t))%mod\\n\\tans=(ans+t1*t2)%mod\\nprint(ans)\\n\", \"def c(n, k):\\n\\tif k > n:\\n\\t\\treturn 0\\n\\ta = b = 1\\n\\tfor i in range(n - k + 1, n + 1):\\n\\t\\ta *= i\\n\\tfor i in range(1, k + 1):\\n\\t\\tb *= i\\n\\treturn a // b\\na, b, k, t = map(int, input().split())\\nn, m, s = 2 * k + 1, 2 * t, 2 * k * t + b - a\\nans, mod = 0, 1000000007\\nfor i in range(m + 1):\\n\\tans = (ans + [1, -1][i & 1] * c(m, i) * c(m + s - n * i, m)) % mod\\nprint((pow(n, m, mod) - ans) % mod)\"]",
        "difficulty": "interview",
        "input": "10 10 1000 100\n",
        "output": "922257788\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/712/D"
    },
    {
        "id": 68,
        "task_id": 541,
        "test_case_id": 1,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "5 2\n1 4\n2 5\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 69,
        "task_id": 541,
        "test_case_id": 2,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "9 5\n1 8\n2 7\n3 5\n4 6\n7 9\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 70,
        "task_id": 541,
        "test_case_id": 3,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "5 10\n1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 4\n3 5\n4 5\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 71,
        "task_id": 541,
        "test_case_id": 4,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "2 1\n1 2\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 72,
        "task_id": 541,
        "test_case_id": 5,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "3 3\n2 3\n1 2\n1 3\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 73,
        "task_id": 541,
        "test_case_id": 6,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "19 7\n4 18\n6 11\n3 11\n6 12\n14 19\n2 10\n11 15\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 74,
        "task_id": 541,
        "test_case_id": 7,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "17 107\n3 13\n1 5\n3 15\n11 14\n1 2\n11 16\n8 9\n1 17\n2 14\n11 13\n3 8\n7 16\n2 15\n12 13\n5 6\n6 12\n13 15\n9 15\n1 14\n6 17\n12 17\n14 17\n6 11\n5 13\n8 10\n3 16\n9 10\n3 4\n10 11\n7 9\n15 16\n7 10\n4 8\n5 7\n2 8\n10 12\n2 10\n14 16\n4 12\n3 6\n2 12\n12 16\n7 17\n7 12\n4 16\n3 10\n5 11\n2 5\n9 12\n11 12\n16 17\n5 16\n3 7\n13 14\n7 14\n3 12\n3 17\n2 7\n8 17\n7 13\n1 3\n9 17\n2 17\n7 11\n7 8\n1 8\n6 13\n4 5\n7 15\n8 12\n2 4\n4 11\n15 17\n6 14\n10 13\n5 15\n4 7\n4 17\n1 4\n1 15\n6 15\n8 16\n10 15\n13 16\n10 16\n9 11\n5 17\n3 11\n4 6\n2 6\n6 9\n1 6\n6 16\n3 9\n4 15\n5 9\n2 13\n8 15\n12 14\n6 8\n11 17\n4 14\n1 9\n6 10\n8 13\n13 17\n5 8\n",
        "output": "13\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 75,
        "task_id": 541,
        "test_case_id": 8,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "9 24\n6 8\n3 8\n1 3\n5 6\n3 5\n1 7\n1 8\n2 4\n8 9\n3 7\n1 2\n6 7\n5 9\n2 9\n4 6\n2 3\n4 8\n1 4\n6 9\n2 5\n2 8\n7 9\n3 6\n5 8\n",
        "output": "6\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 76,
        "task_id": 541,
        "test_case_id": 9,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "17 136\n2 17\n11 13\n5 7\n3 12\n5 11\n3 13\n1 13\n13 14\n6 11\n6 17\n1 8\n11 12\n10 17\n2 15\n16 17\n4 6\n8 11\n14 16\n13 17\n7 8\n1 3\n9 11\n10 16\n9 13\n3 8\n3 9\n7 12\n13 15\n8 12\n2 6\n14 17\n2 9\n12 16\n5 6\n1 16\n10 14\n6 7\n2 5\n3 7\n1 5\n4 11\n9 12\n7 10\n2 11\n9 16\n1 9\n8 13\n2 16\n8 14\n12 14\n9 15\n4 10\n1 10\n3 16\n4 16\n13 16\n5 12\n6 16\n7 11\n11 14\n8 9\n15 16\n7 14\n7 15\n5 8\n5 10\n4 17\n4 7\n2 8\n1 4\n3 14\n5 15\n2 13\n3 15\n6 15\n3 11\n4 15\n3 4\n4 14\n6 9\n9 14\n1 6\n5 14\n5 13\n6 13\n10 13\n7 9\n11 17\n5 17\n6 14\n15 17\n4 12\n3 5\n3 6\n8 10\n7 17\n2 10\n7 16\n8 17\n1 2\n3 17\n5 9\n2 3\n2 4\n1 7\n10 11\n11 16\n6 8\n12 15\n4 5\n8 16\n1 15\n1 17\n3 10\n6 10\n4 9\n4 13\n11 15\n14 15\n6 12\n8 15\n4 8\n1 11\n12 17\n10 12\n9 17\n1 14\n1 12\n5 16\n2 12\n2 14\n10 15\n2 7\n7 13\n9 10\n12 13\n",
        "output": "16\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 77,
        "task_id": 541,
        "test_case_id": 10,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "16 83\n13 14\n10 11\n2 7\n1 16\n4 16\n1 10\n2 16\n9 10\n6 16\n12 13\n3 13\n10 15\n6 13\n1 15\n7 9\n7 11\n9 14\n3 10\n6 11\n9 16\n4 6\n1 5\n7 12\n5 13\n8 13\n6 10\n2 14\n11 12\n8 14\n7 16\n6 8\n12 14\n3 16\n5 11\n3 5\n4 10\n11 16\n3 7\n9 15\n7 14\n8 15\n1 11\n3 14\n4 5\n14 15\n10 16\n7 8\n10 14\n2 6\n8 9\n15 16\n3 9\n8 12\n3 11\n14 16\n6 7\n2 13\n9 13\n5 7\n3 4\n13 16\n5 14\n6 15\n1 14\n5 12\n2 8\n6 14\n5 10\n6 9\n7 10\n9 12\n2 10\n1 2\n7 15\n8 11\n3 6\n5 9\n5 8\n2 3\n9 11\n1 12\n11 13\n2 12\n",
        "output": "14\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 78,
        "task_id": 541,
        "test_case_id": 11,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "20 35\n9 12\n10 16\n8 12\n6 11\n11 13\n10 11\n4 16\n5 20\n13 17\n6 19\n4 7\n3 16\n7 13\n12 15\n17 20\n16 20\n6 20\n5 19\n10 17\n4 18\n2 10\n6 14\n5 10\n5 9\n1 11\n9 11\n1 3\n13 16\n19 20\n5 18\n16 19\n2 3\n7 15\n6 18\n1 12\n",
        "output": "7\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 79,
        "task_id": 541,
        "test_case_id": 12,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "5 10\n2 4\n1 2\n2 3\n3 4\n4 5\n1 5\n1 4\n1 3\n2 5\n3 5\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 80,
        "task_id": 541,
        "test_case_id": 13,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "13 78\n3 12\n10 12\n8 10\n2 3\n5 9\n1 7\n8 13\n1 10\n11 13\n4 11\n5 11\n1 13\n5 12\n10 11\n5 10\n6 12\n1 2\n1 6\n6 13\n9 10\n1 12\n2 7\n4 13\n7 9\n2 8\n4 8\n1 8\n7 13\n5 8\n6 9\n5 13\n7 11\n2 13\n12 13\n4 10\n4 9\n1 3\n6 10\n10 13\n3 10\n1 5\n2 9\n3 5\n11 12\n8 9\n4 7\n6 11\n2 10\n2 4\n3 4\n4 6\n8 12\n4 5\n7 10\n8 11\n2 11\n5 6\n3 9\n3 8\n9 12\n1 11\n3 7\n9 11\n7 8\n1 9\n4 12\n3 6\n5 7\n7 12\n2 5\n9 13\n2 6\n2 12\n3 13\n6 7\n6 8\n3 11\n1 4\n",
        "output": "12\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 81,
        "task_id": 541,
        "test_case_id": 14,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "5 10\n4 5\n3 4\n1 2\n1 4\n3 5\n1 5\n1 3\n2 3\n2 5\n2 4\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 82,
        "task_id": 541,
        "test_case_id": 15,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "21189 4345\n10171 15645\n10849 16732\n6014 18169\n3995 20232\n1557 8296\n2238 15717\n10071 12875\n2148 13213\n14696 19948\n2063 14524\n7571 10285\n2102 14395\n12673 13427\n15751 16347\n317 13928\n9825 17447\n7990 9393\n8479 14766\n6185 6858\n2781 11064\n14909 16382\n8468 9916\n7189 12428\n16941 18034\n8365 20107\n15421 17588\n5470 13011\n6101 13110\n5038 12358\n1985 6860\n8467 19510\n6927 17836\n11859 12049\n12723 16913\n7565 10012\n16983 17666\n2195 5114\n3859 6527\n3252 13781\n4850 17562\n6088 21104\n11530 17982\n9866 11236\n7214 18833\n3947 12468\n4977 8828\n4383 13070\n1365 1414\n459 18354\n859 1875\n1622 20390\n1246 19404\n1339 16427\n8477 10279\n14843 16725\n2115 7366\n4573 15167\n17752 20588\n4292 11368\n1663 4836\n3200 18771\n15106 18276\n9723 18814\n11443 16403\n6922 14340\n1385 11268\n4864 19148\n11189 12945\n13906 14754\n2201 20815\n2728 4366\n13479 19677\n6139 18510\n7150 7837\n14621 16094\n10256 11810\n2297 11415\n275 20775\n2329 5563\n6448 17732\n2540 10097\n15326 19694\n5449 20217\n9937 21057\n5651 20990\n667 8901\n13051 18351\n5273 14957\n464 11737\n2426 12196\n11690 12088\n730 3156\n2275 10094\n13884 15287\n1319 5995\n1160 14323\n16732 20355\n8624 10082\n11372 13963\n11418 17322\n4151 20441\n8902 16767\n1692 16230\n3688 4727\n5378 20890\n3515 15476\n7749 7751\n11427 15972\n4093 19331\n5776 9704\n1657 13149\n247 3439\n12608 15008\n9339 19559\n429 6932\n6329 17180\n7566 19173\n4194 18235\n3470 19242\n1404 17452\n387 9834\n3720 18977\n13540 19979\n15891 20636\n11447 14838\n8039 12405\n14537 15229\n10455 16199\n6149 14345\n2957 6207\n210 2145\n7760 18304\n13691 15825\n12874 15177\n999 7238\n12764 18409\n14026 18054\n2237 9830\n9647 18417\n14837 19057\n8262 10568\n1130 10242\n1049 19855\n8650 12813\n18129 18169\n6143 15917\n1526 3565\n6613 8468\n3308 14033\n5092 17069\n3956 15613\n7903 13490\n13496 20568\n17620 17888\n2673 13112\n1501 13922\n2278 20020\n3867 7355\n1454 14688\n1959 8447\n853 16568\n12634 19990\n10250 18920\n11835 19618\n400 8595\n2852 16228\n1989 9926\n12306 17820\n265 7067\n8054 12803\n9639 17797\n13483 16319\n6445 13114\n14599 20256\n10435 21153\n4622 9294\n10106 12955\n2092 15645\n10888 18215\n8800 11438\n14786 15895\n12080 20400\n9327 12564\n11443 15042\n3717 5591\n10079 21081\n9625 17964\n9521 10757\n4856 8838\n1568 20361\n13504 16076\n18576 19776\n5686 21177\n698 2159\n9204 13239\n9286 15524\n11103 14785\n10885 11909\n3156 8098\n7124 8472\n73 11800\n10701 20849\n1166 11771\n9293 14741\n13347 19969\n8873 15393\n9397 9551\n738 13985\n16222 20639\n4624 18229\n1374 12804\n5283 16797\n5726 7180\n7525 16909\n3764 16245\n12598 13937\n2840 21172\n17478 18669\n4816 11264\n12863 20119\n577 4677\n890 944\n1694 12612\n4906 13536\n18289 20915\n3721 12185\n2507 17600\n5736 11399\n13237 19225\n861 9043\n4422 9499\n3078 12371\n2004 3159\n3591 20394\n6616 17992\n18379 19850\n8506 17436\n635 2628\n4675 13063\n14739 20713\n10915 17452\n17422 17748\n12371 18405\n3695 18483\n10984 19721\n10057 10296\n5009 19028\n568 14349\n2594 9121\n12922 15493\n10904 11704\n12238 19633\n427 19536\n2548 14066\n3008 7262\n9721 15584\n2962 14051\n9883 20416\n3809 15156\n7334 11774\n4381 9769\n10907 11754\n11371 17978\n1917 7103\n12737 20640\n9430 11058\n13369 20853\n609 5701\n18008 18917\n9304 10223\n8220 20997\n4559 17881\n14739 16048\n8697 20520\n13584 18012\n15563 20926\n13377 17972\n16342 21189\n5948 14309\n2715 14536\n2569 7046\n194 1044\n2824 7204\n6656 16721\n4663 9115\n3634 7974\n14368 16480\n3560 9271\n7797 10880\n8356 15725\n4554 7659\n1216 17132\n8769 8935\n6181 12458\n6768 18775\n572 15027\n13057 17090\n15072 21089\n5565 13456\n4037 13479\n3220 17406\n17428 18083\n5517 14946\n6727 19311\n8214 15270\n1731 7498\n7284 15125\n1498 21014\n7443 9978\n1175 7934\n16215 17325\n16398 17357\n9572 15536\n6216 16609\n6855 20328\n8866 11113\n10140 20086\n12474 20172\n8636 18097\n2172 17578\n9527 11787\n2228 19545\n13034 19175\n14775 20238\n12603 14277\n3015 21010\n4665 12216\n277 11170\n10215 19664\n18911 19122\n3939 6368\n12734 19103\n3701 6387\n9058 19601\n10098 20890\n11558 17751\n4694 14956\n10410 14547\n1411 12919\n6779 10563\n2593 3822\n12405 15737\n13235 18048\n14683 15377\n170 6876\n14844 16423\n15069 19337\n5946 15636\n15212 16767\n6527 20591\n1500 20577\n1926 16328\n600 20243\n6443 11520\n3949 4568\n15757 16322\n13586 20265\n98 17624\n4337 15402\n15047 18700\n5484 13754\n5713 19708\n8360 21098\n17092 21076\n12643 18561\n8116 14269\n7087 20525\n4042 8234\n13088 20918\n748 954\n12182 13639\n3982 6067\n4985 18975\n8432 15517\n6505 9424\n249 14391\n3311 20527\n18209 18797\n11759 20012\n10212 16099\n9574 21124\n13233 16544\n11904 18132\n16367 16979\n13735 20807\n19320 19398\n12082 19273\n484 2719\n6200 13210\n1016 17161\n4996 10710\n11986 14783\n15801 16449\n8415 20342\n2816 13573\n10010 11257\n5211 6228\n11678 14316\n2372 9133\n7245 17953\n12752 17901\n8309 12173\n7629 15135\n690 14808\n6437 20749\n17067 20673\n8514 14460\n12083 17504\n7435 11014\n10177 21176\n1940 15854\n11428 11533\n5051 16922\n7296 15171\n4420 7428\n4993 13530\n8833 17532\n2558 9714\n1005 13887\n2334 7922\n2764 12076\n3271 12102\n912 2785\n4243 12849\n12295 16270\n3572 8226\n7079 19129\n5425 17302\n2452 7987\n2303 16304\n4904 10223\n5794 6547\n12025 12239\n5239 16385\n7067 19587\n4640 7794\n3264 7705\n3879 11995\n7962 15886\n13017 13281\n2351 7351\n10971 13691\n5157 7538\n8929 11888\n3993 15377\n1443 9969\n7545 15172\n18172 19458\n11120 15158\n3313 8805\n12604 13570\n3011 18246\n9868 10650\n14120 15939\n4923 7642\n8824 14840\n5648 20250\n8614 14485\n4289 5735\n11423 14845\n7137 14443\n1159 7227\n2720 14067\n1563 16246\n8271 18466\n7347 14632\n11998 17779\n6977 15759\n1135 18444\n471 9003\n775 19571\n5858 10714\n14463 17879\n19029 19368\n1149 7976\n1624 4754\n9199 14782\n416 13090\n1632 2101\n6653 6749\n15061 17739\n4732 21004\n9893 13816\n4903 19752\n1486 5168\n869 20796\n2734 15176\n8581 13945\n10110 16164\n4695 14190\n707 1259\n9830 15976\n2672 13926\n119 11179\n6847 13183\n16546 16933\n3899 15689\n171 12301\n503 20858\n500 14532\n3084 17488\n1080 10063\n14055 19157\n749 3701\n1692 10865\n2181 12452\n2196 9730\n6386 15909\n12212 14620\n7346 15840\n5713 8620\n15293 18088\n1417 14145\n5207 17610\n1175 14784\n605 2566\n16182 19435\n9703 17607\n13715 20001\n4398 9220\n8974 13280\n6848 19055\n11124 17160\n1374 19100\n7181 11953\n4764 16056\n3317 14247\n6191 17244\n3451 10358\n2254 20282\n7739 13685\n2401 18563\n5225 13539\n1409 20612\n7402 9758\n11537 19713\n11627 13451\n3764 11831\n1981 4490\n355 3447\n2460 13161\n18212 20295\n12967 19165\n3198 16720\n577 16725\n4470 10620\n14929 17242\n12423 16416\n11635 12357\n4225 9089\n958 15220\n1647 4821\n12017 13971\n12840 17606\n2264 4364\n11877 20792\n4483 14800\n12738 21045\n3007 14935\n18766 19964\n11722 21134\n12523 20068\n9612 16259\n7957 9026\n12410 20876\n9087 9990\n8965 11448\n2423 6243\n20411 20894\n204 12246\n8704 19219\n1471 11747\n16476 18869\n852 17971\n12162 12816\n8419 20285\n5902 17322\n2462 9134\n8983 9056\n1005 20527\n9484 12461\n16069 18941\n18256 18826\n5498 8615\n11396 17990\n4229 14735\n6727 8282\n11229 15246\n4241 18637\n4388 20907\n10325 16279\n15857 19337\n9938 19921\n2502 8236\n3366 11008\n420 5171\n13723 17595\n12986 16957\n12213 14638\n14004 20177\n2033 3029\n2254 9186\n1494 6016\n1050 20837\n10001 13429\n10002 12273\n618 6185\n9621 17548\n10671 14632\n13672 18042\n1388 8682\n1596 6247\n5939 8940\n150 9019\n11944 20071\n14059 19336\n5717 17424\n12269 16479\n14336 17494\n940 15966\n394 6967\n2459 17969\n895 19893\n12418 17594\n9872 10265\n9938 12580\n4633 15439\n1586 4442\n10343 11163\n4174 14287\n10041 12878\n11026 16568\n7096 14908\n4571 10326\n17033 17860\n4907 14078\n14073 14962\n7398 11585\n15951 18081\n1235 4833\n593 10276\n762 15599\n3822 8169\n2948 11314\n4205 16818\n16014 18508\n8899 18572\n2551 17324\n10521 18996\n14711 20766\n4817 15916\n14660 19939\n11065 14480\n733 13059\n2751 6576\n6241 18953\n17147 19488\n1087 7567\n637 11539\n17813 20005\n59 4428\n2273 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4193\n16475 17861\n12759 17681\n4186 9895\n10571 16249\n7424 10067\n4262 8112\n30 7480\n5605 10732\n14508 18985\n7723 18072\n567 11630\n9317 14468\n829 3748\n10190 10761\n4666 6415\n725 12452\n2887 3578\n4067 9899\n2896 9899\n8741 18816\n4679 17972\n10490 20016\n8025 12344\n10942 16720\n5182 18836\n3834 8885\n5454 13124\n5214 6650\n10255 17153\n5792 13946\n5138 20386\n3410 4965\n8169 19759\n3167 15385\n2539 19204\n8589 18268\n10240 19323\n5736 19296\n1460 19374\n9311 15906\n7400 13844\n10943 14008\n1724 18042\n101 8015\n5835 19307\n438 6736\n12 20394\n472 19204\n3271 5545\n7235 15851\n6457 12971\n3642 17766\n1261 21009\n2640 6443\n11251 15540\n7119 14552\n7293 12275\n16373 21010\n3269 10165\n17298 19082\n9477 15175\n4124 17747\n2599 9706\n3857 6767\n4915 18833\n8083 15697\n7237 16184\n12487 16812\n618 14377\n5859 13766\n1278 2636\n13649 20210\n10136 13128\n295 14285\n10376 13259\n9801 14534\n5297 13081\n6635 13023\n1581 2088\n3043 12289\n10057 15310\n5085 20695\n12892 15843\n10852 17782\n4552 19780\n4561 10739\n4264 19430\n5358 10417\n5104 8845\n1217 15476\n850 15435\n",
        "output": "74\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 83,
        "task_id": 541,
        "test_case_id": 16,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "15660 39923\n9869 14183\n2963 8259\n4190 8981\n4867 11713\n4030 15314\n5585 12429\n2573 7625\n549 11093\n5551 6890\n9153 10176\n10240 11378\n11315 14359\n504 7108\n557 5248\n4934 5009\n9059 15018\n8735 12357\n11662 15421\n8600 9007\n2572 9176\n1124 2322\n1003 10711\n2722 8797\n9390 12017\n6174 12481\n3107 12740\n8546 15192\n3666 12250\n5310 12645\n4859 7478\n4599 14839\n13767 14298\n5806 10439\n1284 10745\n11438 14350\n5196 14597\n3053 14839\n1160 3743\n11112 14726\n1067 14724\n6908 14313\n2667 5567\n5111 12963\n3603 8530\n7963 10989\n6019 14222\n3545 14236\n12328 13408\n651 15468\n407 5624\n2948 14931\n9824 14751\n12 13795\n13001 13527\n987 13101\n8831 9847\n3452 4719\n246 5661\n1583 7625\n6628 7984\n2737 12476\n1854 13427\n266 1072\n3358 5361\n4057 12165\n12239 13534\n5150 11222\n2387 2640\n7985 10198\n3026 12856\n424 3457\n583 856\n5231 13224\n5912 12837\n9762 14144\n11320 14482\n8288 8299\n2497 5212\n9619 12227\n991 12002\n1793 8979\n1628 12839\n1250 11515\n9410 13664\n7230 7622\n7508 8017\n2171 14298\n5502 10853\n8037 11221\n3034 14072\n8743 15083\n6909 9446\n5487 11278\n6244 11672\n3271 11442\n799 15642\n1477 11436\n1554 10732\n3387 10965\n308 2285\n2758 13000\n9318 10975\n4157 8265\n2550 4305\n4317 14667\n4982 7129\n2510 14168\n6242 14924\n2645 4412\n14551 15298\n9743 12719\n3177 6342\n3596 6780\n1393 10789\n5604 7267\n3025 14694\n1493 6790\n609 12249\n1959 12574\n967 13581\n4439 15009\n548 14485\n557 5122\n13630 14348\n302 9744\n1655 2010\n8014 14042\n7936 11990\n743 14041\n11227 14227\n1935 14992\n6745 9458\n4094 5049\n6457 8842\n9375 13810\n3260 13916\n5369 9203\n3448 9013\n6508 11752\n3943 6365\n579 12958\n4906 12923\n4193 15530\n2982 9447\n1602 14179\n11869 13159\n6278 10694\n3167 7778\n2266 4638\n7555 9185\n5508 10250\n6367 15161\n291 12677\n7227 7441\n1818 2389\n6351 12207\n3396 7481\n8188 11375\n108 9297\n12761 13251\n4417 12169\n6383 13147\n5046 6259\n2089 9983\n14336 14806\n11660 13928\n3963 4433\n347 12752\n2411 12502\n1361 13289\n12677 15496\n13465 13792\n12008 12271\n10188 15504\n898 1080\n912 10416\n3780 6805\n6856 8068\n7093 7096\n904 3725\n7627 13017\n5443 14341\n6404 9304\n3680 6184\n12497 14099\n3836 9241\n1021 10820\n7681 11793\n8689 13833\n5647 12736\n992 5256\n10104 15315\n517 14788\n5463 12306\n296 12260\n988 1355\n4887 7492\n9190 11224\n5021 15431\n1448 12716\n411 5177\n1592 8429\n344 15207\n7691 10674\n1989 9987\n11016 14356\n9003 12721\n5054 15191\n2708 14785\n9245 10383\n5260 14238\n9247 14240\n5757 12567\n3854 7581\n7462 12292\n5663 5923\n1979 12704\n291 6242\n530 3642\n5256 10290\n12193 14045\n4610 13497\n1357 12664\n683 10882\n2686 7618\n8964 11411\n932 2117\n3027 11889\n8770 9328\n1644 12119\n2447 11856\n2550 7390\n471 3360\n3641 11408\n24 14131\n2264 14303\n2483 15342\n7771 10728\n908 9910\n4843 12490\n1891 13818\n3315 12511\n1752 2507\n4683 12205\n14178 14488\n264 8505\n8027 9678\n4848 14955\n10485 12027\n3703 10507\n6452 9771\n11555 13944\n6952 10561\n3930 13515\n7272 9176\n10726 14558\n1674 3998\n13869 15175\n1922 2722\n11482 14233\n8049 14884\n11121 13492\n4608 9005\n4044 14047\n11887 11998\n833 1144\n3891 5825\n12375 13435\n2138 4088\n9528 11139\n10931 12998\n4898 12057\n5079 10820\n10193 13409\n6774 9634\n3980 15312\n831 3643\n2067 7567\n5249 12989\n5845 6997\n5662 13829\n2792 12888\n5287 12757\n6514 14396\n4494 4789\n606 9178\n5048 10636\n8856 15531\n6045 13262\n3171 9310\n9384 10941\n10723 15639\n7143 7782\n14654 15480\n2577 3777\n10972 11666\n1413 9883\n4119 13010\n9515 12043\n8274 11697\n7199 12682\n2505 4352\n6322 13092\n1507 8231\n4765 9585\n3341 14387\n1661 4562\n7130 10873\n2231 5758\n977 4352\n3255 13493\n11328 14991\n3257 9164\n7642 12005\n8249 8991\n1172 4831\n9889 11923\n6636 7801\n1984 11814\n9524 11127\n4261 11492\n12641 13778\n1042 9688\n7627 7716\n10471 15364\n2037 3437\n6145 6324\n663 978\n4410 9843\n5946 10778\n6121 7354\n2551 10522\n9652 11494\n3152 7456\n8861 13718\n6228 10585\n13224 14336\n8405 9334\n3185 5741\n2339 3989\n3792 5761\n2532 13538\n2863 5053\n7090 9453\n3707 10981\n2707 8529\n914 6049\n9873 12252\n4991 10092\n871 5260\n2375 11440\n10172 15390\n2972 12470\n5021 10605\n3267 14272\n5318 6752\n13212 14762\n2529 11130\n5747 13931\n5919 12235\n5209 7205\n831 13726\n2420 7971\n1386 11395\n6684 11454\n956 7859\n3493 8967\n6165 8072\n8181 12545\n1384 15514\n7069 11771\n7735 12555\n3949 11935\n6722 13483\n2223 5927\n1247 10274\n3737 10425\n1092 3898\n7121 9103\n6897 9860\n11990 13402\n1093 15481\n3082 3802\n5114 9856\n4678 5382\n11321 12860\n2576 2848\n2575 2700\n6593 10997\n6513 12032\n13279 13356\n10832 12162\n11394 15511\n5273 9934\n8939 10853\n8357 15192\n2117 12272\n8058 12990\n3875 12442\n5481 12487\n6840 10432\n11227 11254\n12767 14210\n7313 10732\n483 716\n1369 9330\n2223 12651\n10371 12835\n7979 15589\n6520 6897\n2337 9018\n11269 15096\n639 1222\n6404 10722\n7970 10466\n4437 6629\n27 6516\n1998 7234\n6172 15149\n7148 8362\n10047 14886\n1061 10044\n11169 14053\n91 9579\n5751 10679\n1623 15633\n1795 8564\n9021 15030\n1397 3027\n9003 13370\n296 9202\n6071 12555\n10188 10372\n5051 9625\n7652 13545\n3767 4342\n7665 8984\n3000 10060\n2832 11612\n12704 13093\n3013 4149\n3513 6486\n2934 8236\n3895 6615\n3372 12305\n3308 6665\n3725 7963\n6262 6320\n4530 11992\n9458 13153\n7895 15580\n6699 9964\n1550 15158\n3079 7579\n12153 13061\n724 14287\n33 13707\n4401 12500\n6738 13141\n7030 9337\n3818 7800\n2904 12614\n2517 4650\n2214 12528\n8812 9642\n1611 4384\n1920 9470\n7647 10738\n2534 7402\n1034 9366\n216 5437\n10508 11365\n5830 15276\n13414 15417\n4270 8943\n2105 2244\n7691 10073\n5286 15103\n10438 11012\n1555 9871\n9134 9464\n3433 15224\n10534 13567\n9950 10837\n6119 6123\n9676 10510\n3319 7458\n11927 12014\n4036 5383\n11256 12636\n10666 12241\n674 1255\n5999 12611\n448 1078\n11399 15651\n14945 15003\n3602 12900\n11543 12921\n3271 13874\n2549 12094\n1837 14340\n1192 10683\n9563 11404\n2532 4608\n5185 10199\n986 11606\n5596 5636\n13118 14675\n3858 14295\n6758 9342\n4560 9780\n1323 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15235\n4111 10985\n5907 6762\n5362 8695\n1900 4025\n2060 13889\n11335 12392\n12714 14203\n4954 15414\n1820 10671\n1255 10766\n8264 14034\n960 1428\n10405 12244\n10977 11862\n2215 10844\n8969 13250\n10876 15532\n5158 10743\n634 6007\n10464 12368\n5182 12525\n11136 11522\n10481 11201\n9460 9971\n9187 13774\n9008 11395\n1354 2445\n1645 4739\n3049 11059\n6027 7650\n8601 9954\n10194 11043\n8069 11593\n132 14292\n1564 6219\n1781 8108\n6123 11389\n4148 14520\n7843 8556\n6181 6205\n8998 9956\n8500 15334\n8985 13651\n8901 14034\n1271 12917\n4624 5654\n4727 6067\n12703 13748\n3078 5129\n2332 13888\n13298 13485\n3325 14652\n3321 15535\n3161 12761\n10125 12591\n3643 14271\n13937 14999\n6525 14045\n3617 5717\n2503 14656\n6888 10841\n4544 14941\n3091 4302\n4337 14196\n11949 14301\n9301 14859\n402 5643\n4974 8611\n1505 8036\n12305 15601\n973 13065\n402 12864\n936 13449\n3988 5896\n4423 15314\n6040 14029\n868 1421\n4191 14511\n6057 6602\n1246 3770\n3293 7599\n5762 13757\n3841 4203\n7417 11178\n5345 14302\n2284 5188\n4012 14989\n8265 12446\n8074 9209\n173 2485\n7376 13749\n7929 14582\n240 5739\n8685 14429\n377 2385\n5063 13936\n1476 4199\n3101 3512\n2152 6890\n50 4643\n3864 8186\n12180 12216\n6347 11352\n3007 3444\n3082 4842\n123 9887\n253 11626\n8274 13444\n11683 12211\n1767 3509\n6945 9422\n6748 11875\n1336 1490\n791 10528\n7621 10935\n111 14562\n14647 15071\n6892 7339\n655 3263\n8254 13623\n5806 11810\n1185 3721\n7450 11821\n1695 10788\n5644 10853\n2800 10688\n5105 6609\n2236 3635\n5139 13541\n6086 12397\n68 12614\n5062 14295\n2501 4746\n713 7181\n6833 11699\n463 5441\n2698 7685\n8448 14593\n4469 14304\n5009 10522\n12682 15122\n3420 3646\n4037 12341\n2598 6488\n539 15124\n1254 10515\n5871 12897\n1104 10458\n1404 9286\n450 2388\n1930 7339\n7068 12361\n2644 3997\n1460 3276\n13133 14605\n5548 13858\n11042 15422\n699 5653\n6506 11987\n4703 11889\n3382 5892\n1052 3779\n168 3483\n4234 6195\n4679 7618\n10953 12169\n8248 8336\n2087 4537\n5155 15375\n2680 12830\n3741 9218\n10725 12696\n6124 10018\n1377 8686\n6268 12807\n4547 12407\n11573 15092\n3624 13534\n6020 11281\n1404 7442\n5648 6793\n2153 3886\n5661 12724\n5266 10930\n8383 14715\n3445 12026\n2034 4436\n6637 9715\n2983 7113\n6831 7761\n10701 13023\n2238 14560\n6100 11309\n7455 9579\n2622 8352\n12181 13133\n2478 5657\n5016 11953\n1394 7250\n5081 14109\n1724 7311\n4199 4420\n1234 5993\n3444 14692\n10849 12010\n5272 12241\n5208 9317\n1191 1924\n1470 8002\n5626 12957\n6804 7708\n298 7334\n1763 7402\n5576 14269\n212 12154\n2954 12830\n9233 13241\n2426 15602\n3437 9925\n3144 4090\n1278 5542\n8945 14336\n3696 8227\n7591 13986\n6519 9025\n164 11634\n3101 5657\n6087 10743\n4366 6367\n3384 7159\n3628 8503\n10958 11279\n5670 9489\n8732 14703\n3309 15477\n7080 9252\n4396 5779\n6896 12665\n107 8257\n3821 8357\n98 12907\n2508 9792\n2811 13896\n5354 10636\n2733 12333\n3934 7271\n6609 12162\n4296 11045\n7033 10896\n10900 11248\n4243 4727\n4741 12481\n5917 10079\n3559 9957\n214 10826\n1318 11679\n8401 14275\n542 14824\n585 13501\n10124 12536\n1836 11330\n754 9195\n7418 8301\n3082 9963\n1734 5043\n14953 15342\n6854 8394\n4627 11866\n5207 12275\n3371 3500\n9874 11260\n1090 7744\n8074 11747\n695 14221\n10004 10158\n846 13426\n1528 8602\n9722 14781\n2540 13379\n1264 6661\n2082 2251\n2637 10743\n11352 11686\n3701 6363\n5044 12675\n1080 5145\n11766 13560\n7903 11880\n9544 15590\n13222 13809\n4324 15061\n9271 13842\n3652 4744\n10591 14722\n8076 12041\n2639 3251\n1755 12511\n13252 14727\n7326 12368\n5399 11263\n523 6673\n2917 8315\n5752 13194\n7348 12694\n4980 14110\n3814 5008\n2209 11081\n1757 14716\n6366 12278\n8389 11560\n14615 15305\n3320 8673\n10319 12064\n1045 13476\n8053 9447\n1690 5485\n6067 9323\n4450 13075\n52 11900\n3826 4187\n5462 15512\n9538 13328\n10733 15059\n913 9335\n12246 13699\n10503 12439\n9117 11039\n1771 4182\n2602 9116\n515 3794\n4447 14572\n3864 10576\n1461 2888\n1088 15316\n1329 10022\n6717 10390\n559 11386\n3832 13258\n3248 4964\n662 13747\n9198 9321\n12162 13851\n11 7579\n9419 11084\n6735 12260\n3764 6421\n1935 9006\n401 10951\n2828 3270\n3925 15650\n6184 7199\n6226 12807\n10995 14748\n4692 6706\n8865 11216\n11878 14365\n861 2196\n3486 14321\n1157 13574\n11048 14270\n3115 5647\n2466 5544\n139 2983\n10723 15240\n8463 12646\n6305 9437\n1988 6436\n3911 5257\n13969 15015\n11582 12106\n8049 11331\n2669 14564\n2889 13916\n6776 7268\n568 3683\n11218 12117\n12179 14628\n1625 12789\n1483 14494\n9308 11331\n2851 3228\n11604 12936\n5245 13508\n8864 12666\n581 4854\n4247 4553\n73 11562\n11880 12055\n154 10386\n6480 9964\n4231 6005\n423 7912\n4475 15153\n5990 8985\n1316 6420\n10956 14080\n5878 11900\n4153 14791\n830 7984\n9164 11615\n8263 8904\n2959 13175\n3359 9402\n2873 3625\n9582 14358\n6915 13757\n7453 13647\n6010 13841\n13093 13448\n1151 12907\n2520 15592\n1782 4780\n10837 11360\n6204 14045\n208 15314\n1334 11243\n9477 11221\n5157 8035\n409 5250\n7623 14283\n3759 11377\n6503 9518\n1006 11196\n2915 4531\n4917 9431\n1100 11906\n4453 12251\n5298 10423\n2614 5688\n2837 15104\n4249 7572\n5291 10682\n5337 13172\n5771 14383\n12827 14387\n4702 10443\n1353 9415\n9486 10006\n5355 7696\n4147 14817\n4152 5384\n7700 12069\n2180 13780\n2489 6732\n1374 14897\n2453 2542\n8928 13919\n36 15515\n3468 12242\n2887 14858\n4920 8270\n6495 15477\n6413 14328\n3494 8663\n9278 14026\n13063 14344\n10421 12606\n7586 9434\n1085 5877\n9311 12785\n6507 13847\n4399 5387\n4578 11219\n8346 13288\n4964 5144\n6272 9544\n10338 11134\n4839 8548\n8271 15372\n9976 14565\n2436 10503\n4439 10515\n9822 11962\n4397 13693\n11269 14803\n8835 13632\n836 9305\n8330 15328\n7763 14937\n2953 11607\n1590 3905\n412 9036\n9223 9242\n9871 15395\n8327 10686\n10685 15189\n4932 11590\n9097 13496\n1656 5750\n10198 12153\n4504 7333\n5524 6100\n10300 14321\n4454 8563\n2423 3954\n293 15622\n6292 13839\n2713 9547\n1925 8286\n2763 11065\n4940 5563\n6502 13735\n7612 12396\n575 11521\n1140 12700\n9398 11933\n10593 13266\n136 6161\n12095 14807\n2427 11317\n5694 13089\n2118 9210\n630 4007\n5133 9924\n6385 10108\n41 5219\n5695 12907\n1103 13923\n4949 15416\n11822 13441\n6086 11295\n2996 12915\n2264 10719\n5632 13754\n301 13639\n12986 15633\n3144 9381\n5876 9810\n8628 10195\n1770 11840\n2860 6404\n981 10238\n2043 2162\n8760 11400\n4188 13454\n1419 2294\n2199 9406\n3870 12850\n9094 12336\n2684 8396\n6309 7740\n8952 10675\n1489 14025\n2137 7747\n4337 14201\n596 5337\n11819 14435\n106 14302\n986 13609\n1256 13822\n10411 14117\n2631 4447\n9353 14076\n9981 13024\n1225 14930\n11628 14780\n12763 13266\n10571 13702\n13760 14219\n2736 15335\n7092 10235\n2605 13227\n8997 13495\n2942 13408\n3299 14994\n2283 9489\n9146 9448\n2833 11226\n3013 3738\n5915 7551\n524 5937\n13235 15286\n6579 10589\n6057 9957\n2520 12889\n2737 10441\n3532 13809\n4124 9751\n13972 14872\n383 6652\n5199 11298\n4706 11894\n1860 12001\n11623 14452\n2734 3781\n1246 3112\n552 12021\n8428 11715\n2152 10206\n13435 13740\n10497 14041\n2518 10675\n1660 14643\n9891 15660\n11448 14671\n5381 12952\n7453 8859\n8191 11373\n12123 13746\n139 10546\n6074 7679\n2431 9725\n8878 13647\n1079 6961\n8733 11061\n6306 11539\n5480 11484\n688 3037\n1158 1555\n9335 13254\n3031 13349\n2948 12327\n7904 11332\n14941 15377\n9199 13448\n732 5306\n5285 9486\n1411 8963\n10959 11485\n1188 14574\n9149 13101\n10639 13603\n2981 5461\n5109 14636\n562 9451\n6304 13286\n7199 13193\n4604 11112\n794 15372\n10574 14694\n6120 11438\n9834 11923\n7761 13088\n3429 3744\n26 15227\n3241 9618\n8019 8233\n1983 7730\n6262 6298\n1297 14471\n6276 10153\n10704 13536\n4193 9610\n1325 3255\n13674 14755\n5638 9970\n7702 9110\n2723 7610\n1861 14620\n5627 8368\n112 3983\n2912 12037\n3838 4936\n7096 14100\n12108 12285\n7994 11902\n11834 12189\n855 11133\n4628 14246\n7581 12351\n1786 9212\n373 13512\n3738 9729\n13704 13824\n5755 7020\n3148 10057\n3672 13732\n465 2891\n5486 13358\n6802 8353\n988 8056\n8021 10659\n10228 11571\n826 14572\n11878 12771\n772 5695\n2383 4847\n8523 13984\n4958 11763\n7412 9981\n13995 15083\n1723 10169\n10944 12472\n4570 9047\n1792 13742\n920 4078\n4372 13939\n4496 6774\n4993 13982\n5578 15271\n13161 14166\n12102 14779\n10382 12977\n1246 5493\n164 10837\n6124 14588\n3207 13007\n11332 15083\n5091 5465\n323 2532\n6088 12049\n14495 15216\n5945 12759\n3129 10211\n4520 5179\n4234 10205\n2082 4140\n8175 10613\n773 10006\n128 616\n6422 8113\n5788 6524\n4134 7317\n6866 9111\n6557 7893\n591 8501\n4954 6986\n4992 8598\n138 5280\n6054 15395\n35 3313\n",
        "output": "231\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 84,
        "task_id": 541,
        "test_case_id": 17,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "93178 88605\n53812 72785\n37753 59496\n1127 71075\n2901 18755\n51703 77866\n47093 70356\n3410 63840\n47140 62117\n15307 36680\n13331 34230\n38365 88877\n3932 54930\n24227 26336\n32244 44842\n7078 75807\n38294 66527\n11782 37423\n73985 79089\n33057 54790\n4230 92304\n33551 56667\n16609 63485\n14114 22108\n47013 61960\n45371 69107\n34572 43934\n31605 91023\n19557 43669\n38623 85755\n73769 85184\n4015 64489\n14994 18908\n16584 85119\n1178 46875\n29100 91199\n78954 90990\n34261 66845\n13 20684\n56807 91575\n67506 86434\n55263 88877\n63844 68018\n47928 85818\n16556 84942\n2116 41430\n24775 79126\n69090 92627\n29333 90814\n47898 87385\n22204 47068\n3200 82708\n7807 22188\n51784 82392\n12556 76295\n22453 74843\n1342 58929\n13893 24514\n8872 58079\n54643 68158\n12466 34397\n43274 88865\n40025 59524\n30127 60944\n2900 90606\n20716 90210\n5987 87980\n19267 19754\n2182 16815\n60325 68514\n29697 71613\n43451 70426\n27095 32926\n34693 40956\n49160 66487\n11119 69954\n7422 84379\n25246 55905\n13211 43169\n39450 84270\n52540 62582\n6133 28036\n9677 79031\n5540 48245\n4776 36319\n23997 59639\n12197 61472\n24028 88141\n5053 77814\n27937 57675\n9618 65316\n43705 70878\n47983 93129\n21100 88631\n25143 68140\n44253 89141\n2471 58532\n5903 35412\n1387 6244\n63468 84560\n16873 23677\n39963 82243\n7655 92718\n2208 72212\n87046 92067\n16955 23342\n47932 53302\n7987 91907\n13568 61204\n64119 68311\n19724 46256\n8385 68328\n1962 13722\n8904 83224\n43857 75082\n2099 18056\n67012 81584\n12984 22880\n20576 33458\n19955 22769\n37682 81952\n7110 58879\n44349 88872\n20598 38862\n21468 31134\n67290 73684\n6544 44506\n13010 28648\n40094 86273\n60958 91380\n7090 18405\n29824 68319\n47707 89766\n61486 66778\n60235 62313\n16932 50685\n22410 25844\n19979 80838\n20769 60571\n34333 84184\n59154 89033\n11712 74144\n19039 51023\n6635 13494\n34432 67491\n60699 86551\n40222 67605\n10863 16855\n11713 33869\n38864 73565\n9156 18249\n78168 89489\n4198 42572\n56938 67185\n36348 82668\n1334 51535\n18184 62307\n15498 45304\n27441 48201\n19809 62475\n29833 45060\n20485 31181\n21440 63811\n47260 53125\n49291 54196\n39093 89190\n5079 85854\n36156 90171\n26858 68396\n59019 80836\n53669 76980\n24296 86120\n42942 54603\n55160 64258\n29948 52244\n4123 19157\n60324 91139\n45098 49790\n19750 58824\n3491 52684\n219 57221\n18837 93045\n2448 36573\n52815 66534\n32780 72131\n42346 84341\n51833 79704\n26986 56539\n19756 91226\n48257 64030\n24447 49496\n39042 70708\n11824 26607\n5122 90830\n65477 68761\n8628 72516\n30377 37460\n39309 39569\n16690 84667\n35987 42854\n37136 48445\n7101 8296\n2651 36307\n59606 72783\n11138 80482\n40684 53414\n16105 76793\n19433 86926\n43292 75004\n21819 55011\n33269 34796\n43383 48790\n6985 90044\n43404 90270\n20016 27886\n8063 22962\n57606 61660\n18905 77408\n14849 90150\n38254 71013\n74082 84713\n2262 14257\n61565 72003\n24272 69546\n11345 36235\n89705 91206\n8858 35174\n20011 91077\n42377 88916\n53799 68564\n51342 89338\n28059 59673\n74338 89861\n48789 63413\n30802 59202\n47061 49577\n18528 80684\n2 81347\n36842 66596\n16386 33701\n24009 79390\n14857 66470\n28110 50161\n44135 55058\n69320 79724\n2899 3724\n45795 48043\n8160 79274\n29928 59350\n58182 86990\n29984 49220\n18670 60248\n11635 85209\n41090 80715\n49753 52924\n45844 69741\n3122 53978\n12730 59990\n32355 63809\n10047 79299\n13477 74760\n13325 70628\n44283 56385\n1993 51735\n18314 79296\n26780 69910\n39574 70036\n13827 21881\n30930 90696\n48250 73606\n32222 67509\n26126 85978\n46817 69830\n3197 46016\n1347 49284\n22768 75229\n19607 24515\n60014 61801\n15972 48336\n12598 72155\n24152 43484\n14349 30626\n8364 90073\n1347 26877\n45240 90092\n58627 86215\n8962 9476\n52633 74037\n78300 86523\n36938 76147\n59197 87640\n42253 67865\n28039 61256\n77546 90138\n35201 88178\n24467 79135\n30117 83221\n30175 43501\n37755 38601\n8088 44096\n20415 71455\n13367 89735\n42653 66834\n65994 68015\n2492 29368\n54438 63782\n25008 32532\n53402 82580\n4252 53444\n1425 32780\n42976 50971\n40456 61077\n33635 39845\n36524 63754\n24868 89012\n52668 55914\n24998 88805\n40773 47445\n17933 75502\n31841 68423\n1655 12078\n50919 78087\n14922 20426\n23522 58179\n60119 80477\n11596 72095\n19625 25129\n60588 72372\n8969 61229\n79946 80797\n43975 58050\n19050 37944\n22816 87183\n15389 75949\n54923 75905\n35327 68062\n1322 30497\n209 61817\n1499 7712\n16095 16140\n55358 89833\n26145 38211\n2119 57398\n4658 39631\n40595 53401\n40277 62682\n74100 88438\n6965 8756\n42833 74486\n50843 90784\n29698 91774\n51198 81789\n10997 40352\n54111 68046\n23289 69194\n1794 54675\n20342 73282\n32993 62523\n42781 62346\n62977 88258\n10117 87768\n39441 50811\n1514 83814\n48421 71590\n16777 79543\n12591 87757\n61122 68057\n7520 7610\n20506 74319\n17294 42648\n21801 79800\n12806 36913\n39198 65691\n32341 68477\n14555 90274\n1629 65349\n1519 8840\n56554 82516\n12349 70782\n669 26782\n30090 47237\n45465 64141\n30035 86455\n58500 82359\n20055 70443\n35800 76753\n57386 86375\n1535 7190\n29822 56163\n42007 57136\n27881 60806\n29079 65900\n30442 90047\n88899 89112\n87 55752\n32816 84551\n19711 29090\n15119 20216\n27950 72562\n40258 92904\n25013 31748\n22097 38977\n43009 54300\n22227 41535\n34096 64812\n60614 72819\n10412 52667\n14139 59569\n63985 80303\n12686 92173\n25021 61693\n39088 71296\n59417 64769\n11935 20353\n58673 73865\n16069 31204\n35114 63143\n63148 82953\n61903 73935\n51579 83756\n10188 28537\n33099 69646\n43166 62425\n31404 83500\n57974 67729\n20228 63550\n7977 57458\n69979 82534\n39189 42487\n47960 74739\n1476 14082\n52877 77932\n22737 42840\n12721 68024\n35520 68589\n16870 23361\n48464 88527\n14518 63537\n30575 63718\n37403 69099\n38145 43288\n42538 67764\n1717 44560\n51727 64797\n44509 74144\n52402 52548\n6043 60044\n11566 32528\n49748 77433\n49664 52336\n13463 35168\n13937 62462\n2989 64571\n22223 36929\n46559 64734\n8513 32386\n42407 74660\n23136 49341\n35665 59487\n70263 72982\n42105 65374\n17823 64668\n68667 69707\n72067 77939\n14566 18969\n51315 90829\n39146 48575\n24574 28543\n33334 59776\n38755 88253\n30371 41764\n60065 80807\n2715 44008\n46869 85132\n85389 88539\n67871 82362\n17682 18828\n54439 62557\n52939 56597\n33614 57813\n50506 85220\n9054 26399\n8488 10542\n9347 58473\n3915 64415\n10060 87900\n18368 65297\n56130 57862\n9278 77479\n13277 81894\n9523 21306\n9424 72311\n37541 75911\n68655 86088\n3753 92739\n58847 69059\n11486 52876\n22582 40387\n3714 5150\n21467 54823\n49888 66243\n3968 31446\n35973 58307\n65412 92706\n15449 18520\n15088 15877\n45665 89808\n26189 40754\n56006 64540\n20372 69794\n11072 57859\n24017 55934\n12273 76536\n17621 38978\n19746 60920\n6042 22429\n75179 91618\n37681 43929\n34329 78785\n5190 20923\n23127 47602\n79882 83690\n29511 31208\n29517 89087\n13 77563\n17374 89192\n14645 70966\n42777 72642\n41288 86879\n36755 55523\n4413 72394\n51720 64147\n25542 90550\n30191 78419\n91823 92410\n2365 68617\n12534 70765\n5732 25355\n41252 42387\n55176 65930\n8935 27632\n12960 32198\n5259 39566\n19552 68349\n78949 84199\n33264 78682\n6263 65594\n25077 31729\n32248 41803\n85582 86195\n4725 46234\n60383 76289\n72837 80643\n48607 92426\n42099 42939\n46287 51063\n9899 80357\n9232 76000\n5708 67096\n14259 59768\n23298 50835\n61789 76242\n14027 88635\n26531 58385\n15812 34742\n31700 37212\n83429 84310\n5486 48965\n41273 53304\n18323 26748\n21483 59458\n10773 24737\n14022 78782\n26454 57712\n23092 74006\n298 78768\n49222 62421\n10097 16376\n40692 63123\n43488 56961\n18938 36463\n56760 63955\n44187 91603\n32126 33838\n10840 53374\n42031 46741\n44694 86477\n49247 58889\n19938 90394\n27183 68399\n21452 73597\n52853 91288\n7506 64356\n39477 47855\n62261 66315\n28441 42399\n76924 90601\n29973 87538\n67530 85397\n44932 49484\n43165 59123\n47198 86581\n51971 65287\n57165 80740\n11644 46371\n2305 4075\n50525 66640\n63572 68707\n13545 90770\n17299 65557\n44315 50631\n36886 52414\n12157 81730\n12039 55836\n4135 19185\n6838 33735\n201 34524\n23129 91854\n23371 48907\n10623 81347\n66074 90104\n76587 81788\n17038 51600\n21447 87130\n9369 54949\n13334 53516\n20823 28756\n53004 89329\n252 69392\n63416 78625\n40099 56917\n24231 92223\n5193 25399\n27517 79315\n14565 65370\n12951 32858\n25257 67130\n67572 73388\n44910 66111\n57148 82591\n43146 69399\n19266 26877\n18264 25666\n64154 79141\n43414 46551\n54729 73125\n54091 79794\n17306 42721\n9689 64897\n68525 84145\n1889 69914\n7287 52336\n15865 46659\n74216 74298\n84616 91610\n33701 57759\n17315 91079\n57381 91489\n29690 62554\n15366 84656\n42332 76241\n33750 72417\n2016 24934\n14333 65107\n46050 61230\n33731 39377\n60058 79134\n46558 85025\n55667 63592\n51496 55972\n11632 33922\n6805 40389\n66714 74716\n11982 65662\n59530 73167\n21321 74005\n81754 88336\n19733 65809\n2003 24285\n21172 44815\n17248 20519\n5720 86238\n14896 60262\n45985 75023\n35287 41030\n16179 42398\n35128 65754\n6230 15738\n53065 86789\n38168 60851\n78469 81345\n36662 79989\n5484 89813\n47899 75378\n35200 59529\n4186 19278\n3991 65922\n44849 67818\n5851 39907\n75321 76457\n52698 75752\n20332 35184\n2257 26459\n23443 33253\n904 70482\n34931 43965\n20866 30021\n8235 86252\n7140 10561\n11378 91462\n41136 55486\n45177 74053\n35163 65990\n46253 83723\n12366 22972\n38537 74648\n23963 73323\n26125 32520\n55028 76980\n22057 37191\n11706 59505\n36219 45950\n188 15859\n10270 88368\n14366 16853\n44825 46019\n41124 77359\n894 43287\n653 4355\n67103 82156\n11306 61475\n11902 67958\n7037 82663\n2251 13598\n17013 85980\n31980 75447\n3306 55436\n40336 57803\n62204 71324\n48155 78451\n31768 41585\n8218 28549\n60315 64343\n14144 79218\n21848 38215\n24957 33961\n23578 72674\n43724 87798\n51631 89566\n4638 84988\n13899 32878\n12841 33219\n64724 66099\n6862 60563\n60526 63084\n3076 70109\n50010 74229\n5276 81968\n10560 33375\n73978 79569\n38380 74058\n35472 56291\n9289 25100\n54932 77338\n14052 90635\n7666 18716\n35729 82630\n58192 62119\n77520 85888\n15589 87322\n66554 72327\n67702 85193\n56644 83048\n60353 89364\n36614 52561\n38702 75413\n9439 88940\n56 40321\n21555 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87556\n49895 52677\n5215 45116\n32716 89662\n6781 91904\n11041 38868\n72133 91195\n47762 60633\n49831 79272\n28563 28588\n57606 88652\n50141 70996\n12004 82297\n80690 81424\n35515 44277\n45163 58873\n15401 51450\n8484 38088\n8427 54672\n11380 70299\n4078 92924\n58355 85724\n37228 42432\n65745 81621\n32624 76191\n7536 37989\n3526 80178\n24707 86531\n74613 84476\n22113 45261\n60531 70387\n66864 81490\n38964 84784\n771 74625\n638 3159\n21496 27056\n68711 75473\n72858 79288\n5662 7205\n65211 72880\n63808 77772\n2633 51627\n58250 81067\n60861 82993\n31647 50635\n27194 46605\n38388 50582\n22288 23350\n25548 31520\n22618 36878\n69906 76262\n5775 40392\n62495 72954\n3832 14600\n223 64537\n50818 71428\n12915 91164\n43481 76954\n30885 57017\n10088 13753\n63896 71884\n46582 68993\n26635 86650\n3587 80901\n53297 88094\n17181 66995\n17926 78981\n53508 91144\n35956 70225\n59453 61435\n10484 59706\n18219 27177\n3653 57697\n18133 32137\n16216 60910\n69544 81293\n33536 71316\n36632 83493\n65001 67510\n20969 34140\n30440 43281\n21647 92244\n14639 30585\n43344 71423\n11859 75373\n41458 75860\n55923 86389\n26285 87541\n60114 60195\n9733 27227\n17797 59998\n50061 83875\n11652 61707\n55171 73663\n84249 89365\n74727 88954\n24518 44600\n10176 57645\n45837 75377\n6476 43999\n758 7757\n76123 92425\n79284 86815\n55896 78344\n31294 38058\n40798 68323\n5193 36611\n34100 89439\n30588 41533\n40766 62902\n8701 21903\n61319 75424\n16655 32929\n12560 27939\n54074 84817\n44817 81209\n2177 8605\n35117 63616\n7880 11512\n50217 62181\n3793 91582\n63804 90414\n42325 81818\n36474 58555\n17972 80007\n43 16870\n81461 82855\n64570 79971\n1928 38631\n50001 84685\n35832 66433\n18543 41484\n10572 45967\n42332 79342\n41486 74961\n3070 10348\n48594 82343\n20052 90588\n2008 92024\n18092 23236\n40518 47912\n54128 81471\n35373 70581\n40127 88693\n64962 69460\n53742 76652\n37220 89621\n57576 69855\n28932 89326\n54729 66180\n16003 36269\n79815 88969\n40427 89233\n14129 71050\n54206 55209\n18583 26528\n73893 79313\n11382 58624\n4030 49168\n6662 49774\n46633 63996\n960 36621\n46506 52165\n26663 59816\n6310 31079\n20128 90010\n75964 90713\n3102 17410\n57480 58380\n44084 89546\n11162 84449\n5762 82002\n27570 39179\n44078 52814\n48658 76076\n30177 52650\n24916 76034\n5528 67307\n32033 34039\n23465 31810\n270 7415\n8994 73207\n21585 78325\n35324 38592\n36838 44530\n25569 53132\n64709 74493\n68798 68867\n33267 74382\n9625 64217\n25411 31092\n196 31296\n21817 66189\n82871 83620\n15553 73928\n54781 76980\n10452 39425\n40145 51713\n38490 51487\n10250 40316\n68675 79049\n16723 42164\n63747 75361\n4260 54118\n17602 80292\n24958 39809\n1654 65376\n20088 48078\n60094 68296\n8517 71963\n80065 89118\n75202 79178\n5300 18342\n10038 30587\n14439 65141\n29058 88072\n20161 34025\n882 64519\n38750 74207\n18860 26444\n49801 68899\n19182 55158\n72981 79562\n3487 26452\n48973 83832\n20067 92713\n3430 19246\n40075 72518\n1233 74369\n4434 58219\n14514 63051\n20426 51097\n3573 43423\n28784 45141\n44766 70786\n5354 41334\n54703 65343\n41526 90683\n37798 64649\n44484 63752\n44773 78771\n25001 36707\n634 85766\n50182 55493\n23819 57892\n2356 82935\n14069 18742\n42014 75326\n31150 33959\n18125 58108\n5137 7391\n17762 32636\n62066 80991\n53557 89299\n10420 47500\n45554 60560\n34261 75116\n51515 52014\n57960 64201\n45358 89026\n52739 92805\n803 49411\n17390 26977\n3521 89400\n31630 85233\n44855 68178\n40486 53892\n17459 18457\n2233 24280\n30689 58866\n14312 39661\n15710 26196\n82100 82893\n6970 16146\n72107 81958\n6149 39359\n7148 79030\n30289 33522\n19052 72917\n31897 42115\n57551 68701\n26506 86224\n13098 84005\n3630 81301\n75049 92972\n83841 87921\n38888 51546\n74850 78768\n28134 85156\n61743 92103\n15864 31161\n47 81021\n21015 87085\n26816 35465\n67717 91648\n62892 71515\n15525 80622\n2859 3374\n13618 64349\n27751 48042\n8911 33656\n24530 55259\n13373 31224\n28632 49884\n19353 84532\n22379 73074\n62758 63846\n37800 46375\n42556 90573\n33012 80500\n12094 22572\n35121 45767\n",
        "output": "330\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 85,
        "task_id": 541,
        "test_case_id": 18,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "48681 91099\n5272 5707\n3606 13957\n1818 26614\n478 45657\n14231 29176\n11227 24275\n901 38469\n19032 19629\n2827 22228\n13426 42118\n26737 48519\n7050 13769\n8716 32006\n26425 44610\n7702 11036\n5872 29304\n28571 34387\n29141 37368\n12827 28657\n6445 31364\n22970 30240\n3615 34494\n38198 40622\n23992 35288\n8301 36134\n23982 40288\n2052 38887\n5761 19649\n32154 45386\n3264 33227\n27713 43050\n3686 27984\n9383 26775\n7319 43360\n13734 18637\n21891 43564\n22079 27929\n4798 26943\n9125 39642\n41097 44194\n32546 33939\n36823 39807\n4169 35351\n25463 38001\n23135 41531\n1971 43968\n38760 40605\n18047 32170\n23546 38240\n39190 39301\n11628 37488\n17775 32613\n42163 46084\n29288 38968\n15767 20025\n7191 36595\n6017 16914\n13495 24295\n332 48255\n15329 36273\n12866 33305\n1655 27574\n30306 43809\n5291 21804\n13788 24208\n28834 43947\n5788 16520\n3219 11233\n24168 27268\n3188 23617\n8691 25920\n2258 11437\n9894 46995\n35670 38600\n29416 31514\n35116 45210\n39832 40849\n20155 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44628\n25703 31142\n24727 47740\n21121 22909\n11300 24212\n41577 43824\n1766 31939\n3124 30431\n8172 41214\n5216 45491\n21474 36459\n3568 24465\n7072 30949\n9849 19738\n10059 30978\n20498 25151\n16321 33705\n135 40165\n21617 44888\n2414 15183\n7818 35306\n3826 34575\n39029 43347\n5240 42190\n172 17001\n3179 4039\n12220 40123\n12507 37719\n13595 15464\n11212 34903\n24396 38090\n28876 42438\n12065 17134\n14588 16545\n12741 26313\n9571 15412\n12737 36554\n34381 47097\n4502 5728\n27358 27839\n31452 47637\n24543 36189\n29538 39716\n16403 47453\n4181 28427\n20941 36559\n22414 38235\n45515 48621\n20449 46555\n12980 40027\n5084 33136\n17420 41223\n40803 46599\n1941 21513\n7829 27522\n22174 24838\n21030 38615\n16124 24965\n37078 39311\n18099 41418\n6327 44758\n41868 48345\n5440 11935\n10296 38685\n36836 48160\n28398 37780\n17372 30215\n28722 32458\n26864 38807\n20189 47025\n30521 38049\n30351 46603\n15802 35082\n29787 46468\n7997 10614\n2613 43261\n24879 37084\n1362 41920\n29064 43141\n1803 48132\n35305 38295\n19155 46346\n29048 41195\n6646 9535\n1085 7379\n4373 27750\n12684 25486\n30355 33822\n3813 17337\n1428 22109\n17521 26096\n23550 34441\n9966 40399\n25590 29868\n10767 39918\n13552 42935\n4892 20494\n21884 32888\n14830 20930\n23100 39375\n16987 26758\n40197 43914\n18871 31816\n21202 46805\n32390 36116\n14588 46039\n3565 32625\n18138 32334\n7542 40441\n2645 44722\n14813 33180\n8478 47331\n3063 22442\n17589 26660\n7532 12553\n5672 29142\n2722 7334\n17448 35435\n10632 13096\n12590 47780\n20202 26536\n12225 45779\n15666 44734\n40288 48032\n1458 7067\n12705 31344\n5625 25619\n14629 22089\n10091 32281\n42424 44199\n30509 45182\n1702 21716\n21614 39351\n455 47198\n29828 45229\n8346 33146\n30309 45092\n15060 43804\n20831 26679\n1926 16050\n28974 47353\n1018 12711\n11441 37196\n3060 17087\n31256 33384\n10171 11765\n5567 39484\n14193 33255\n4402 6937\n22511 22883\n22522 25587\n16170 31755\n4857 7609\n3426 24232\n6791 29523\n19366 28597\n7630 32170\n30120 32450\n11709 27944\n1758 30600\n11176 34851\n32 41478\n15880 34990\n15657 42877\n8456 44413\n24917 33830\n16509 41495\n8620 38257\n45336 46305\n6175 37835\n11986 17960\n36451 37661\n830 12083\n784 16027\n17329 30764\n10357 42068\n17932 37978\n93 34658\n23851 29404\n6033 47989\n36628 37237\n16511 27324\n25753 42089\n5673 44575\n800 1330\n3736 22024\n33711 35881\n19070 46775\n40080 44873\n6093 33490\n6230 34816\n36220 37630\n979 26534\n3446 31272\n23716 26347\n9781 48074\n12694 18978\n8380 41084\n2313 3363\n10734 16902\n1968 6360\n27349 40160\n16840 18740\n33547 44987\n26529 37362\n27632 36077\n821 42081\n5456 24931\n22454 28269\n655 18892\n27863 39632\n5404 8136\n22222 44246\n5885 32430\n33681 46072\n3474 38892\n18299 33540\n23848 32142\n39424 41442\n12662 14686\n31323 45930\n15666 45641\n16790 47720\n5715 7223\n16411 17646\n2297 48089\n15712 27786\n36461 45458\n6535 19582\n9936 13964\n13617 48297\n6614 10903\n23496 46249\n13483 32530\n14539 47607\n34295 46765\n19119 26336\n30566 32981\n28029 29467\n22378 30501\n20575 35946\n17980 48222\n3812 47314\n14346 15956\n1990 7578\n15671 44780\n20478 26788\n892 6027\n6214 31925\n4356 22647\n16320 35269\n17144 36301\n4442 30005\n14293 25420\n16364 18083\n33830 44283\n1871 17370\n6893 16584\n10854 17504\n26108 42846\n5248 23259\n5954 32578\n6024 28064\n12922 36655\n23474 40611\n1961 14325\n19344 41893\n34472 38173\n38257 42524\n7112 25824\n2414 42335\n965 23343\n8598 28279\n4260 33354\n19328 44922\n12150 28015\n20843 32240\n22510 36701\n30975 38085\n3886 7262\n6038 46144\n26814 32875\n35091 35395\n3376 11200\n27886 38176\n18904 40843\n31393 48100\n26785 47302\n5954 16884\n26387 26741\n2931 33194\n33325 36072\n18071 36546\n41932 44454\n22389 47615\n42402 44524\n17283 21139\n1308 17266\n3497 37571\n6999 18039\n6019 23401\n738 44371\n20714 41707\n5257 23015\n30245 45772\n14965 46060\n2913 46745\n21735 29516\n42151 45402\n14890 16458\n32601 41925\n11965 31205\n32811 45291\n13881 33259\n15186 35531\n33233 35533\n5407 11482\n24199 31629\n5082 24651\n13476 25854\n5357 15013\n26900 27770\n2998 27420\n2956 21070\n16585 25422\n11379 48312\n5529 48177\n24208 48035\n15985 17075\n34909 42243\n42896 47750\n10268 15813\n23734 26695\n6875 38222\n9156 44432\n42738 43980\n3036 14597\n1590 19487\n30552 45675\n7270 38049\n24956 46240\n14293 16234\n12794 17073\n23536 28471\n20954 36640\n22315 33693\n24313 36498\n20644 42191\n33779 36182\n23305 33171\n3674 8189\n7354 27268\n29914 37409\n13161 21755\n5877 35176\n34907 47800\n39443 48249\n12238 15568\n13614 29283\n13812 14031\n18041 40893\n17854 30832\n12930 27353\n5996 20892\n9525 41655\n3806 44100\n10202 39269\n33948 35429\n10372 12027\n3494 3949\n3125 40606\n6186 41694\n24689 33050\n4073 33734\n2384 33048\n7795 29110\n35372 35608\n12165 25665\n31501 35982\n4040 22615\n1606 20698\n20391 23842\n43205 48153\n23914 31990\n13029 37432\n44541 45829\n24016 36958\n34534 39630\n27903 31271\n2132 37810\n32027 44880\n12993 18572\n43658 47794\n261 43756\n770 9497\n24115 32734\n10483 15776\n5722 43142\n11587 23928\n26315 46593\n20690 43806\n35394 48319\n3766 30592\n20564 32068\n8546 19229\n16018 16160\n8231 19604\n9460 18929\n8630 43468\n15703 23777\n43627 44508\n5008 21230\n1678 26572\n26925 40582\n41225 43447\n16968 37691\n16342 32707\n5944 11902\n3132 16000\n34794 40814\n",
        "output": "332\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 86,
        "task_id": 541,
        "test_case_id": 19,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "53916 13533\n22066 23718\n32600 45298\n3040 14219\n3443 23405\n28942 52980\n50210 53348\n31593 48636\n29609 51862\n27092 34876\n1365 40467\n19778 26176\n37860 45055\n42899 46246\n3429 51171\n49891 50648\n13352 21912\n14797 29590\n4176 53522\n11719 45835\n13245 52031\n29079 53613\n3473 46765\n22515 47682\n4784 31098\n1426 49011\n10140 25662\n25621 41358\n7350 35233\n3932 26417\n16132 32930\n26652 42442\n23447 51797\n11772 38069\n40729 50259\n10344 38471\n1294 39677\n1796 8063\n3789 20879\n4103 9753\n7308 40306\n28659 53193\n23034 39987\n14894 23171\n15414 48391\n12638 36490\n48469 52129\n8438 16505\n37213 40913\n12635 45342\n11025 17815\n4813 28092\n31447 34741\n18325 46719\n9707 24701\n3205 31013\n26469 51473\n14799 44012\n16239 30339\n21582 40920\n3137 36798\n10603 47713\n37940 53061\n29540 31294\n33391 53259\n30332 48838\n46572 50047\n5165 42248\n15845 19100\n20535 35340\n38000 39376\n2127 35419\n8056 48881\n22143 32519\n7520 22993\n1723 21933\n13540 36148\n12789 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45373\n16257 22879\n20268 23449\n12287 28024\n9420 30938\n2838 40726\n25090 31862\n7053 20131\n754 46312\n7800 53819\n25306 32732\n21966 49709\n47706 50069\n29739 31232\n25096 42172\n35595 46270\n8859 28473\n12294 27265\n11217 13312\n3840 15401\n34319 46522\n22267 32832\n7106 32561\n1580 51172\n32518 46785\n7334 42976\n1498 13262\n19399 37055\n18156 25498\n10763 31524\n27146 38730\n15074 15462\n1246 10421\n24736 53084\n14349 32820\n27447 44903\n7499 25056\n32336 52902\n20923 33790\n18461 52627\n10350 24822\n12290 32552\n21668 28325\n2874 7319\n2839 11663\n9685 10822\n28564 33145\n9247 48928\n16183 44602\n11450 19039\n18952 29564\n17206 52094\n29455 35106\n741 39794\n5873 15219\n17577 36088\n16665 18324\n17874 27680\n6795 47801\n8769 31721\n10557 39609\n1967 13635\n40303 42961\n8793 25240\n15785 32306\n4096 24789\n37286 53009\n7955 21041\n5296 22426\n31307 37714\n11493 17064\n5866 31763\n17466 47086\n6977 11994\n8699 45698\n13504 50340\n35428 42070\n41941 48977\n10746 18859\n24093 48787\n31158 36151\n12257 18637\n16630 49112\n19076 35901\n22731 45784\n2183 18808\n18861 52846\n33459 53577\n2423 44270\n7486 13518\n41854 51511\n26267 38483\n13141 15241\n23808 37506\n22020 44169\n50085 51570\n10813 40129\n343 50262\n43453 53135\n25230 31506\n35488 46916\n2704 28355\n26000 42392\n10699 41011\n12430 45019\n14234 21898\n24324 39428\n3556 5980\n29375 51961\n43272 44477\n426 30864\n7829 18405\n8401 19897\n33178 51195\n23978 37079\n686 31672\n15861 24257\n27550 33531\n45730 52399\n34464 39739\n19952 31795\n16994 43511\n46955 49439\n17315 24384\n26898 41266\n23788 39351\n30181 50506\n30478 48980\n30975 49025\n35531 43545\n16363 43559\n4850 51583\n1008 38876\n40995 52652\n11365 27051\n1303 33028\n37128 38913\n10374 17266\n4153 24744\n27796 51974\n22682 44838\n24740 30655\n5187 43956\n6641 53909\n21861 34516\n17000 31712\n2392 33668\n26026 51894\n29197 50239\n28381 34030\n18133 25189\n9781 25772\n26954 52871\n848 4258\n33097 40919\n12071 48527\n7109 22228\n8306 22350\n619 8934\n30302 46929\n35972 36541\n5380 31370\n610 35594\n18255 24424\n5401 53493\n41260 51591\n27334 46480\n18594 43980\n17150 44997\n15400 34615\n40669 46796\n5539 41106\n3116 46812\n26756 49955\n34774 46438\n20722 45885\n25276 27766\n5543 37963\n4063 32826\n6617 8026\n30941 44570\n1133 17496\n13365 29065\n13224 14989\n6457 22999\n19463 51927\n11707 22724\n4924 23751\n24441 42439\n15150 24878\n1461 36428\n25420 27961\n3336 18574\n27125 32351\n14098 25662\n11361 48936\n12325 37886\n27673 32345\n15686 52107\n8904 41114\n7244 32465\n2769 29399\n19565 33171\n2854 37662\n38191 49111\n21386 41972\n23530 41218\n34468 38122\n24324 36601\n39462 47422\n18236 27030\n37802 45672\n4106 38319\n28267 42791\n14582 27210\n9201 49222\n13214 41005\n14272 47440\n1439 39969\n5974 41419\n32598 53752\n18214 21330\n37003 46685\n38786 44185\n12190 29273\n10713 22901\n15718 23922\n40602 50835\n27604 32404\n21697 37192\n11364 22497\n6851 43496\n1016 43966\n29099 41429\n13559 36503\n14249 25583\n17606 40204\n23834 46905\n20357 35036\n19118 26925\n1556 14271\n19779 33432\n15868 39017\n760 16602\n14713 31412\n34306 35707\n39742 44180\n8621 53050\n15259 25463\n24637 34643\n3114 32830\n31423 44900\n1695 43262\n3063 15632\n6844 23763\n24839 40407\n33434 41655\n26347 43647\n1498 28727\n18982 29679\n8229 50798\n24904 46676\n8661 52578\n51854 52289\n5375 21521\n2899 51988\n2164 38372\n20360 40948\n11633 15260\n10944 42280\n17827 31677\n22401 39917\n9048 14696\n17731 48028\n1751 44862\n15774 42175\n7190 13305\n19674 40457\n7560 30053\n33848 35466\n3652 33069\n26547 53801\n19790 24689\n2743 37257\n24419 32025\n29974 44638\n14351 29646\n4715 16926\n13415 38379\n39798 47286\n24281 52710\n9910 38120\n25077 45526\n23127 46833\n4769 48406\n8658 38965\n17165 20520\n16082 40169\n5557 28180\n53257 53689\n12042 37017\n25088 27648\n36482 49059\n32341 33531\n18187 23517\n29918 39359\n14466 49080\n5682 40129\n7195 43074\n20082 41863\n7166 21388\n27963 51072\n8643 34555\n24257 40134\n3497 25634\n12 22338\n3726 41583\n22914 35889\n1823 15393\n22389 40557\n20663 34205\n31673 34805\n4232 13338\n20203 48787\n22682 33320\n35277 50607\n1992 19610\n19034 25301\n39180 40049\n42341 48308\n5781 53417\n36853 47002\n1862 17300\n18971 37589\n7342 24777\n24203 39881\n5115 21626\n10266 46832\n375 1194\n23896 37541\n19933 39669\n4064 8644\n",
        "output": "120\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 87,
        "task_id": 541,
        "test_case_id": 20,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "20289 78356\n15324 20162\n2209 17880\n5490 19540\n117 19391\n416 13724\n8739 19133\n10884 12669\n6804 17419\n7945 16887\n13407 15963\n2674 3485\n6994 7631\n10169 16047\n717 18388\n16852 17133\n3220 9758\n416 19719\n15206 18532\n6531 14501\n1738 6720\n773 13818\n15185 18500\n8460 16680\n17730 20019\n9559 10440\n17275 19889\n3799 14121\n7927 16110\n10329 18401\n6138 12426\n2205 3132\n7791 9905\n1295 14476\n667 14526\n16058 16168\n13722 14811\n14094 16544\n1149 4958\n11065 12385\n1912 17830\n6980 11234\n10969 16240\n8183 14879\n7224 7483\n897 1882\n9199 20224\n11568 18338\n3397 18306\n16725 16975\n12049 13073\n7163 16855\n9476 11632\n7393 11304\n4415 17816\n2012 11628\n28 13399\n2083 4340\n11451 18467\n8309 10240\n7121 12125\n1399 18870\n8924 14582\n15506 16243\n1776 11239\n3578 4070\n630 13098\n7622 18126\n7660 12708\n10371 10541\n4201 15240\n216 18011\n7499 18794\n1381 8065\n16639 19508\n4032 14976\n4781 7957\n18629 19084\n1918 12480\n4176 13850\n6162 6754\n12099 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15184\n4521 12848\n4723 14236\n10775 17373\n13726 16196\n3230 10252\n652 3445\n11389 16012\n5589 11786\n5557 9610\n14462 15621\n7498 14640\n2729 19257\n6267 19571\n8898 17994\n6445 17171\n3286 9489\n8958 20245\n14240 19780\n6004 10226\n6080 11694\n6451 9329\n3164 3353\n16409 17279\n12857 18063\n9566 10318\n7436 12866\n4605 12896\n6557 17115\n822 6022\n1655 6692\n5167 17735\n11883 15534\n5991 13526\n15901 16746\n4797 16742\n14189 16435\n12406 15676\n3428 18488\n11357 19732\n7983 12035\n6408 8473\n8528 16193\n14611 20009\n13306 19310\n8382 10230\n15159 16402\n4139 8866\n7112 12266\n9830 12626\n8454 8965\n6063 15883\n3637 18936\n4520 11058\n4869 17144\n3018 6473\n2 8802\n7358 15175\n14896 17723\n14296 18244\n6294 8030\n19320 20198\n2413 14203\n7041 14976\n7294 8070\n5693 11445\n11296 17901\n16848 19126\n3828 11204\n1359 16778\n14684 18678\n327 7505\n9432 12985\n8418 14907\n5534 15073\n437 6509\n3599 6706\n3967 16789\n11816 12806\n9030 15967\n3190 10161\n7569 10761\n6689 15279\n1123 4729\n2329 12900\n6012 18049\n10087 19621\n7788 14059\n2763 13894\n7432 19822\n14834 17972\n2741 10109\n12867 13983\n6037 12054\n3538 9137\n12207 15005\n4942 5497\n11769 17921\n16541 18726\n9949 17600\n16366 18605\n12170 13473\n6634 18204\n820 13393\n2067 14359\n15232 15333\n10510 18992\n4037 12606\n3715 5945\n9641 10984\n12508 18417\n11245 14405\n11359 12472\n1390 2281\n14198 14833\n12581 16664\n15296 18536\n12817 16955\n6281 19512\n3194 3764\n10422 15165\n17545 19523\n1029 6543\n5465 16829\n3883 5340\n771 9630\n7899 8605\n6746 16698\n5393 16977\n5158 13772\n9872 18240\n4873 12910\n4524 13795\n6786 7765\n1723 10390\n16664 16677\n4307 7985\n5743 6525\n5975 14292\n14687 15263\n5861 14268\n9074 16404\n2328 8737\n11536 13518\n19105 19752\n476 2758\n14384 16333\n366 10011\n493 3338\n1701 20257\n9920 15081\n766 10699\n10386 19331\n17078 19622\n7347 19848\n3588 9744\n11640 18408\n10998 16575\n2794 12611\n3879 17865\n1747 17041\n3081 12775\n4935 18823\n10510 19630\n10098 18174\n614 15736\n7823 16645\n4497 11561\n13215 18924\n11038 14924\n7469 10213\n7987 15857\n18008 18715\n12802 13924\n793 4027\n3205 7793\n3868 17110\n247 5242\n12687 16786\n9462 15405\n14787 18905\n9786 11060\n14466 17791\n577 15461\n1370 13057\n5871 12648\n10176 15445\n11106 20211\n7446 17027\n4349 18378\n9108 10652\n9617 15123\n6701 13575\n16745 20275\n5576 5839\n1279 3167\n617 7541\n802 6821\n10806 17106\n577 3584\n11934 17132\n16282 16915\n3475 9571\n7122 9530\n9494 10714\n10120 15557\n10557 17318\n7745 15544\n6160 13969\n512 17962\n6372 7605\n6012 8716\n8962 19207\n8683 14674\n4280 15233\n12149 18063\n8939 13545\n15987 17397\n7872 18715\n8020 15631\n5285 15949\n8867 12694\n6127 13891\n7644 11363\n15238 20085\n1225 18095\n2351 7129\n18546 19114\n249 17790\n10975 13059\n3657 16853\n6093 14899\n10966 14328\n8402 10055\n5921 8095\n11910 15782\n2982 11324\n5361 6342\n4358 12219\n5064 6106\n15954 17007\n10180 10828\n602 16269\n1009 19665\n1540 18327\n7508 18884\n16002 18930\n1969 6522\n8513 16401\n7820 8870\n6771 9875\n7815 14781\n7117 17570\n19 18128\n4831 9765\n5126 12852\n7987 19284\n842 18983\n1598 2314\n960 15118\n2126 9857\n1284 10817\n4362 18366\n14839 16269\n1142 5354\n3582 5805\n5033 16122\n7251 17600\n7674 15829\n9402 12980\n7699 13728\n6627 8011\n10358 17723\n13840 16897\n3534 12186\n6708 12762\n6311 11935\n6499 8910\n4828 10647\n6636 12841\n11172 12708\n2008 7414\n19379 19699\n4187 5481\n4116 6498\n4785 16330\n1300 12294\n2743 19242\n12064 18364\n5239 12037\n16851 19257\n3667 3805\n1615 14979\n11547 17561\n6131 8960\n4538 5863\n3420 8511\n12515 17220\n7491 15624\n3640 8153\n12086 12474\n13353 13626\n12910 17122\n17859 18219\n8683 12766\n444 16053\n617 7254\n10498 14657\n4828 12752\n4770 12125\n3581 12324\n5875 15392\n311 15869\n7141 12405\n122 14257\n2589 2637\n16365 19320\n1238 17022\n817 19093\n8096 12787\n483 6321\n2219 2528\n14638 17099\n4089 15083\n9554 17525\n6264 10240\n2308 18914\n425 19790\n14708 19197\n1862 2175\n4448 9299\n10911 15860\n11871 12279\n8661 19580\n3734 10498\n2335 17963\n5832 19049\n3680 16304\n1538 18749\n2724 6701\n6702 11128\n3384 10111\n10086 19307\n1036 11730\n3415 9355\n2644 7753\n11385 16155\n3921 20176\n831 16432\n17978 19892\n9698 14805\n6062 8520\n257 9622\n2945 11937\n5212 17767\n816 11371\n5834 11155\n12872 16346\n1440 19218\n1194 20241\n18314 18610\n12356 17762\n5962 12438\n3490 17923\n7676 10157\n1461 8791\n8634 15842\n14683 17765\n9964 13983\n9497 13110\n9312 12141\n10063 10671\n16832 19012\n2372 18373\n5683 9689\n810 18188\n29 7134\n15351 17907\n12141 16515\n1285 17098\n7189 10898\n1161 2083\n7333 18168\n7575 11856\n8324 16274\n6946 13049\n3596 5067\n12353 18187\n3061 9576\n2368 5985\n9518 14532\n3351 6777\n6186 16287\n8659 11274\n8218 16808\n654 4588\n14609 16628\n564 2191\n3611 9873\n3482 15352\n3990 13906\n4148 5887\n5210 6432\n3001 14828\n782 19860\n7619 12170\n12 15439\n3811 20176\n4773 11120\n3107 17370\n936 1711\n9522 17892\n14143 14403\n12667 13826\n9250 14969\n4872 4991\n4666 16316\n1492 15609\n4011 19393\n2010 16917\n7453 10499\n1052 10537\n6232 9794\n10082 10748\n1724 12842\n14288 15606\n13930 16658\n3859 12777\n11467 19262\n3273 6831\n653 13852\n5671 19171\n4671 15993\n13807 18502\n9285 11722\n13402 17691\n5342 18369\n4770 4792\n8034 17839\n390 5607\n1331 7105\n6142 8341\n6618 7341\n3935 6032\n11109 15531\n8106 11116\n16254 17660\n2041 7947\n10248 14846\n6515 14614\n4776 9478\n2788 4317\n3684 4517\n3427 5892\n13275 20116\n2010 12477\n8229 11357\n1599 1969\n8955 9511\n13639 14722\n6687 11598\n4412 17866\n2486 20130\n4923 8544\n5803 6954\n12468 16184\n2566 5466\n13439 15821\n6947 12819\n7502 14484\n5009 19666\n121 3425\n4129 19103\n7589 15354\n2074 18655\n10666 11953\n10688 13618\n18460 18991\n13825 18416\n9785 20111\n14469 19281\n1954 8393\n5133 6972\n4767 18864\n13979 19352\n2167 10600\n89 90\n2004 8824\n9570 16953\n6687 17591\n12635 19077\n2292 4439\n6032 18514\n318 484\n7432 13938\n7726 13420\n3390 12474\n1811 7208\n7960 9659\n9933 14285\n2812 7203\n537 7777\n9342 17128\n5639 10194\n3778 9745\n3675 17034\n12552 20194\n1367 4842\n3128 13244\n4190 10146\n1473 2443\n16442 18290\n9158 16290\n24 6675\n7009 7779\n5626 10875\n6170 10551\n2214 7953\n6716 16370\n5833 8238\n16119 17117\n1839 3934\n7648 10149\n7571 19789\n12168 14611\n4981 5479\n1776 8548\n2804 4770\n11281 11895\n683 9576\n2376 17784\n7351 9176\n1922 8077\n5755 19270\n12537 16041\n1372 1458\n753 13545\n2820 8699\n4975 19854\n6053 14158\n8529 9824\n6071 10905\n9587 19294\n6390 16592\n8509 18103\n5538 16822\n4106 10319\n12344 13877\n9043 19207\n1089 1426\n10737 19912\n5767 12493\n4623 16954\n6578 13997\n2727 16269\n6933 16095\n11434 16467\n8799 12011\n5958 8386\n5399 6288\n1549 2004\n1123 15042\n6767 8711\n17856 19891\n9854 13933\n15287 16511\n16738 19177\n3074 17262\n574 18168\n9045 13775\n392 1732\n7602 9311\n641 8682\n18136 19852\n10341 17885\n15885 18910\n3379 9552\n1396 17092\n10829 18647\n1473 16394\n17902 19100\n4864 8294\n2210 5586\n1507 8381\n10102 13513\n167 14259\n27 10328\n7924 12647\n2216 2354\n5893 14884\n14605 17961\n3395 18647\n6528 11390\n543 18386\n79 4857\n7778 18341\n3467 18862\n6078 16426\n7311 12930\n8277 18155\n4868 16774\n53 14847\n1659 13319\n1069 4295\n8804 12740\n11778 12157\n14431 17440\n12117 17926\n3238 3344\n17572 18650\n49 11812\n10617 12139\n5967 13323\n4589 11023\n7277 13508\n888 6786\n9469 14478\n15705 17363\n955 10099\n2841 19048\n15955 19504\n16794 19515\n9969 17297\n5609 16519\n5952 7670\n1611 19300\n10778 12848\n10735 11328\n2178 7360\n16471 17424\n55 13402\n13295 18829\n11560 14647\n5300 17311\n10832 11212\n4308 8822\n5822 10507\n18534 19036\n5623 10711\n13663 18845\n1804 19541\n13840 18163\n135 7519\n468 16522\n10536 16143\n1668 8134\n2827 16564\n9978 16725\n10041 19448\n12096 14677\n3097 9701\n13111 18170\n2173 11797\n2792 5441\n3075 8651\n153 1109\n953 13227\n7332 15912\n495 12822\n5414 17546\n9668 18320\n9864 16022\n5575 18785\n5027 10330\n6139 10625\n7329 11307\n834 9938\n14008 19150\n4491 18859\n10998 14334\n6128 14835\n12598 17409\n13437 14539\n4275 9780\n5244 10903\n1053 3984\n9135 15721\n5008 11180\n11793 14500\n2442 15365\n1602 7108\n16357 18356\n11278 19724\n12313 18533\n16907 18642\n2139 18199\n301 909\n9639 12923\n8219 9704\n6597 11641\n13136 18729\n3579 9107\n4633 10006\n10970 19533\n16293 19612\n2085 8963\n5464 6708\n4016 19289\n5651 6989\n11254 16292\n8719 16210\n1569 18797\n5442 6176\n795 6626\n8204 18087\n6050 8375\n3747 13981\n10647 13899\n10436 14461\n4811 15127\n6735 9319\n497 18627\n2633 10217\n7690 16537\n2596 20258\n4920 20042\n8141 15315\n4819 12422\n15992 16050\n6522 10033\n13779 18692\n184 18473\n3572 7374\n2411 14495\n9039 16074\n1918 18339\n4396 15617\n1754 5310\n66 14070\n13216 13849\n2880 5265\n1868 13786\n14832 18740\n12227 16320\n2535 13131\n1337 7124\n12467 16711\n12378 14556\n8340 13436\n18330 19115\n1056 17358\n10154 14273\n14673 14883\n1441 17507\n16930 17212\n14039 14966\n4763 14353\n7584 19649\n2398 4368\n5824 9842\n4234 5799\n5408 8992\n16581 18502\n4689 18256\n12848 18993\n8442 19266\n1691 18902\n3462 11698\n7519 12494\n415 10020\n10556 10616\n7282 18021\n12901 15326\n12508 20058\n7769 15604\n5500 12171\n3320 19258\n14642 15486\n186 6517\n2208 17906\n545 1615\n5231 12314\n1907 4732\n5721 10624\n10081 15360\n7032 19405\n12139 12765\n12348 19752\n13242 14770\n1576 8148\n1862 3843\n10719 14045\n13483 17428\n13839 14050\n4673 16512\n3346 11747\n359 10344\n9341 11320\n10339 13863\n7754 15508\n9557 12235\n10279 11456\n8701 10064\n2724 12464\n2277 6826\n10755 13710\n816 10314\n12178 18509\n238 11288\n13695 19581\n422 15633\n16815 20276\n9409 10256\n11585 16764\n3358 8903\n13545 19078\n18489 18560\n7101 19881\n13345 18965\n8174 20079\n2614 3675\n8617 17503\n171 17954\n2685 19314\n7637 10423\n292 20277\n4535 10635\n8459 18486\n12353 14754\n1299 15509\n1031 3389\n1023 19413\n13106 14321\n2532 9898\n5120 7855\n337 2304\n8927 13493\n6651 20184\n3929 18377\n9714 19234\n2389 16688\n8409 19094\n5024 11662\n16385 18695\n4652 11383\n3373 10928\n1480 14234\n15947 16088\n14541 16209\n1893 3056\n10160 12715\n19438 19511\n4412 13412\n1444 11835\n1594 1867\n10037 16890\n14523 14863\n10089 18628\n9177 15967\n5281 11470\n5455 17386\n3416 17000\n7119 12775\n1475 12835\n9023 13645\n",
        "output": "301\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 88,
        "task_id": 541,
        "test_case_id": 21,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "86006 41493\n12116 50666\n33826 48398\n31285 71729\n9166 32794\n34728 39198\n38113 57887\n7185 20257\n44570 69607\n11907 82061\n38604 55269\n52558 82182\n3246 78509\n2103 20463\n8075 19870\n541 5548\n4936 33378\n39881 47742\n21941 29705\n55598 69654\n2397 61383\n46677 82131\n49268 78261\n47127 85680\n4845 68093\n35297 47954\n19686 69250\n46379 61805\n73173 80830\n1847 13540\n48807 61856\n36486 40014\n20128 43402\n25579 81606\n10630 27976\n866 5001\n3030 8622\n50508 54436\n10697 13135\n51597 84135\n35696 49464\n11126 77302\n15622 76733\n26851 72414\n3531 19677\n38123 52439\n31093 48478\n16984 27314\n59073 61546\n12785 15511\n41876 82587\n25507 62715\n39871 50360\n12554 27231\n32933 38764\n73794 79887\n38143 60557\n40849 65179\n9414 69415\n13246 30548\n10044 68542\n32811 34369\n55580 74896\n16713 32491\n26025 76825\n63398 78970\n14862 75860\n2789 61938\n22590 79646\n8741 53372\n60685 74130\n57451 63234\n1944 2446\n39982 54442\n18752 85544\n65543 67815\n16907 54374\n63174 66480\n30623 42677\n13654 73778\n18899 25183\n24566 61867\n6529 69018\n52955 65141\n65 30057\n13856 70025\n70265 84613\n69052 82247\n39303 53295\n9834 31201\n31033 47215\n17760 78008\n30991 66266\n18292 73644\n54925 77942\n57086 61621\n19711 61188\n33141 84471\n9195 18472\n8953 24911\n9760 59621\n32437 39407\n18191 80006\n21151 80373\n4999 69881\n43767 82858\n99 40441\n15317 79882\n4168 28201\n25050 79382\n37487 41178\n25092 28682\n37937 75510\n4581 11893\n2784 71781\n17802 80787\n10300 25970\n14618 51141\n30232 40057\n49815 85839\n11449 37924\n461 51858\n8639 15211\n4385 55025\n4095 82186\n26043 52290\n9282 73552\n56172 74052\n7644 61941\n39689 73641\n70935 77766\n24310 78286\n7944 31506\n33095 39353\n54922 56817\n37451 72336\n9237 42387\n17876 52491\n10244 57155\n42589 81447\n6263 29947\n7767 69450\n15548 36616\n25031 78640\n64220 70296\n55110 70712\n39779 84151\n35530 68446\n7165 81824\n56441 85437\n14548 49471\n37672 44262\n38518 43504\n8408 53301\n12370 77576\n40878 65949\n9267 77620\n19357 23386\n26309 73351\n14213 44329\n22601 67075\n37694 37854\n41054 54703\n21006 48925\n32005 85440\n35529 58307\n58371 85422\n39876 41463\n21325 66492\n19612 82301\n41874 47453\n16929 19701\n39780 70194\n220 24371\n2973 36343\n68515 80369\n20969 51886\n69852 83573\n27394 62548\n14523 21397\n36471 51268\n13610 58689\n21151 26006\n55438 78510\n61511 73357\n47389 58442\n18918 41147\n30305 35103\n16932 37538\n6095 48421\n25822 27089\n19551 20295\n36465 39186\n28386 45560\n27987 41003\n47343 63655\n13871 52170\n32909 40809\n51791 75380\n30571 65144\n36232 85824\n32268 73453\n7255 31673\n4179 64763\n48142 49346\n4894 75001\n28056 83280\n1688 80088\n17063 62606\n39278 57363\n16131 27400\n16243 74612\n42652 74847\n78334 82519\n17007 76689\n23839 52883\n19277 45004\n67369 76954\n38326 83953\n52513 84465\n11861 26803\n20400 50418\n21543 45165\n8487 14797\n9123 15519\n35089 75533\n19296 68287\n24261 28922\n31287 54221\n50312 61563\n24215 84476\n27932 47451\n62268 79959\n25009 66746\n8291 30547\n10722 65425\n35727 78511\n57741 72113\n26792 77774\n28750 66660\n58882 67834\n42459 79362\n31056 37106\n51608 61924\n75320 80256\n24139 57753\n40011 50016\n12355 42260\n58575 67259\n10098 54498\n12672 81555\n24855 69492\n16344 41197\n34429 36858\n22552 72662\n39413 48530\n59200 71705\n43968 63873\n18549 73657\n25777 68938\n19928 53825\n34406 56181\n17472 49365\n16000 77645\n3072 12406\n5162 27682\n13 76018\n20335 55505\n8254 34518\n21208 64955\n84867 85790\n676 40687\n15390 49579\n24584 25769\n50935 51662\n14744 70014\n17124 36358\n16589 82433\n34169 37547\n6366 71110\n14734 52822\n25693 56525\n36190 50649\n37867 57859\n45635 58756\n31074 43457\n75658 82376\n26899 67881\n41664 74363\n9878 76947\n34320 44806\n23971 63529\n49761 73929\n9150 71623\n42361 55296\n6580 16559\n553 79292\n35786 73365\n65674 83183\n56772 56802\n68459 80679\n52838 68224\n23948 55419\n51294 63405\n38074 81079\n6749 16807\n24345 82697\n44421 53753\n26681 31994\n2357 26332\n68894 83355\n15212 78084\n17756 45891\n23861 33268\n9190 54824\n6710 29614\n5321 12652\n1541 20005\n18741 69548\n16551 74729\n27426 31667\n53059 77561\n24098 39745\n75496 83770\n29930 71281\n6886 16907\n38755 77852\n1371 50271\n16051 28624\n9844 44180\n31809 52153\n14195 23792\n30267 59006\n52998 58943\n65588 70935\n69761 70711\n58395 78209\n2901 52240\n52636 73900\n75518 84051\n16850 71241\n20011 30836\n47643 77504\n29953 61701\n1004 9344\n10784 43877\n66303 78836\n56895 57026\n13132 82937\n29344 46534\n49383 72678\n62825 83824\n3359 72358\n18510 65635\n27403 34538\n24767 44062\n36655 77258\n1329 78958\n77782 78874\n10993 28559\n7674 11628\n17666 62197\n10902 31680\n5321 39215\n12655 69117\n791 2141\n63328 70697\n30796 49603\n43817 64355\n11205 32027\n971 51105\n48369 73856\n27438 82351\n6983 25565\n6174 31125\n19742 66420\n9117 73508\n42892 66077\n30617 34753\n16743 74556\n8769 36535\n13807 76409\n13084 31382\n17144 17149\n23201 82518\n2838 8323\n22998 81886\n31256 53213\n1761 5294\n23363 60656\n9458 31607\n47418 54591\n5987 80961\n27572 74859\n3457 36953\n45981 83481\n3975 48594\n6836 77962\n547 22346\n26020 36209\n23553 59943\n23805 33600\n68728 73702\n9625 41205\n3588 10874\n12386 37198\n34469 53849\n5076 27302\n25448 33124\n16202 54331\n55893 74432\n3485 14452\n3417 35852\n39171 46902\n43283 52840\n14407 30427\n32394 67077\n10675 53821\n65400 76895\n12026 72593\n4720 30385\n26485 41477\n43799 69001\n41424 65472\n49575 59323\n17659 79982\n5604 49536\n27764 47131\n37629 78732\n7995 16257\n23593 31651\n11404 42982\n3842 54080\n47319 78080\n68699 80141\n14916 36935\n46426 56635\n32454 38355\n66534 71430\n39538 77664\n29050 44930\n31889 49694\n31958 58334\n6434 79571\n3361 42282\n28 74612\n553 62053\n2520 4562\n3008 83981\n19662 56484\n31440 53981\n22042 41371\n41247 65529\n29436 29447\n33740 65501\n1844 12439\n11785 24101\n26170 69472\n75172 81392\n47764 59765\n16139 39853\n9535 38349\n8626 71277\n59387 81719\n2387 48173\n15590 34887\n73452 78266\n4057 12312\n5000 50843\n20487 66167\n7392 45904\n3451 26152\n18932 63625\n40454 76663\n66244 83391\n31430 57071\n50962 81222\n53399 84363\n2986 8270\n60085 66575\n55123 71245\n58543 67781\n31958 72496\n58083 85022\n13924 44022\n22194 71147\n50596 84869\n17096 41437\n33937 76081\n15694 40834\n2234 58087\n37817 63636\n59543 82017\n52529 70764\n45716 76365\n27582 27608\n67359 70095\n40050 78658\n70515 73347\n10067 33760\n8566 25011\n15338 28666\n1265 14899\n52453 59330\n9739 80622\n2811 34175\n46506 74965\n19903 44477\n34731 70446\n1155 62201\n67228 79851\n10592 64083\n20622 70840\n16540 62055\n31300 67008\n65863 82208\n19772 40280\n13432 14367\n76548 80525\n24474 68053\n56892 79750\n77033 80380\n42730 74567\n56276 65069\n12089 42334\n17780 63708\n35211 48997\n81474 85732\n2053 57509\n27165 79562\n70643 72437\n21811 40762\n3227 73472\n11976 85765\n7597 18673\n758 80887\n35270 59134\n35712 71668\n3398 17073\n10975 80734\n42312 84132\n38483 77123\n73815 78744\n799 72209\n45818 53692\n35086 58040\n42586 66704\n44878 81322\n1391 54275\n28938 36016\n44295 52312\n75808 78578\n23005 70409\n49266 55651\n21235 49509\n27792 53120\n9114 18601\n3609 12701\n19098 43800\n1659 49552\n3138 81073\n15001 59797\n16540 48618\n63622 68457\n55964 68918\n17062 52576\n11411 51200\n51744 75044\n36683 76977\n28313 82872\n11589 15343\n9767 30998\n50949 58026\n18204 62557\n20654 64573\n20097 26928\n42240 44575\n26969 68236\n10952 51651\n39201 71859\n26732 34645\n61560 78632\n52246 84501\n47857 62113\n24482 27871\n71851 73448\n48994 72104\n43344 81811\n11399 85502\n39069 61601\n35335 44690\n36501 64263\n6156 55267\n22355 35205\n47300 74598\n48252 53928\n3640 68112\n22408 44953\n9263 58893\n35016 36602\n73535 85865\n10817 62845\n45080 62931\n15639 35865\n62396 78931\n6785 78520\n3285 11692\n12657 82679\n51574 83626\n34 83260\n28842 32021\n51565 60893\n24453 32974\n53238 73234\n66628 76113\n14214 26307\n54729 81894\n56662 62781\n43290 61771\n18941 85551\n55772 82823\n15580 49240\n57413 59421\n56388 63193\n21965 71956\n58832 72785\n65776 84238\n11460 34493\n15240 65041\n19744 53481\n8645 13418\n40856 81947\n883 65417\n7915 7935\n63592 85142\n17246 46331\n31905 38370\n9196 78817\n24886 75182\n63894 74551\n31772 47842\n35862 37811\n15071 19811\n36458 47994\n55876 64377\n13041 35480\n28260 66036\n15187 54168\n58183 78427\n12267 28169\n12682 69946\n42079 83905\n3866 55182\n5986 84676\n35535 82069\n39186 50931\n40534 47192\n1496 70709\n33508 84352\n8762 59782\n4738 10298\n28471 30138\n71559 72091\n49249 79105\n5225 33463\n8146 82892\n68066 74818\n15367 63349\n55783 70288\n17015 63889\n42480 81696\n35720 49345\n32819 66726\n58565 77253\n53578 70112\n55471 70987\n27937 59891\n30828 71804\n16289 40936\n21361 51405\n35888 77364\n45627 50341\n4125 44881\n10522 44357\n1349 30082\n15436 73573\n31115 73268\n30504 59951\n39524 45692\n56604 77140\n44718 70954\n11937 41209\n30617 81156\n12368 17138\n16642 65905\n13608 73929\n66075 79088\n47616 55675\n35037 76511\n23539 54435\n2737 52828\n63569 76631\n14755 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44594\n49145 56630\n2636 84136\n63674 72401\n78855 84755\n637 62117\n38287 42859\n51005 59871\n1476 61654\n16539 72839\n23452 33127\n7362 37484\n51366 58377\n1891 17656\n10656 67095\n46794 74552\n39575 40664\n34579 79286\n48739 74331\n6600 66842\n22671 85039\n18564 38929\n68963 85277\n19460 81816\n11911 80959\n16319 65820\n14847 20878\n9383 64167\n52492 58575\n16749 52388\n19965 68235\n6857 50993\n10761 53821\n6341 43107\n31518 41496\n131 14825\n75821 83970\n62055 85058\n29091 71642\n5777 57098\n64126 73546\n6746 69056\n30065 45640\n21508 64757\n27582 77554\n53245 73806\n18349 42744\n12179 27033\n14768 33737\n18212 77246\n20473 65486\n14623 46068\n22491 76883\n28994 37688\n41533 57844\n21109 42473\n10012 62490\n1557 61068\n18772 32292\n48542 52039\n67121 73429\n26254 80551\n64598 80641\n21837 79533\n57403 69865\n2789 27887\n31407 78939\n16968 73160\n17315 82928\n26518 81395\n21479 43667\n44123 69511\n10915 22346\n4736 38879\n53285 65909\n26251 65121\n42917 65355\n38572 66975\n41015 48213\n21593 85803\n2596 69784\n8735 59224\n2187 10161\n51438 67409\n16375 61683\n48556 49541\n33899 39998\n61570 64366\n24949 72264\n73761 84969\n29896 83735\n14617 43680\n29761 49449\n55649 68640\n16277 27814\n2538 67137\n3106 70595\n65454 76626\n18702 45850\n20706 41042\n6199 41817\n2814 64497\n39248 61056\n43277 65421\n44661 74586\n59868 77123\n12776 15443\n3901 54740\n3150 8339\n21188 84058\n26645 31204\n44070 49004\n14307 77786\n43108 84581\n4604 14122\n9273 65350\n12866 77058\n21158 39348\n9689 34491\n20698 71055\n4071 37688\n15867 58515\n14682 83858\n1381 45118\n27697 49035\n43564 59613\n26001 76225\n1228 53069\n59020 62176\n48377 73342\n13238 67769\n3941 12120\n16321 85463\n51960 73350\n17019 20835\n12023 79447\n62679 77615\n24336 54396\n46836 56750\n58255 62735\n2943 6008\n48493 83985\n25903 69455\n13867 85822\n28844 36554\n4374 82386\n26569 55697\n29099 47302\n42589 53847\n14513 60165\n1014 32243\n48895 73156\n14986 70130\n21080 39930\n31019 48759\n43296 65898\n40844 42131\n12197 25797\n47226 70666\n12843 13088\n33355 36159\n15294 84213\n11844 41058\n13929 61918\n57605 85675\n8811 24811\n46968 57777\n24432 62423\n55888 74542\n13589 17175\n5060 15848\n33242 38896\n18147 80472\n16121 53783\n39684 67139\n20464 58177\n40527 84892\n68992 84995\n20138 22706\n66917 78298\n933 83917\n34332 77643\n11191 69442\n",
        "output": "233\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 89,
        "task_id": 541,
        "test_case_id": 22,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "12196 74450\n4341 9532\n4232 4741\n9517 10976\n4139 5871\n2948 2949\n7593 11071\n6203 8061\n3004 6690\n60 1834\n7027 11981\n272 8192\n6826 8689\n4374 9368\n3620 6042\n531 11723\n3733 6874\n954 1334\n145 707\n5026 10008\n4864 7650\n1938 4120\n571 9863\n3391 8122\n273 7715\n10149 10896\n513 8698\n2230 4263\n662 11060\n7153 8123\n2751 4418\n4072 7390\n3167 6876\n6572 9953\n1635 4452\n451 2617\n4033 5522\n330 5922\n5676 9641\n3721 6347\n8096 11677\n542 8872\n1849 5765\n10274 10984\n7890 8351\n9737 10467\n3803 8603\n697 11382\n2808 10784\n4978 6611\n10117 10247\n1458 8382\n1136 10154\n2373 6211\n2418 3252\n4094 9428\n44 468\n9032 10488\n5711 9747\n5228 8091\n4957 9926\n7208 7642\n6208 7619\n1541 3473\n3040 3204\n652 8276\n7341 11524\n1660 10107\n1768 1959\n3200 10583\n432 9103\n5379 7067\n4052 4811\n3732 4423\n3992 5637\n674 7461\n1994 10141\n758 2982\n9797 11096\n1042 2087\n2077 2899\n5421 7688\n2823 12081\n11338 11865\n9873 11412\n3717 9613\n5565 10249\n1018 6670\n1165 9251\n3124 10997\n136 1593\n2663 9052\n6965 10215\n6203 9687\n1493 9892\n2010 12184\n7799 8941\n8705 11942\n3969 8192\n4040 5187\n6051 9771\n4660 7210\n4984 6658\n6756 9468\n2819 5440\n545 11073\n4505 9495\n1739 10327\n5090 6844\n8193 8876\n489 6457\n3712 7013\n6363 6610\n3778 11626\n2043 2195\n9396 10579\n1405 4915\n3770 6194\n6466 6682\n5235 11186\n6870 10023\n362 9071\n6936 11200\n437 3160\n6787 11940\n9235 11313\n370 5284\n5317 10419\n7292 9085\n478 9002\n6292 10470\n6518 8441\n1999 3208\n1471 4510\n6097 11967\n9167 10898\n8006 11321\n5347 5873\n4536 8721\n4780 6021\n7415 9532\n8228 11185\n8944 11585\n6603 9607\n2283 2750\n6073 6962\n5048 6801\n3989 7846\n3670 5861\n1339 8208\n1876 9318\n347 8695\n7557 8171\n420 12162\n1928 3507\n1707 2760\n3967 5669\n4843 10984\n2987 7342\n4733 10381\n2652 6339\n1919 11621\n3687 9048\n107 7930\n1660 2894\n3777 9367\n1411 6202\n2828 3995\n8492 11562\n5994 10032\n2152 7714\n2054 6217\n6529 11345\n1351 5087\n1567 3208\n3391 8190\n3381 4788\n8438 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8185\n6035 6285\n5675 12061\n8955 9864\n2694 9223\n7353 11773\n7128 11099\n8266 8348\n7195 8236\n5861 10924\n8694 9789\n1783 5081\n2344 11401\n4823 5402\n2307 9709\n3215 5620\n374 2959\n1690 4252\n838 10161\n2311 11274\n4180 8350\n675 991\n10671 11887\n5361 7310\n2389 4424\n10402 12060\n5133 7220\n3597 3856\n1571 9719\n3385 10543\n8059 8437\n2354 4747\n1791 6778\n2018 8444\n8565 10355\n7 8558\n92 6303\n5662 9397\n1425 4178\n5432 9743\n4297 5460\n310 9210\n6911 11340\n1856 7387\n3391 11783\n677 1890\n8093 10378\n2774 9459\n94 4086\n2774 9479\n2322 10961\n4449 5718\n4088 7931\n723 8621\n4136 11094\n2166 3302\n9176 11465\n11194 12143\n395 11648\n3690 9514\n7644 9501\n6812 10302\n901 1172\n105 7498\n1878 10208\n2040 4991\n7601 8843\n439 6400\n709 3662\n3505 8954\n4739 10175\n1419 3080\n557 5023\n6275 11586\n7815 7949\n10125 11603\n6055 7825\n6783 9157\n7427 11446\n3702 11508\n5255 11761\n3307 5103\n5237 11796\n5045 5590\n124 2871\n2282 10320\n7423 10704\n1436 9685\n5262 9574\n3857 8992\n10080 10630\n7917 10664\n1274 11169\n640 1821\n3766 8718\n1671 10805\n8329 11734\n2082 9663\n3284 3558\n4119 7698\n9654 10031\n5682 7515\n4582 9571\n3450 3924\n6737 10476\n776 9839\n4240 8033\n378 4609\n2413 11667\n3413 7675\n7820 8525\n3986 11298\n3339 7213\n6954 8561\n3687 11927\n7196 8708\n1440 7526\n4185 6504\n8514 10054\n7386 10327\n5541 8409\n1054 11271\n4279 9094\n1282 8617\n5775 9313\n2582 9036\n2544 5362\n3887 10512\n1219 8719\n1243 5143\n5333 11180\n6876 9968\n5622 8600\n3768 10231\n242 8164\n5864 8917\n2014 6075\n4657 8782\n3583 8531\n1084 8456\n2788 7989\n1717 9082\n5600 8838\n6785 12186\n4768 5685\n2325 6650\n1137 8493\n4908 10882\n1057 3361\n7408 11474\n7204 9881\n8699 9448\n3898 9786\n8511 10630\n2240 9742\n2592 2823\n6050 8407\n151 5026\n3434 6947\n1427 1632\n1726 2103\n6197 8298\n9957 11136\n3109 6947\n1086 4422\n4643 7459\n3567 7515\n1463 6357\n7346 11944\n608 11784\n6174 6301\n914 11813\n5777 9858\n1106 6223\n3509 6580\n5219 6491\n1689 10656\n2750 9833\n3140 10872\n5640 7655\n3974 6305\n3891 11257\n4763 12166\n27 5023\n8842 11655\n7252 7532\n3703 10811\n3025 7010\n4774 6340\n7417 9627\n2352 10982\n7675 9038\n5941 6201\n2936 10072\n1259 4015\n2940 4507\n4114 7025\n7489 9570\n8263 9671\n9001 9959\n1785 9088\n6862 9446\n7945 10680\n7315 8331\n3257 4163\n8203 11797\n1483 10459\n2284 9073\n7773 12085\n2550 4241\n3577 6383\n7860 11864\n7900 11483\n6966 9963\n3033 9817\n370 1878\n5701 10619\n2860 7012\n7167 11240\n5248 6823\n238 4674\n2814 5317\n4896 5143\n528 3748\n2217 6574\n6614 9312\n4495 8458\n10795 11175\n2358 10672\n6090 6555\n6290 7282\n3333 11341\n4094 10324\n1356 10916\n3509 7394\n5867 11365\n5928 11446\n8369 8968\n2613 7674\n3134 4515\n6804 7249\n7880 8879\n3956 8313\n8088 12007\n3377 7605\n969 8813\n9419 11107\n384 10109\n3826 5441\n3119 7149\n4038 7204\n9137 10447\n5303 9088\n4569 6780\n1597 11560\n7831 8528\n1051 5141\n2804 8278\n5421 9057\n1210 10880\n2734 5005\n2700 5769\n2310 10923\n6238 7784\n2978 5337\n8556 11318\n6893 9098\n1941 6493\n3767 6241\n3510 4204\n2486 4983\n4406 9457\n2382 7014\n8135 8895\n422 4964\n2210 8528\n2833 4688\n8422 11976\n3554 7978\n3949 8066\n4163 4924\n8367 11407\n591 2717\n9270 10618\n2119 10350\n3383 6704\n4375 7617\n9384 10775\n182 4841\n10828 10845\n1479 7064\n31 854\n4949 5436\n2549 4078\n1087 9927\n8924 12158\n5799 6715\n3534 7587\n2111 7547\n7818 9952\n624 9328\n649 5189\n7935 8851\n1325 11277\n2094 11964\n7054 7272\n1018 5086\n7450 9485\n3766 9626\n2556 4655\n221 289\n9109 11049\n5415 11134\n4424 7205\n4467 6185\n7210 7957\n4886 8806\n2892 3973\n4911 7139\n645 4668\n1951 5884\n8 11748\n4168 9432\n4825 9890\n2030 5342\n2579 9276\n5324 8691\n7185 10285\n2739 11667\n3828 5417\n8510 9804\n125 3934\n72 12101\n1239 7020\n4809 5368\n385 4461\n9107 11990\n3706 7442\n1143 5547\n2740 11550\n3074 7578\n6425 8471\n5435 9913\n365 10189\n1664 3579\n6839 10699\n1617 9381\n9108 9227\n1071 3231\n9254 10058\n9986 11995\n2298 3856\n7588 7716\n3611 3964\n3739 7833\n7816 10654\n3166 11270\n3778 11267\n4804 9033\n2808 7635\n8697 10882\n52 11639\n526 4580\n563 1884\n4849 11834\n5051 5833\n5815 11099\n4747 5712\n1944 9876\n7121 7820\n4438 7849\n7407 11869\n2911 7297\n5565 8051\n6974 10702\n10106 10219\n7152 8943\n5772 5973\n2657 4613\n1862 10247\n2898 7488\n1764 2599\n4122 6229\n4538 8334\n3370 8357\n913 8883\n1415 1818\n8142 11214\n10112 12043\n5414 10030\n4437 10077\n11123 12061\n2051 11338\n4915 5243\n3286 10206\n5351 8828\n53 10015\n5310 10616\n7949 10103\n9395 9882\n3890 12023\n9 5839\n929 8841\n6204 7235\n4447 6905\n10535 11530\n3502 7671\n7112 7415\n4231 5686\n6035 7272\n7597 9651\n9707 10255\n4208 5031\n4062 5998\n4650 11802\n11749 11991\n1619 9370\n1360 8326\n180 4441\n",
        "output": "306\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 90,
        "task_id": 541,
        "test_case_id": 23,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "15307 30669\n2520 2824\n3445 14590\n10329 11458\n1850 9225\n6548 12574\n1368 1515\n3585 10955\n10891 14714\n4631 7386\n7896 11067\n4034 13994\n3783 8148\n8594 13785\n2171 14805\n3144 12118\n1779 4548\n622 9209\n1612 9681\n2200 12945\n3854 14613\n3406 11619\n772 2118\n5763 8156\n3067 10474\n11935 13341\n6102 9452\n10791 14972\n1022 7607\n5513 7612\n9 11438\n2984 12779\n5155 5686\n8970 12320\n11732 14806\n3202 8329\n9729 15282\n3933 9764\n2406 7682\n1447 5440\n5545 6656\n7832 9964\n503 9136\n2907 13487\n7360 9361\n3235 11195\n9693 13346\n2741 4608\n235 1565\n4847 13182\n7442 14287\n2575 7234\n1261 8382\n3512 4464\n4127 13540\n7230 12750\n98 10183\n6269 7901\n1199 7356\n9694 12604\n1016 1448\n3090 9095\n322 9160\n283 11637\n654 12367\n1189 10467\n2089 12363\n10636 13689\n10105 13487\n1273 7942\n3181 4464\n830 5147\n9171 12385\n5479 11631\n6090 9630\n1449 6229\n9046 13809\n694 13360\n2044 8181\n545 15194\n7254 7319\n4523 11188\n5992 6066\n10046 13576\n9202 9650\n4006 8903\n3579 12414\n210 8782\n10963 14998\n7326 7537\n2534 5457\n2559 11449\n1618 7335\n2489 11029\n2092 5777\n2125 8546\n8602 10127\n625 13117\n10856 11554\n5138 11027\n2663 10124\n10605 10780\n13270 13677\n10346 14357\n1446 14338\n2307 6405\n14 9331\n12373 14574\n3289 10514\n624 10222\n4776 7405\n709 9275\n933 11626\n320 9235\n4672 6284\n15 7731\n873 6350\n1294 13446\n163 5326\n2695 6507\n3952 7980\n15035 15046\n7929 13514\n5134 8096\n11197 14697\n3042 8973\n3604 7738\n6483 6661\n6479 13314\n3979 9934\n5376 12230\n740 13356\n13243 13691\n6183 15152\n2471 7540\n2981 11953\n9954 12194\n1093 14264\n6074 11264\n3849 12783\n8357 12879\n3779 4370\n8753 12324\n9957 11247\n1957 6244\n5450 14099\n4572 15073\n4632 11384\n5567 14142\n14100 14711\n3728 6314\n5031 12782\n6616 6797\n13273 14962\n4187 13844\n2192 13742\n2900 6135\n2874 3366\n5579 13571\n3756 15092\n429 8521\n1103 6079\n7516 7604\n8122 9687\n5718 12841\n8824 10721\n8230 9157\n7211 8231\n6494 10180\n986 2157\n6332 14966\n6017 10808\n7583 11458\n173 5657\n1169 4294\n8512 14068\n6478 6650\n10668 13099\n8602 9488\n3740 9485\n7582 14550\n226 5722\n1239 6295\n4651 10562\n6122 6663\n3647 14091\n3080 13281\n771 1353\n4666 7477\n5210 14499\n5130 8567\n1729 11154\n3275 3435\n1066 1840\n415 9251\n2176 13041\n296 2683\n4089 13275\n3947 8645\n7983 14691\n408 3601\n1117 5208\n8590 13955\n5962 11510\n5017 10328\n720 5944\n9389 10092\n3056 13664\n727 14549\n1549 13663\n11003 14848\n4466 11517\n5521 13572\n10649 13140\n3572 15109\n6069 14850\n12764 13877\n728 6333\n4985 13778\n21 1593\n11675 14532\n9440 12708\n10661 12352\n4981 7585\n9508 12310\n888 10957\n7815 13204\n4965 9657\n5610 14429\n13010 14222\n5203 8170\n699 3715\n1587 11184\n5096 8773\n2258 2877\n14584 15054\n64 12675\n1056 11198\n5385 7280\n278 15035\n4917 9327\n8978 12502\n5713 7514\n1808 4206\n369 408\n8571 8945\n8341 10892\n11781 13717\n7368 15194\n5780 14139\n3951 14443\n4393 10431\n9362 12835\n2682 8201\n1106 7238\n5642 10384\n9105 12367\n2697 12082\n6570 9786\n6161 13827\n10923 11715\n1416 13372\n9539 9757\n250 3059\n8583 8947\n11749 12891\n11088 11797\n4924 12662\n7819 14673\n7486 13947\n2904 15080\n4528 14217\n2122 5352\n2004 2749\n6756 9951\n3768 10372\n2923 14190\n6767 10996\n5011 14357\n244 9181\n1734 9208\n2551 11530\n3211 5393\n8500 11124\n2543 7119\n4589 11261\n10105 11857\n6796 8051\n8363 13294\n9064 13193\n9379 9883\n6880 11723\n1903 4302\n1821 4962\n3864 11390\n2157 10078\n2504 15026\n3201 4648\n4799 9130\n6923 15144\n4487 11771\n4108 6568\n13005 14958\n11277 13774\n556 13117\n542 14612\n773 2710\n2790 10871\n4369 6333\n422 7833\n424 6802\n3178 10113\n10846 15132\n2955 6787\n7791 8394\n10373 14750\n4645 8306\n4314 6670\n4004 6936\n1074 9222\n5923 6514\n13952 14981\n5805 7878\n1390 12174\n4388 13095\n4543 8676\n11237 13719\n6559 14340\n64 9993\n2050 7655\n2309 2358\n7361 12643\n4203 4580\n7331 15111\n3104 10107\n3613 5763\n7097 11130\n8546 14306\n3553 12458\n10915 10986\n2000 13679\n1969 11528\n3485 4509\n7567 13989\n5724 14856\n1776 5875\n7578 10879\n4861 5824\n2478 14126\n2236 9015\n3239 8364\n4307 14595\n4937 14105\n7230 12028\n3804 12678\n1661 15233\n3438 11898\n6306 7479\n2399 8533\n6330 11648\n6095 14634\n10934 13415\n14309 15105\n8594 13959\n8796 13909\n8402 8933\n1563 14064\n742 7722\n6835 12340\n8195 13798\n3227 4992\n4832 13555\n1861 10715\n9845 10491\n9065 9194\n3322 6263\n13179 14999\n5712 5808\n5097 11910\n9679 11177\n279 1262\n11275 12619\n333 3912\n4042 10625\n9113 11496\n7122 7617\n5309 8269\n11580 12162\n8693 8952\n10488 13710\n6914 7180\n3780 13090\n11559 12545\n4418 15207\n2115 2491\n3280 3815\n9583 10560\n3469 7026\n496 2089\n9000 10902\n8255 11376\n1358 5762\n3225 10138\n7550 15076\n5093 7449\n8666 12132\n3854 11216\n5127 11616\n7679 14458\n1229 4212\n12862 13571\n1178 11415\n8885 12537\n3114 9213\n11354 13477\n2934 9276\n6563 14088\n6242 13645\n9742 14611\n6772 10257\n2542 3088\n4488 9303\n2582 13918\n2186 9560\n9344 14985\n11610 14046\n171 8027\n1055 9472\n4558 8887\n5088 11649\n2468 9536\n3523 4394\n1831 11591\n2563 9631\n4052 11281\n5107 8620\n812 14526\n2543 4701\n12038 14215\n8915 9962\n4441 9824\n11762 12205\n2550 13293\n334 983\n146 6929\n565 1987\n2240 9023\n9378 10138\n2803 13523\n10980 12614\n12810 14754\n7048 15241\n4250 4861\n880 4414\n82 1512\n246 3298\n6183 8538\n7561 10608\n10736 14747\n7183 10750\n12873 14255\n7588 10894\n1531 2206\n1708 6278\n1459 6356\n4511 10625\n817 10084\n12858 14996\n7068 13703\n3240 3977\n2335 12374\n3258 14075\n5371 8635\n14875 15202\n1435 12914\n660 4410\n2786 9351\n3545 5375\n3342 4573\n8432 9837\n9032 13617\n10724 10870\n6358 9091\n10435 12680\n4700 10946\n929 5969\n1118 10204\n8692 14703\n10122 11062\n9689 12424\n1518 15011\n12073 15265\n479 5681\n12764 14999\n8748 13450\n1657 4459\n7383 10779\n2058 15288\n957 2081\n662 3641\n1640 12499\n4440 8220\n10071 12825\n7792 15285\n5010 13749\n12474 14330\n1022 10770\n172 1187\n7190 11674\n2188 3279\n3532 11999\n149 15182\n6462 13925\n629 10997\n535 14973\n12109 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14731\n3696 4194\n13222 15253\n1451 6760\n3904 14639\n1032 13952\n2399 4390\n12616 15171\n10541 14760\n6471 9238\n6220 12819\n1795 6954\n1584 12176\n1037 13746\n4326 14640\n11266 13144\n1578 12131\n12231 13938\n2625 9997\n1265 2465\n342 8181\n2982 4612\n2141 13203\n7519 14107\n12802 13875\n8833 14792\n3443 8604\n2769 8823\n3914 6288\n1183 9200\n233 697\n2820 12672\n5622 6179\n2679 6092\n10866 10944\n4465 9796\n5933 8423\n65 2831\n1498 6614\n10813 13350\n5352 13905\n11853 13137\n4571 13475\n1335 14532\n1495 14317\n2682 15065\n1304 1547\n5982 9063\n4164 7162\n10355 13999\n1911 13455\n5513 14788\n8603 9487\n6848 7668\n10269 12549\n2198 14072\n4431 6471\n3400 5598\n12413 13730\n7078 11966\n5930 9110\n1175 5341\n1146 13200\n1730 6063\n8083 9654\n7145 11026\n7352 13258\n1813 7049\n1185 3445\n6053 7635\n1261 11581\n3394 9214\n4136 14347\n4968 10728\n7291 9499\n8959 12373\n11799 12402\n7494 11296\n1309 9704\n2885 6566\n1430 3239\n7323 10186\n4332 4407\n6797 13192\n500 2132\n5629 10880\n5488 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5384\n9025 12166\n10648 11019\n3549 7510\n5228 13465\n2936 4354\n70 10037\n1996 9489\n2733 5543\n2333 10020\n8619 15168\n5751 12926\n290 4521\n4895 8283\n6021 6197\n4004 11846\n13478 14333\n11376 12643\n2868 6932\n802 9309\n7256 10530\n4113 5538\n8363 8616\n12094 13127\n290 14639\n2513 6036\n14827 15243\n707 14581\n4976 9981\n5227 5899\n6641 9953\n14563 14594\n6526 8168\n3646 5403\n3655 8508\n1585 8505\n11064 11065\n5586 14747\n882 5670\n10599 12322\n2276 13747\n11062 11443\n971 7528\n10772 12209\n1923 1996\n8954 10485\n1108 15277\n13059 14721\n1338 7930\n2245 4137\n4082 5846\n3316 7082\n3006 7014\n2124 15184\n9786 13078\n4764 6883\n762 7962\n468 2265\n2001 12893\n7704 12252\n4389 7679\n7721 11494\n2365 14969\n795 11109\n4335 8623\n907 3203\n5259 11964\n1495 7969\n2333 14830\n3133 10156\n11899 13649\n360 2076\n277 10222\n11507 12283\n4183 14462\n7619 12050\n4015 9080\n11074 12825\n3102 9540\n10608 11937\n7258 12988\n1151 14019\n5648 7731\n56 14431\n3468 14208\n385 2068\n9762 14079\n7026 7227\n2514 10620\n2683 10596\n5213 11098\n4447 4840\n412 14968\n10387 12536\n9999 12320\n1771 12814\n11619 13265\n7213 11243\n815 7682\n1645 7077\n2437 5850\n5750 6287\n6818 10036\n1647 4960\n1145 12797\n759 6351\n409 719\n3748 13425\n1538 11053\n9336 13269\n4170 11292\n2130 9466\n6175 12270\n6736 7465\n1739 4277\n2370 2898\n2538 4289\n4005 8256\n9256 14672\n1431 4227\n722 10388\n11518 12991\n6372 12088\n3838 12747\n3259 9092\n9376 11095\n3033 14404\n3143 10004\n8876 12488\n11536 14519\n165 8140\n4087 5053\n7625 13777\n12366 14621\n8573 8576\n11770 15298\n4613 13418\n784 10946\n4940 5635\n740 3843\n1045 3085\n1980 4671\n7366 12325\n1943 6181\n10267 10948\n6330 13919\n11870 15304\n1397 5322\n2030 9459\n350 10339\n141 8983\n396 2543\n11628 14894\n6682 7461\n2975 10043\n2417 4225\n6024 9091\n6067 13728\n2547 10851\n3243 5759\n8014 12428\n5435 8615\n12097 13124\n3242 9260\n9177 13499\n1845 7781\n6761 10376\n6756 14449\n13032 14983\n11992 14298\n1851 7391\n4278 11770\n7402 7493\n2216 2807\n1003 2144\n8745 9581\n1254 8809\n7469 14761\n7946 10674\n9384 9780\n12916 13567\n13440 15295\n9466 13276\n6699 7929\n5013 12640\n10224 14921\n6921 13387\n10000 13390\n4452 10125\n1113 6495\n1052 3356\n11005 11182\n13110 14834\n10577 12574\n2154 12423\n5416 13634\n678 11801\n6566 8638\n3809 12022\n1553 14421\n4672 6783\n7653 10292\n1727 6519\n2611 11755\n901 3604\n4935 8989\n4216 11308\n9695 10648\n3212 11217\n1427 5649\n11123 11265\n4520 13213\n1582 11351\n10796 10842\n4815 6324\n9007 10942\n1207 14676\n1626 14956\n88 14612\n3002 5733\n427 8478\n10108 10526\n6706 11931\n10597 12773\n4857 11223\n5 6448\n4604 12944\n3018 12108\n1858 8789\n1228 7877\n2262 5872\n10028 14877\n1272 2170\n4788 11562\n4482 5961\n379 6758\n1207 7953\n3156 6323\n10894 13284\n2800 10530\n5857 9323\n5137 7774\n10542 12553\n11929 13038\n2198 3436\n6119 11910\n181 929\n706 6861\n4380 8569\n13988 14837\n6755 11139\n4102 7964\n1976 12105\n1219 13347\n5225 6831\n4065 6137\n4043 4198\n6457 7616\n9559 10845\n1692 10199\n5100 8203\n723 5956\n8291 14715\n1320 4069\n696 2835\n426 6149\n12743 13151\n5524 9749\n6537 9929\n652 5288\n5534 12473\n1075 3769\n13333 14409\n10934 14448\n5653 15146\n11140 12088\n6379 11400\n3815 12354\n6662 8578\n8658 9194\n10833 13239\n3900 4048\n10029 14819\n3699 3702\n2684 9314\n1784 4612\n6441 10674\n5378 14284\n2846 9627\n5134 8299\n5348 11336\n6011 6175\n2847 9973\n2862 12266\n8333 9997\n2 14911\n1289 6793\n5717 10046\n361 6732\n1157 12841\n8143 8290\n8854 12793\n3010 9745\n6433 13056\n9240 9689\n5251 11903\n7787 8904\n4023 6243\n9824 12857\n1096 14358\n6268 11678\n4733 9112\n8377 14456\n6621 13319\n3876 4867\n3306 12086\n6994 10779\n5935 8205\n6623 7222\n7032 15037\n3864 7191\n3036 3635\n6104 13968\n1138 15030\n1126 11389\n5648 11616\n3774 9657\n1806 7458\n6106 9280\n2962 9355\n7807 14373\n8083 11884\n392 4579\n4117 9198\n1122 6225\n2034 5788\n3873 14293\n12805 15010\n13037 15231\n4878 11102\n10914 13826\n1475 10887\n9018 9860\n10584 12706\n6602 7891\n1771 3974\n2378 11129\n8421 14495\n3060 6826\n2812 9938\n4468 4476\n9624 15130\n7653 11356\n4954 9019\n5089 14689\n9631 13180\n3051 3451\n4269 5773\n7951 9831\n4438 5449\n1096 14554\n8300 11381\n3616 13949\n12277 13056\n2100 7369\n9529 12683\n6649 9849\n4446 8240\n4638 10063\n1959 9118\n65 9090\n10883 14179\n13843 14873\n1540 13519\n9512 9691\n4665 8082\n174 14021\n1122 4483\n2976 3740\n1576 8040\n4514 12083\n3789 10090\n1490 12771\n13162 13266\n1263 3852\n494 8784\n7741 12069\n972 8046\n7168 8315\n834 13312\n3 5769\n11752 14278\n2146 15132\n3856 6693\n6910 8349\n4119 7348\n4490 5734\n4491 11157\n1552 14780\n5463 6949\n10477 13182\n3870 9557\n3850 14817\n6693 11051\n6975 8889\n3536 13909\n13535 14943\n12425 12654\n1200 10337\n8853 15147\n424 13864\n6745 7605\n5746 10525\n5691 15014\n1760 11900\n6638 6701\n10835 15040\n7275 13689\n3417 14194\n6111 7252\n1528 8487\n4797 5207\n1190 10979\n6062 9391\n4834 8032\n3797 9536\n9571 14950\n5091 10140\n4238 14528\n792 13806\n10470 15254\n8079 14800\n5088 10076\n8187 11623\n2388 8013\n1030 14553\n10455 13801\n7947 15031\n7997 8322\n2214 7705\n11806 12580\n5781 13209\n8592 9236\n500 12424\n2248 9960\n706 5875\n5686 9123\n1260 4219\n2101 2198\n14089 14195\n942 10579\n10199 14662\n749 8625\n8372 12555\n12098 14384\n12560 13762\n7750 12786\n1891 8690\n845 7226\n2567 7638\n5555 9848\n1772 12299\n5445 12373\n8646 13180\n5929 10018\n8198 11807\n5527 13916\n5193 7233\n3201 8260\n12535 14069\n701 11419\n3721 5764\n5280 6822\n4830 13384\n10264 14277\n1220 2932\n81 2008\n2626 8707\n2339 8212\n2562 7641\n1135 11287\n792 14026\n360 452\n220 13516\n1285 1916\n3666 11456\n8853 10150\n11848 12430\n3435 15127\n4589 13045\n10779 14633\n4321 7308\n2301 11710\n10539 13549\n9992 14291\n197 1305\n260 4908\n4966 10645\n1370 4420\n5166 11722\n477 10902\n1183 8703\n638 3423\n4682 11444\n476 8819\n7001 15059\n670 3978\n256 7897\n1102 14609\n1328 10480\n12473 13847\n1289 14399\n10394 12001\n3046 15131\n654 14856\n6203 8693\n9055 10365\n523 8688\n8729 12745\n3983 7576\n2909 13328\n590 10626\n2797 2806\n7748 11762\n5008 12085\n2994 5378\n6632 14224\n4428 6582\n411 12964\n4368 14376\n7584 8724\n699 8264\n9057 11216\n7906 8730\n3039 8848\n2102 12138\n4259 14718\n9347 11656\n10382 14864\n14062 14632\n1014 9807\n8165 9184\n2438 9957\n3455 8364\n13803 14507\n874 7354\n12601 12734\n3773 10971\n70 14131\n8942 11167\n7053 14657\n248 7588\n8453 12721\n3122 11280\n9578 14794\n1041 1289\n1863 6985\n4017 10248\n78 5880\n1651 8154\n6376 13279\n10280 11076\n8359 11205\n11718 13004\n1799 7838\n7545 12533\n5435 9228\n94 3670\n7766 14650\n2812 6194\n11682 13962\n1403 3246\n4455 12161\n5912 7667\n8495 12543\n1580 6435\n1093 8675\n5243 6351\n7409 14846\n6049 11260\n6445 6563\n6073 15163\n3019 14748\n6678 12945\n6461 9881\n3944 7388\n4140 7096\n8885 9882\n8749 14419\n1335 5428\n4463 11063\n1273 10779\n8028 12174\n4219 11576\n5376 8595\n3655 11003\n6164 7617\n3818 8644\n8713 13004\n9517 11629\n5686 14005\n1005 9230\n4769 14732\n3248 14612\n1912 6502\n6799 13041\n3377 7090\n8285 12497\n10346 14226\n383 3309\n5023 8482\n5041 12509\n5670 6909\n2471 8946\n10996 11403\n6749 8378\n12287 14372\n3295 13514\n6352 9056\n9292 14397\n11515 13122\n5065 10260\n10393 15216\n3844 8653\n464 1622\n944 8052\n6841 15044\n3726 4902\n6599 8237\n9230 14947\n601 6561\n1173 10600\n481 2081\n8734 11951\n738 3222\n6938 7061\n4954 9338\n4401 7363\n3435 10242\n917 11840\n53 11569\n3267 15212\n7260 8195\n529 3513\n3826 6749\n4529 10850\n2675 12236\n1281 4339\n1752 2078\n11990 12301\n9991 11843\n4574 5730\n693 14341\n2451 4323\n6824 13408\n4295 4604\n4308 12429\n1531 10202\n10928 14165\n11273 12661\n382 10827\n3825 5944\n2719 9321\n14094 14917\n8327 8515\n9759 10228\n8313 13341\n1309 14880\n6339 11423\n120 10987\n2240 12176\n1024 11585\n946 10205\n8900 13374\n351 8090\n7281 14222\n3113 15007\n5941 9166\n2572 11071\n2339 2353\n5685 8697\n10398 10746\n1517 13455\n710 2848\n1575 8615\n167 376\n10042 13371\n7411 10037\n11482 12423\n10267 13496\n14175 14495\n8460 13311\n2001 12078\n4774 9760\n3895 10737\n3741 11499\n865 3995\n2533 10326\n4281 5251\n3026 7402\n2267 14110\n4438 8454\n14384 14671\n2958 13643\n6430 13413\n4011 11903\n7848 10232\n7693 13150\n6067 6141\n304 13607\n5936 9028\n2034 2392\n3409 11697\n7450 8191\n12929 15161\n3351 14702\n8196 10449\n2678 3692\n14792 14850\n15 663\n11333 15050\n10785 12334\n775 9901\n239 12741\n3196 8048\n1770 12192\n5430 13484\n5969 14829\n4452 9891\n3552 11688\n803 10655\n6468 13700\n4932 13838\n10271 13177\n4894 8311\n327 3093\n3624 13451\n1411 14041\n9424 11780\n5903 9993\n2919 6744\n10419 12033\n6818 12483\n2856 14932\n5104 9632\n554 3470\n636 13954\n371 13123\n2945 7289\n4580 5441\n12268 13210\n7249 8608\n2449 11666\n2479 6716\n11314 11740\n7898 13118\n5364 5467\n2132 14089\n7076 12691\n766 14431\n55 13250\n5637 10843\n4365 11904\n10788 15124\n4559 5353\n3060 5901\n7602 11561\n9577 11277\n4513 14447\n10217 14578\n2455 13721\n3892 6297\n7606 10737\n3252 6296\n4879 9932\n6812 7453\n5697 10224\n2674 12958\n3279 10015\n3150 14085\n2420 12998\n5 6187\n4506 11577\n2888 3756\n1018 6860\n9649 12856\n3092 9501\n893 5951\n3438 7029\n1155 4485\n41 3596\n6300 8349\n11327 11869\n5478 8758\n2442 11876\n3631 11047\n8939 8950\n7928 8504\n6575 7517\n7064 8090\n8430 9570\n337 12069\n479 645\n4091 10587\n5169 14609\n4777 5341\n3052 14618\n8461 8905\n713 2454\n898 12355\n7678 13687\n12545 12911\n8672 13090\n4891 14546\n5814 8135\n12395 15081\n1279 13080\n7290 7832\n11193 14324\n7251 8965\n3162 8350\n10024 11340\n4209 9379\n3807 3887\n200 5443\n2534 5933\n2076 13282\n6008 14324\n12496 13338\n13319 15041\n10301 11558\n5308 7410\n2041 14298\n1787 11216\n7618 12047\n6502 7571\n716 8209\n2935 12654\n3379 14924\n4621 12751\n12150 12452\n1328 4402\n6258 13159\n10755 14914\n5929 6790\n8331 9013\n238 15137\n11150 11500\n5504 14863\n3019 5324\n3273 10075\n6115 7548\n2549 13638\n8028 15024\n6292 9070\n1373 7200\n",
        "output": "205\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 91,
        "task_id": 541,
        "test_case_id": 24,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "17462 87055\n8272 9101\n1341 8445\n5294 14864\n4621 7010\n13932 15041\n8440 14812\n7166 16025\n13253 15062\n3482 11791\n3501 13275\n12459 17433\n2745 7256\n13859 15303\n11363 15520\n3870 14847\n4298 7253\n543 12534\n2698 6523\n2442 13495\n802 6099\n11500 13599\n9529 12219\n1902 3760\n7747 11119\n2914 15477\n4891 13982\n2803 6674\n3906 13965\n2305 5756\n1555 9572\n3909 13815\n2413 4725\n1208 12976\n4676 8232\n13161 15331\n1242 10676\n4892 8607\n10951 14532\n2811 16350\n4532 5404\n1427 4569\n7187 7939\n6400 7907\n9074 10333\n7617 10621\n636 14185\n1264 11180\n5146 10236\n2361 5035\n4454 16970\n6541 8221\n4436 16749\n7963 9445\n8734 11933\n867 883\n7215 13338\n13876 14949\n3296 9066\n4674 16930\n4343 17252\n6049 16359\n6113 11432\n6404 15666\n211 12532\n9147 15852\n12097 13100\n8123 14574\n7294 13380\n13609 16004\n3601 12798\n5299 16220\n833 15552\n5963 10816\n7613 12822\n11986 14928\n2802 12229\n6149 14155\n6225 12623\n859 14157\n6353 12236\n11330 11607\n6152 17307\n13201 13289\n14481 16998\n3591 6473\n2359 6904\n203 8867\n2236 15352\n3168 11086\n10631 10978\n5727 8763\n4209 13526\n6029 11549\n3229 3264\n9366 10915\n10538 15557\n1108 7058\n3184 15962\n1185 4632\n12301 13339\n2012 12636\n8402 12488\n10204 12215\n319 15223\n1706 8173\n7840 14516\n11866 17044\n7085 12213\n5033 13274\n3141 16436\n1126 17317\n7872 13271\n5984 12325\n4504 8244\n14560 14652\n5406 7897\n4922 15751\n1051 3315\n5461 8727\n3891 15530\n3618 5302\n13146 13930\n1559 3225\n7412 17338\n4531 6372\n2738 11216\n11030 16658\n2334 14091\n2637 15692\n806 4066\n6401 16039\n1317 11570\n10150 14865\n3823 14795\n6127 16040\n2566 14251\n12923 17424\n4566 7055\n2220 10936\n13873 14108\n5612 10741\n7362 13730\n6452 8321\n6638 8056\n279 16394\n4537 4770\n4461 9107\n470 16168\n5820 15595\n4566 15085\n2510 14396\n4542 12345\n6533 13843\n4448 17322\n2491 5437\n3693 8624\n5572 9552\n6884 7706\n1486 2203\n238 17257\n8140 16939\n2952 7513\n4515 14229\n7125 11600\n10139 13135\n10033 17199\n6100 8374\n8872 16135\n366 13959\n1173 12073\n10945 15272\n9633 10004\n11439 14885\n10950 16640\n5811 6269\n5260 10325\n2873 5250\n1030 9841\n410 11705\n4013 13120\n180 13559\n5667 13531\n3540 8169\n7138 11296\n9028 10272\n3843 10027\n1154 1805\n256 5793\n4818 13714\n12780 14254\n12714 16395\n735 4859\n9510 13951\n1718 15110\n12190 12405\n7128 8345\n8428 10491\n10358 17294\n7139 9466\n12875 13047\n6397 7158\n7605 10391\n4566 7875\n8421 11137\n3581 16838\n4663 4843\n11697 15011\n7414 10949\n2965 13522\n8028 8536\n1740 1963\n2271 4754\n3095 7222\n4321 13091\n6496 14731\n11172 15187\n8794 10020\n10067 15239\n11344 11830\n6211 16667\n13485 13655\n1298 6094\n659 11127\n4844 6723\n1765 6789\n873 8731\n5618 5955\n5827 11871\n12620 13613\n3353 8674\n10461 11579\n4065 13581\n5806 16537\n2748 10271\n960 15358\n5908 11469\n3565 6194\n575 9149\n2082 8570\n11305 11568\n7255 15409\n7475 11499\n560 13041\n9413 13769\n5556 6063\n5773 15924\n1984 13499\n2666 13006\n6364 13505\n11589 14159\n13266 17254\n81 14829\n15604 15672\n7870 9611\n3858 5384\n3215 13692\n2232 8717\n194 1863\n4274 4446\n12729 14937\n5583 7935\n4426 7514\n8739 10546\n4405 15743\n12013 12635\n4984 8973\n4933 11454\n988 13663\n8495 15938\n1136 7729\n6661 10012\n1526 13505\n4637 12837\n8504 16634\n11063 13616\n8585 12698\n43 7893\n1432 3434\n2445 5480\n14335 15293\n2339 6107\n3569 10984\n13486 16759\n13580 15385\n10164 10819\n8667 11474\n3353 15466\n1770 8469\n873 11138\n10121 15510\n10382 15806\n8504 9831\n4696 6555\n14903 17207\n143 14472\n410 7817\n2091 8140\n8924 11662\n12120 12495\n382 6990\n7022 15182\n15974 16038\n479 6018\n4943 7249\n5419 15469\n346 10142\n7460 17175\n2732 6721\n5436 11080\n8624 12703\n5276 15507\n3421 10735\n2510 8022\n4431 9738\n481 4944\n9092 13763\n11311 16758\n9095 11723\n118 903\n3072 8193\n7617 10955\n5696 13380\n6666 14848\n8327 9084\n3690 7713\n7229 12592\n16011 17362\n6780 17134\n5636 15390\n5207 15908\n8206 12432\n1609 10404\n3128 11057\n4225 4344\n11208 15027\n6313 10022\n7258 11765\n9103 15981\n825 15571\n10959 10977\n671 1507\n3277 10303\n4864 12509\n2831 15311\n3813 10113\n1763 3447\n6828 9627\n430 6071\n1090 11819\n4815 8751\n8541 12600\n184 8401\n11035 13391\n5953 9775\n9242 13977\n5036 16743\n12973 13538\n8979 9488\n14159 16434\n6059 17213\n74 17376\n4933 12033\n8154 13850\n2821 4675\n3366 10948\n12506 15332\n2020 11471\n3597 14551\n9654 13631\n8884 15784\n9301 9979\n11443 12874\n4469 15647\n954 7102\n6876 8956\n1796 11207\n58 2181\n605 9001\n5534 16241\n5935 8338\n2636 2715\n12005 16219\n12644 15773\n6592 17245\n317 1872\n13788 16018\n2339 10027\n5271 9787\n1106 3537\n2646 11293\n108 10213\n9074 14081\n10256 16113\n5562 14580\n11867 13062\n2533 5359\n10038 10049\n4074 4928\n1494 10593\n1572 11442\n11471 11674\n8030 16395\n9396 17415\n2257 9853\n2593 12920\n6714 15323\n2624 13266\n2819 10126\n398 7681\n3988 5655\n10178 12218\n10484 16956\n6425 14719\n12212 14644\n5074 12203\n13708 14762\n2909 7491\n4844 12687\n5844 9061\n4832 9553\n3949 8578\n3063 7784\n10655 12359\n5689 14496\n3186 12204\n1565 12699\n681 12204\n8363 16318\n2173 12603\n2328 15739\n4773 16554\n3067 7559\n3787 10493\n890 8472\n11118 15619\n4008 8791\n7929 11877\n9936 13323\n5914 9975\n10168 12131\n9966 12038\n7697 10511\n7085 7344\n12862 14063\n4017 8988\n6548 9139\n1491 11720\n1385 15968\n3799 4984\n3060 11824\n8350 9862\n5724 16661\n735 10959\n10263 15895\n3582 14145\n3572 7975\n2235 12600\n1032 5858\n5585 14568\n1890 6816\n8457 9665\n12206 16628\n3449 6535\n5214 5683\n5159 17318\n13769 15329\n2208 15275\n4890 6021\n8515 9536\n1138 12376\n6927 7094\n8382 10558\n5508 9758\n6491 7379\n2596 15004\n13148 13736\n1589 7587\n4173 9641\n8939 16164\n4586 12901\n6475 7912\n385 5439\n12863 13610\n5317 15818\n14172 16160\n1768 3873\n1647 13390\n3771 10846\n2379 17133\n3215 15287\n1613 6816\n8585 9730\n1828 10392\n6727 12005\n474 12372\n11380 16560\n10956 14500\n6832 12341\n13781 17396\n10664 13970\n1059 14806\n7150 11155\n4406 6357\n2916 14081\n6636 13368\n13996 15291\n10011 13105\n13454 17018\n1113 13354\n10684 11685\n6305 14989\n5310 11815\n1359 3817\n13702 14841\n1138 4445\n11697 16264\n7721 12446\n636 9882\n1555 9580\n3016 5106\n2083 4728\n5062 6336\n3061 9623\n5511 7374\n15676 17232\n4259 9259\n1249 1782\n2347 14974\n3506 4861\n1732 5407\n4184 7458\n7300 15436\n6866 11419\n4612 17161\n2143 6663\n4623 5498\n4656 17023\n6671 16560\n1784 5775\n11139 13397\n11287 12874\n12686 15786\n14027 17028\n13516 17221\n4534 8885\n5970 16114\n2967 7993\n12517 16509\n380 8760\n14840 16272\n5526 14047\n1464 12226\n3190 7317\n1437 6652\n7155 14013\n751 10593\n4237 5928\n7182 10371\n1263 10217\n3976 11594\n12688 15572\n7152 12032\n13067 17230\n9838 14878\n2881 3761\n8172 14024\n2804 13918\n6317 11135\n4062 7303\n4811 10854\n10285 12486\n2657 8998\n3523 12766\n2337 16105\n2903 12864\n10568 16135\n8028 8828\n285 4887\n2058 11986\n7014 10398\n7943 13652\n15089 16162\n11328 15626\n10120 11030\n4518 11082\n13836 14768\n432 10984\n1166 12690\n1495 10994\n2772 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17218\n5907 11655\n5332 6436\n11603 15127\n1212 12772\n4560 6397\n4175 9895\n4211 8121\n1639 7310\n4351 10939\n7838 10028\n1156 15915\n1926 13361\n531 17137\n11154 17123\n142 5612\n3823 13007\n7205 9005\n4229 11203\n1571 3361\n4167 15947\n6147 12342\n3261 7300\n10015 12909\n41 4851\n1974 14424\n16546 17038\n16826 17164\n10898 14382\n4049 10977\n6473 15077\n2376 8056\n8018 16053\n15666 17160\n12563 17140\n2971 14662\n9465 10977\n13672 14954\n6284 16573\n5791 11317\n15316 15381\n6358 11190\n7464 11118\n11329 11858\n5356 11109\n10946 13456\n1039 11970\n2939 3497\n5385 14034\n12226 16357\n10878 14461\n3712 9602\n11056 12505\n3037 7688\n1065 14591\n10449 15016\n4643 11607\n5260 7624\n1481 9220\n7831 14259\n5525 11129\n156 7585\n1178 14267\n9381 13596\n15379 17246\n2907 13091\n7561 11877\n7468 11205\n3295 15018\n11549 11928\n10817 16753\n7069 11219\n183 3847\n7417 15930\n3350 6890\n15103 15786\n1562 6272\n7019 10449\n9148 12492\n7379 10828\n7040 13313\n9111 16348\n7027 11343\n7026 16074\n8403 13484\n3861 13631\n7282 12529\n4910 15330\n2564 14804\n2366 15697\n14504 17353\n873 12011\n213 8865\n4546 6705\n1000 8504\n2316 14236\n1366 16807\n13452 16352\n649 5195\n4479 10251\n865 13098\n12119 13159\n7970 8228\n8401 9362\n6823 11854\n5717 9483\n8213 12393\n9145 9885\n316 6087\n4152 10392\n3694 4479\n6358 6907\n175 4764\n1749 16475\n6686 15320\n1680 13422\n9819 13776\n144 765\n1047 11499\n5258 13857\n7053 10862\n3809 8600\n2484 4171\n7575 9155\n3083 9319\n4408 16796\n2118 6411\n6938 13660\n7504 9243\n2422 16238\n6730 16112\n7626 7754\n14664 16773\n297 12522\n12905 14276\n10943 12671\n11041 11347\n2592 15369\n3773 15129\n10306 11267\n415 6224\n3449 12911\n4735 11660\n12141 12215\n63 4421\n829 11794\n6078 11779\n11982 15854\n6853 9684\n41 10475\n1946 8681\n11140 11386\n1567 8323\n528 5349\n10864 13299\n8168 10597\n792 16913\n8223 12630\n1684 14865\n6623 11443\n2787 11306\n4138 5346\n5277 13988\n11717 15477\n4470 8964\n16346 16773\n12004 12218\n5246 9052\n4060 15781\n3492 16015\n2054 7319\n781 9778\n610 15312\n7085 13121\n7322 16092\n2657 7899\n5341 5614\n8837 13569\n4859 7650\n8977 17189\n9464 16440\n5370 9008\n10829 11002\n4131 16986\n6707 10907\n4803 10714\n6922 10068\n5803 6264\n1158 16185\n6166 15857\n4869 14004\n10184 15554\n761 7818\n4344 6804\n5933 13086\n7055 7550\n2193 11852\n14418 15307\n5689 16570\n12005 12967\n4341 5438\n6646 11309\n8000 16225\n12306 15923\n7436 12512\n4067 12677\n5607 5886\n1478 11654\n7478 7730\n4348 16922\n10253 10842\n4 14065\n670 12510\n5147 14990\n13859 14780\n15270 16709\n2682 14133\n14099 17029\n6972 7754\n1492 12612\n2123 2355\n9849 12277\n1341 8286\n3145 13853\n468 8753\n3329 17151\n33 13656\n944 7175\n3613 14893\n12038 14458\n6258 14685\n4117 13853\n7298 11368\n1658 8782\n738 15578\n4141 17359\n3044 7031\n4487 7648\n2832 11628\n2091 10744\n14671 16470\n14467 16483\n4491 6168\n8977 9279\n1318 12043\n88 6055\n2451 11868\n3561 8155\n8879 9798\n14397 17448\n8800 9719\n777 11123\n6730 7406\n137 5026\n1338 15737\n12887 16316\n1598 13738\n16412 16459\n6685 16826\n11451 15617\n13714 15381\n9728 17042\n3774 4696\n1331 14340\n10099 11597\n4557 11810\n4042 16894\n132 9396\n4388 11594\n1425 10997\n1072 9225\n1706 13263\n17110 17380\n3404 8569\n5036 10594\n13360 14837\n1322 1430\n2819 11086\n7839 10030\n4061 13371\n1041 7887\n5703 12793\n537 2564\n4426 10655\n8211 13535\n426 7491\n5752 14218\n932 13164\n2364 10133\n1400 15173\n7804 14038\n3703 8351\n8673 14462\n1256 5470\n4692 6077\n2502 13842\n3779 3959\n5333 10671\n5567 12216\n6226 9506\n11394 11987\n4074 11380\n6012 7581\n1276 3650\n6018 16858\n3981 14912\n2468 15070\n3956 11361\n359 9209\n8164 13514\n7228 9545\n1348 13259\n14840 14974\n1510 11276\n12905 15033\n6402 8828\n722 3261\n9099 9360\n7538 16688\n5320 7275\n16436 17059\n12770 17372\n12332 16290\n8293 16498\n11065 16967\n3303 5859\n6312 6954\n805 15103\n3537 8889\n14474 16465\n4046 4600\n4806 5362\n8862 14304\n2081 6896\n204 4268\n9883 12090\n10725 10952\n700 16317\n8477 11826\n7328 11214\n12601 12833\n7735 8666\n7412 9039\n4667 14496\n6175 8080\n4476 13263\n9717 14154\n4922 14914\n5911 14454\n1243 9318\n4945 7176\n8683 14776\n7042 11072\n8078 12228\n4032 7169\n8686 10774\n5777 7856\n1053 8131\n1771 5099\n1574 15123\n1673 13689\n2967 15602\n11434 12322\n4661 15220\n8519 15123\n380 7323\n2529 16693\n5061 10715\n3460 4371\n11343 16554\n14253 17247\n3639 8474\n9603 13192\n1743 7496\n15094 16849\n4751 6352\n1657 8841\n5395 15337\n2393 7925\n7035 12341\n7913 10588\n7589 8676\n12078 13503\n2851 10507\n1827 13425\n9592 11365\n1791 9709\n3357 15918\n9054 9407\n5927 6522\n4418 11257\n5625 7028\n8433 17293\n2183 14353\n138 5724\n10978 16521\n11183 12599\n1234 12093\n5836 16700\n9998 14346\n848 16877\n5923 10009\n1971 2708\n12495 14727\n16499 17157\n4808 9863\n5885 10595\n10240 12394\n2218 13916\n695 16216\n4817 11432\n10575 17445\n1654 15436\n11189 16328\n1637 5405\n6700 9075\n11 6343\n9334 16201\n8684 15720\n4894 6333\n4202 7670\n5442 8941\n4315 9419\n1549 7485\n8310 16313\n11804 13145\n6615 13526\n2142 11746\n3162 4028\n4778 9993\n2188 6174\n10280 11517\n4673 7244\n162 15250\n12106 16256\n2333 2879\n7049 11491\n10679 13250\n6235 11427\n538 9189\n3628 12336\n6572 8479\n3601 14721\n560 13297\n8195 10615\n11810 14399\n3066 7876\n2277 14622\n1445 10340\n5618 11163\n3443 5572\n9721 16627\n11884 14672\n9489 12303\n1021 14829\n5287 9723\n3561 7105\n1123 7937\n10538 15984\n561 3441\n12512 14630\n10181 13733\n8825 9656\n8666 10076\n5302 5651\n14836 16305\n4058 13519\n15880 17380\n4555 6666\n3835 16320\n8253 16490\n11268 16975\n5194 12095\n10381 11002\n10269 17095\n8739 12120\n3177 12314\n1291 9411\n3467 3635\n898 14637\n5077 6037\n13013 13830\n11431 13838\n3823 11563\n12860 14122\n587 8740\n5902 13840\n7934 15353\n8059 17459\n724 4929\n3160 6051\n2585 13468\n16977 17187\n2189 16522\n6047 6580\n4712 13929\n417 8424\n3223 13978\n749 7518\n14578 14892\n9073 12622\n4968 9348\n4112 8462\n1699 3259\n12660 14302\n2396 11771\n7325 16574\n10501 13899\n14994 16481\n2869 15314\n4394 15301\n4797 14335\n2105 8657\n6973 12389\n2463 9695\n7452 11930\n3485 15335\n123 5628\n7779 11300\n2172 3820\n9045 14821\n9305 10674\n4279 8706\n4074 11081\n3224 5251\n7322 12786\n11697 13009\n9698 15465\n11881 14210\n14420 14734\n14991 15929\n7105 9405\n5962 6325\n1332 7090\n5382 12508\n1748 16349\n8782 11363\n1635 15543\n6709 15062\n10461 14392\n6077 14779\n1810 3223\n5784 5820\n12634 15267\n4335 12660\n2930 16822\n2296 4866\n3923 11697\n5356 9550\n8466 14161\n14356 15754\n412 1996\n486 6816\n14220 14413\n9946 16849\n4645 4662\n3382 16301\n8805 13591\n7972 11395\n8602 16337\n1813 14564\n615 13363\n4748 16989\n8473 11368\n7834 12703\n1557 11817\n5677 11277\n3734 9972\n3389 16963\n6243 16157\n4424 16846\n732 6509\n7396 10034\n12059 16969\n15160 15290\n4620 5360\n5843 11483\n6555 15639\n480 8821\n4105 8784\n1631 16900\n2643 15707\n1423 3726\n1557 10251\n6931 13402\n2700 12098\n10577 15027\n3864 15477\n5963 6530\n8923 14477\n8882 16071\n8890 10586\n2320 11106\n6776 13154\n9570 12411\n11857 16831\n5253 6908\n6029 9472\n3127 7891\n1318 14186\n11955 14779\n10500 10667\n4080 14649\n1477 1692\n11236 17452\n1319 8495\n7206 8222\n6537 9793\n5404 7784\n4243 13847\n2064 11443\n855 14535\n11662 15542\n13407 15808\n5724 7328\n6521 15894\n2432 10875\n604 15524\n3884 17352\n726 14710\n10122 14036\n10162 11637\n2993 12672\n3732 11735\n16257 16586\n8849 16071\n194 16260\n6696 13589\n6729 14044\n11889 15043\n3518 3840\n4269 17237\n511 14139\n5643 17367\n14866 15065\n7278 11262\n315 10488\n7871 10354\n11730 13751\n6453 14901\n13938 15513\n14364 15017\n2693 7937\n10754 16411\n6721 13993\n3225 16877\n2332 7047\n9816 12101\n8471 9161\n4090 12865\n7979 12727\n733 11705\n6574 17342\n6441 15890\n8447 9778\n3845 7861\n4399 17133\n3400 12190\n762 13099\n2814 7059\n3866 11791\n8369 15172\n9471 15148\n951 1186\n7818 14413\n9791 9965\n6440 14596\n3449 14535\n207 1597\n590 9776\n5 8088\n4687 15874\n6654 15800\n8586 10284\n12665 16791\n14523 16695\n4172 7233\n3746 5007\n1590 11572\n1805 12156\n7315 17249\n509 3432\n381 10954\n603 16160\n6002 15316\n2376 6789\n517 7771\n8191 14711\n7777 13504\n14531 16030\n1347 10337\n7866 12208\n8145 13952\n14564 15850\n7320 12136\n9254 16298\n7619 8144\n1438 9514\n13555 16202\n2207 11937\n367 9698\n1585 14453\n46 10896\n3090 14967\n4484 16737\n",
        "output": "335\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 92,
        "task_id": 541,
        "test_case_id": 25,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n33854 53632\n11306 78941\n41825 88756\n5511 85242\n76893 79376\n20737 84637\n21611 32189\n12885 72258\n8262 75256\n3393 96798\n58946 64936\n40033 54093\n27583 67143\n3119 47043\n36172 50518\n52452 62952\n96552 99678\n18677 36360\n31762 72529\n15669 80973\n6656 59068\n65799 85145\n18383 68446\n56947 90726\n16354 44222\n66493 81181\n14855 51954\n15034 20649\n41832 80017\n70937 98181\n75935 90412\n21864 88642\n3550 33862\n31086 42209\n66351 92986\n13992 59498\n3587 7156\n69071 69681\n67083 74291\n61991 80725\n90767 97190\n14550 84630\n15600 92428\n44978 95898\n14940 75043\n85089 97412\n13160 70979\n17766 50631\n68199 73088\n24108 39184\n4112 79989\n19071 84831\n42239 74309\n25780 61442\n1966 57691\n8813 38009\n17845 67317\n529 90445\n12782 72865\n55246 83988\n12081 53168\n15109 30770\n46300 65716\n31997 73086\n47227 77026\n18257 47117\n39448 47624\n11218 28411\n7414 8655\n26653 67356\n63648 85996\n76533 80039\n47254 80014\n71431 94651\n47813 84240\n61819 95915\n52755 67862\n3880 88199\n34786 37204\n21366 49083\n62876 77966\n17745 73885\n5408 39342\n3489 79181\n22140 40984\n67687 97469\n13281 17764\n17570 91212\n1188 13856\n5068 17687\n8793 16982\n11184 87310\n5695 24705\n16670 98096\n15042 96455\n36177 61732\n72888 91880\n80063 98704\n43260 81728\n10347 67660\n21790 57600\n46081 99934\n66177 89522\n26476 81205\n52303 99272\n75145 77751\n47602 96894\n12945 85671\n24538 95136\n6892 53619\n39264 41778\n18873 23982\n33191 41330\n2098 26794\n697 84378\n9574 77576\n28451 58111\n36580 96313\n891 12059\n3042 38735\n15340 86215\n38659 93487\n32885 76844\n11233 96026\n39437 45815\n9523 74399\n25215 42755\n216 80935\n26710 96887\n64053 95961\n9530 21441\n57858 86625\n15214 45945\n44896 80933\n32869 46813\n34032 39920\n13082 78991\n52928 58979\n2036 91939\n21164 68251\n67641 81575\n46932 53815\n38189 76583\n14277 19555\n46116 73605\n7946 58683\n7382 26965\n66275 76367\n3481 13612\n13281 40675\n1199 62987\n28805 40361\n36144 77508\n51894 74779\n14885 51422\n24829 96407\n3176 45693\n20562 72461\n11705 14788\n46451 61895\n8116 41605\n1150 95358\n9129 70908\n16390 23269\n1205 53657\n46791 94022\n9680 98944\n42622 96066\n6158 18797\n8818 21821\n2665 98155\n33603 96394\n51961 88232\n74386 95211\n708 51548\n80762 99345\n34243 87621\n16290 37171\n66355 67888\n27364 84020\n31171 36931\n16466 77726\n12218 78941\n21119 53565\n61105 90809\n81786 86635\n39369 53919\n48154 71425\n68921 70576\n2716 48711\n48854 49859\n2888 89346\n4687 51783\n57187 67133\n52592 76151\n18117 87227\n16104 26104\n35504 78888\n27523 61194\n16509 29178\n50834 61223\n25402 54447\n2078 19502\n7119 20181\n68039 97417\n22444 24675\n58226 90330\n52909 88713\n28592 38004\n53270 60464\n60992 94635\n33774 66325\n18763 72368\n10058 63696\n63993 94701\n12176 78491\n2072 66878\n2769 86567\n66849 86487\n26872 94154\n21045 53386\n7341 40131\n27912 44833\n33610 88597\n1747 26703\n50878 67347\n82265 98598\n17310 67944\n84707 92604\n33061 79620\n42517 55619\n8511 44301\n53194 79829\n5977 88075\n987 67107\n61446 82344\n17716 89975\n17435 58967\n1948 42703\n22662 57669\n27959 80551\n56976 70370\n24104 90633\n20854 46472\n41453 97123\n37577 44076\n25683 39719\n15626 58124\n16194 58317\n33527 50818\n68678 83725\n31684 50901\n41136 56515\n35239 97581\n9768 65009\n60558 75596\n16439 50059\n17870 84201\n34578 85391\n3471 13786\n16322 47180\n6854 11533\n19776 35933\n3214 16548\n39096 84755\n37625 89320\n11256 94658\n63662 73609\n53015 55342\n1813 90976\n23620 38834\n23725 96537\n16276 82201\n12934 81958\n41242 91998\n29912 36385\n39260 81467\n19119 26206\n5972 35473\n33994 72682\n24193 73153\n90748 98020\n26175 65431\n54017 73534\n16640 23594\n83566 87943\n75596 99996\n67440 92826\n61645 92779\n33682 89178\n12179 40636\n11784 48755\n9125 77383\n19403 91141\n2667 87792\n15654 24982\n55128 92288\n21899 61710\n82606 86812\n2120 8823\n6966 31903\n52862 93554\n20606 57268\n23378 40141\n54473 70856\n39088 42287\n24231 77942\n47791 56783\n6181 53669\n12331 75526\n53211 94723\n15817 58930\n34586 48987\n12233 16913\n43382 66090\n13350 58859\n14177 50517\n82123 98129\n16970 66190\n38205 64840\n78447 82525\n45652 70374\n4530 82400\n23845 81560\n30315 30733\n37655 84378\n72984 91194\n54515 55464\n16249 22338\n5836 61845\n37007 43898\n39260 92502\n50616 90999\n41222 74273\n14827 36114\n15178 22551\n6188 54112\n7600 60631\n53971 98386\n46081 48837\n45290 99609\n78978 83262\n26057 68890\n59312 59889\n21593 90791\n10495 75751\n2156 57488\n1247 36862\n16727 31205\n39973 96413\n40454 69742\n55094 95521\n83070 90881\n18440 94617\n18859 27358\n9444 19817\n9237 83187\n19196 71975\n985 71135\n23821 98575\n57821 87850\n35856 50923\n12055 84037\n50889 95857\n464 48584\n48309 63656\n9152 92216\n55243 64742\n22763 81180\n19292 50787\n16661 67162\n1862 76768\n72035 99111\n28875 67267\n6479 8098\n73395 94587\n22636 63590\n29586 94718\n28873 49892\n64444 92888\n35640 56068\n5078 69126\n70273 76091\n7547 49953\n21043 76250\n16972 27789\n15115 90605\n12478 76433\n21049 93261\n58136 81645\n1139 15249\n8276 15686\n12672 66888\n6718 79578\n19227 30015\n15370 91613\n35795 65878\n6981 79858\n64689 76938\n15150 18574\n31569 77041\n31787 90656\n35441 58864\n43452 72089\n58777 99188\n24171 27628\n1737 3542\n49154 89830\n29148 60998\n43634 89138\n82675 87180\n33676 57274\n70839 87883\n20837 66833\n4824 67752\n43454 69021\n25553 26309\n19454 59694\n13172 24209\n41107 68417\n6831 72969\n9970 70537\n37121 48300\n81502 86884\n46059 64376\n26197 84129\n36589 61798\n30773 45755\n42280 81871\n54308 67942\n20350 93462\n21481 28785\n62087 73775\n1720 31484\n43890 98602\n11239 38971\n30482 77617\n52082 63267\n2024 36284\n45412 81829\n29310 99633\n64506 84224\n24152 80375\n18286 83005\n27241 51413\n31478 84388\n35101 46572\n41874 41938\n41158 80810\n88303 95210\n29335 95952\n52162 63748\n24216 24353\n19298 25829\n28821 65239\n42416 89258\n32244 84719\n10835 14737\n46208 87652\n8598 49533\n33576 47557\n35130 42876\n12168 20882\n8127 84892\n65996 67360\n37298 59703\n24229 43921\n33065 96268\n48891 65620\n47411 70456\n44648 54220\n8339 68725\n41560 99408\n50161 61500\n25125 89707\n10977 45692\n15436 33583\n3073 40253\n61180 89517\n24910 67476\n5342 10703\n36897 56158\n52967 68696\n13590 86542\n23351 54656\n37423 99259\n24722 55602\n4430 96397\n36649 43723\n52867 89182\n34201 76752\n15187 54174\n15640 15930\n47036 79286\n4442 27716\n1980 47875\n53090 97256\n53786 75767\n13849 96242\n84847 94075\n20451 79180\n29461 50557\n44831 44862\n10891 88132\n5671 14597\n20702 76776\n74023 84436\n24906 39038\n30080 94376\n11000 11647\n71568 86348\n6685 68220\n81080 99540\n53062 53588\n23111 70802\n6861 28509\n62029 66246\n944 35343\n15440 89768\n7295 30081\n2728 81178\n9759 20096\n26754 82465\n30119 57786\n4651 28428\n62375 97316\n87612 97810\n7811 18892\n40294 94633\n42790 64098\n82212 91811\n39858 93582\n21849 68174\n12396 33772\n9575 39244\n66758 82023\n74091 93232\n44518 72050\n4317 77372\n31168 65106\n17115 51380\n25386 29095\n4931 49110\n84760 99905\n28681 86594\n44519 90082\n10616 90347\n35870 48113\n14047 95590\n58185 74949\n15816 45009\n20948 29355\n32505 53166\n51426 70578\n11201 93777\n8242 84330\n68374 82965\n27044 74109\n41687 46680\n80113 87940\n9898 73643\n7374 92948\n16555 38253\n38919 89569\n44832 93354\n17416 19962\n29508 69086\n45860 96029\n39020 45068\n58723 72690\n38007 53953\n16597 45975\n25201 27053\n38131 62425\n3730 11428\n3110 46675\n3403 41374\n8821 34106\n3275 7123\n5301 71134\n76244 87388\n1304 86665\n28281 88623\n4730 99955\n40681 63728\n53761 61618\n20624 90373\n48000 62656\n48527 99719\n67158 83413\n20472 66338\n15448 49499\n33168 57992\n22107 30091\n24177 37724\n8433 82657\n34656 71325\n50737 79703\n65605 86406\n45555 98054\n38839 87657\n15080 28115\n89586 92090\n16308 99736\n9842 56938\n36625 92373\n14101 88681\n46263 96707\n22132 91419\n48119 66256\n57751 63999\n46130 94045\n5377 5689\n50687 61849\n46058 51391\n51335 61047\n13172 95523\n38864 84756\n56397 69649\n50133 58210\n23548 34519\n24781 80286\n77721 84198\n18333 99847\n42440 76236\n17990 48910\n67051 82138\n22163 68787\n19891 89385\n43000 60897\n52268 85869\n41931 78266\n35439 88569\n46306 56378\n14569 96713\n18446 61094\n37049 82524\n32974 54731\n12679 46938\n33383 38600\n37519 42933\n31932 96002\n84195 89849\n20889 46484\n67525 74998\n39183 80586\n39517 93451\n33544 42769\n10887 49900\n6917 52183\n32814 59178\n19573 24316\n60188 91007\n73805 83367\n19851 79598\n56846 75556\n94607 94841\n60585 94946\n67600 87377\n21382 27874\n67995 82569\n37747 93262\n74797 79662\n33396 65626\n60329 67301\n362 80762\n38757 95225\n55366 83055\n11075 72606\n10506 51296\n13626 68149\n24421 87369\n44036 73232\n4279 52598\n520 73505\n77762 98108\n11702 62663\n34042 84085\n83873 92232\n1300 98169\n72406 90929\n4119 13688\n35735 42969\n15027 71705\n7492 81614\n63105 77012\n21587 86120\n45795 67247\n3730 22692\n9630 83303\n54922 95696\n51600 68329\n23528 87868\n26390 75968\n29351 69041\n68467 89079\n56109 87358\n402 19376\n47576 54680\n33514 45306\n20106 66608\n5553 99245\n8428 52496\n49029 71966\n24032 26465\n14408 22561\n23400 53948\n16964 37873\n51618 80253\n78942 81011\n55716 96972\n13813 82710\n36278 79377\n50794 53569\n65530 77017\n30012 60850\n48234 86200\n65334 98628\n15979 63136\n74212 87499\n7325 97751\n57026 94525\n25222 83618\n27194 39829\n17298 55220\n87055 95128\n31011 34090\n16814 50673\n14625 69888\n8231 96815\n20277 89418\n17210 33914\n7641 98164\n85861 94650\n25343 61414\n49513 95850\n26451 91879\n16447 67043\n27936 61276\n50580 63255\n13855 21916\n68347 77574\n77978 90144\n17371 35846\n320 41490\n33140 52509\n52847 88945\n65119 81201\n13017 19062\n13089 48864\n34987 95603\n42910 55470\n48847 59498\n73995 87957\n23697 91018\n17507 54892\n13014 94297\n26204 62751\n33819 46609\n25954 61598\n19133 75033\n41520 93573\n2859 45414\n37699 56306\n2394 12152\n30859 55304\n4642 81723\n13549 15644\n76201 77325\n7924 40204\n51794 90402\n79553 98238\n28474 39282\n70693 93278\n36639 78774\n34946 54571\n65724 96705\n40629 72539\n2247 63478\n45974 80504\n3355 67164\n26429 31474\n30653 32726\n48079 75571\n8161 64831\n15943 96264\n32067 34038\n2636 27083\n76798 90973\n37103 52039\n1191 95445\n90661 94926\n17628 43859\n24158 47314\n74579 77832\n53595 58509\n31291 71362\n6512 7424\n49078 82723\n10014 87838\n72796 97602\n7278 65631\n14073 91236\n14944 68725\n35316 73118\n41884 94232\n34208 62157\n13790 77719\n34765 88155\n50471 94104\n49490 82517\n5717 32443\n14058 39216\n8051 69411\n35428 81159\n1756 12921\n15803 21689\n19443 85086\n54132 55903\n40032 69350\n15829 51770\n75556 93270\n79802 97303\n10031 71137\n48564 87109\n18900 85041\n35073 61889\n45305 82873\n43985 68568\n52138 79531\n11964 67258\n381 9553\n1725 25006\n44951 77053\n40291 51714\n54381 88497\n4223 44958\n11144 98077\n81007 99501\n51155 98953\n63658 87414\n10868 31829\n16843 28660\n1350 62701\n2534 90608\n41373 67175\n24904 99258\n36069 82782\n14327 23750\n17892 50484\n33901 95967\n51975 81383\n46757 96997\n90869 92734\n50509 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87819\n9231 28201\n65994 88686\n74097 75629\n9274 24450\n7982 98000\n41081 74807\n50153 93750\n22393 34635\n64156 77245\n41640 92240\n28269 32729\n41111 60854\n72584 96028\n4672 8574\n1719 12919\n32971 48032\n73481 76062\n58634 93753\n53228 98490\n17629 63632\n14428 75478\n25460 42935\n27991 76584\n25040 25434\n15284 63204\n23441 33728\n27698 85609\n45342 51608\n40577 89198\n4719 41415\n525 78127\n56209 75253\n16544 21223\n23648 31648\n15896 86545\n50642 99450\n38401 71804\n26061 66413\n51105 64797\n43617 64567\n38607 57657\n6974 51381\n75404 98083\n30068 61131\n67295 77007\n32793 51929\n70934 74089\n74907 95646\n68440 82024\n61770 88488\n16615 89119\n28713 94593\n22509 47772\n21920 67616\n32660 44617\n51002 72699\n7770 43038\n32925 51135\n44365 97410\n20166 85709\n16252 97481\n31176 57396\n30774 73608\n59083 71537\n31095 82850\n16251 93389\n16139 84569\n24706 98105\n54724 80888\n2333 82843\n80493 96294\n23192 55683\n17337 82833\n21518 60153\n83237 91761\n44619 76803\n52123 96320\n6363 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59950\n5419 89501\n22075 31958\n10364 45232\n41076 94467\n24755 78680\n24405 47148\n43766 53525\n35217 86203\n6529 38406\n19893 42124\n8741 19485\n36227 40872\n2381 55812\n5092 90514\n34191 73350\n6095 6939\n22620 36061\n261 16105\n44798 84512\n50570 98513\n20336 38260\n25246 51102\n45356 88978\n18609 30729\n16519 31442\n2853 91963\n36632 84778\n45639 90696\n82033 95387\n43068 78315\n35070 61233\n84910 89477\n3438 76363\n38138 43254\n52178 68752\n51300 94744\n69325 94981\n299 89225\n54407 69893\n6710 46617\n26867 73720\n7688 67926\n32825 64973\n55456 88716\n1465 26751\n3386 8654\n18226 25284\n14567 52407\n52703 82083\n33177 87023\n41257 62142\n70303 82161\n41545 98448\n62035 84910\n40208 76655\n24474 96426\n5647 55053\n15813 51245\n76299 78416\n50401 87612\n20146 93197\n73308 99613\n26627 93353\n61987 96117\n41434 60744\n38162 51732\n83816 92260\n19474 62453\n16312 96352\n18236 38974\n13808 59937\n10912 38334\n37220 99506\n14907 52044\n1705 64485\n13096 23747\n53534 86365\n18184 99992\n3085 18372\n18140 25591\n13526 75094\n14445 45132\n20808 36842\n19269 32136\n41888 85042\n42471 59187\n15927 49555\n20496 80685\n36476 53874\n8399 52430\n7238 57235\n38397 85683\n38726 66411\n40346 41614\n3014 97518\n27249 59711\n953 16364\n7063 60571\n20608 49960\n51627 71935\n10315 91872\n25241 65691\n18819 36339\n6674 64402\n89583 90442\n72611 81583\n53091 82140\n4763 61937\n31671 36108\n63615 65795\n27200 74846\n19461 21591\n78401 90963\n18193 71480\n4921 86763\n77821 87131\n22169 78191\n46387 66216\n82716 92601\n42161 56982\n30108 88155\n12903 37403\n15683 25629\n11583 97412\n17886 36445\n40890 58247\n10214 55405\n4883 38261\n46429 72418\n1561 73736\n20140 52138\n71757 77068\n10374 54133\n41118 58332\n18032 74549\n1886 44639\n7047 50632\n4888 93087\n21001 88507\n12335 31357\n2471 44369\n50665 95692\n25784 72234\n34466 80590\n43591 84097\n45091 60550\n9226 93557\n2331 83410\n6558 16215\n4945 18979\n51991 68866\n42609 46440\n57918 93686\n42388 53791\n4021 10662\n49322 82086\n3076 8021\n35257 67702\n16864 33445\n18101 90689\n4907 66748\n42001 77054\n24258 98869\n44570 80424\n5362 80212\n26649 89763\n11974 30992\n40046 79347\n14634 71191\n44177 82765\n5625 72223\n6515 27607\n19496 97494\n16447 72866\n77453 88832\n13725 74251\n36546 41101\n59501 74890\n14326 78442\n33274 73618\n34468 56102\n43575 49306\n13318 70201\n358 81933\n27541 86184\n39402 90892\n18989 72791\n19751 24501\n10729 31218\n76944 97339\n30315 74334\n601 20339\n64390 76422\n23814 59415\n13971 92372\n41190 77492\n19679 36402\n25795 62171\n30450 52924\n27858 68222\n43332 97042\n21928 28581\n44364 45655\n39071 56729\n26484 74232\n18102 93566\n1765 91393\n3484 46990\n34979 77768\n13852 57824\n1818 41115\n47979 71123\n36204 52186\n644 49280\n6736 83316\n64320 64618\n18420 56584\n8219 61954\n18908 53946\n57695 93920\n52938 94086\n71400 81669\n73660 76207\n94979 96531\n42403 66761\n14408 26914\n36692 97964\n72902 77531\n34608 74559\n7139 23072\n25927 66219\n35953 77192\n27543 69783\n13370 73462\n16397 72191\n55632 62117\n2288 43599\n8029 49150\n31183 70827\n88059 96063\n27079 48812\n19672 98223\n1168 70244\n4095 5739\n56511 87982\n19763 27333\n11841 90491\n28572 38279\n23486 76601\n1983 25760\n22893 53478\n52634 99550\n41183 84752\n23769 47245\n18557 52764\n26857 45062\n14700 97406\n10139 34106\n1886 14676\n47706 96910\n4526 55217\n5180 25554\n3508 81829\n43045 65568\n69230 93785\n44224 55333\n24497 58873\n",
        "output": "366\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 93,
        "task_id": 541,
        "test_case_id": 26,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n38392 78476\n39511 57090\n52451 88073\n41475 42837\n9703 97059\n32223 84264\n62222 70955\n35446 93712\n197 41912\n33930 82434\n77135 84065\n31850 85372\n45779 69903\n34525 73219\n19700 23076\n4196 63854\n13628 24276\n2315 3595\n21879 53502\n27064 27321\n6816 51858\n19172 58316\n72335 80026\n9182 88807\n68686 97014\n51897 52320\n31621 93114\n33278 85200\n57554 88436\n39896 64524\n47597 52059\n97911 98572\n73245 79945\n2850 80666\n9178 18597\n72704 95029\n32985 48291\n22028 96267\n42496 90128\n10061 38323\n79492 97090\n18708 27144\n48116 61962\n6696 28177\n31007 32689\n1804 62234\n7431 19888\n9064 87151\n14968 98305\n21196 45293\n25632 37428\n55742 96180\n33075 35102\n66068 92025\n5626 35197\n57858 88828\n16167 53080\n27672 47412\n9129 67747\n14788 92653\n19061 79623\n7229 50697\n15082 34091\n23774 90222\n27547 86188\n13584 14679\n62895 63013\n7461 67219\n43156 81033\n38711 60774\n24823 63943\n52926 53930\n791 45174\n14886 32266\n43760 69808\n23851 87880\n44032 90441\n69778 99430\n11307 28608\n18096 90119\n22866 98254\n30954 58598\n66786 87626\n22937 63719\n34997 68154\n68792 81114\n43287 50567\n8214 80708\n6766 55399\n6531 35445\n3243 71758\n30173 62181\n19186 57811\n54927 58498\n23986 82431\n64690 99032\n26384 90182\n54700 95362\n70066 95542\n2228 17435\n9282 58810\n43198 92533\n11008 74552\n3733 76205\n7504 34972\n9154 70891\n41796 57759\n25072 48228\n39629 78622\n94536 95497\n72777 84535\n45458 61217\n47979 60798\n77741 92765\n70944 97572\n10363 86211\n71591 82173\n25732 99173\n1001 77174\n83470 99769\n24291 90496\n6943 87637\n389 3273\n58328 82415\n5336 93622\n69085 97157\n12843 57662\n12305 79155\n25268 68967\n4938 35396\n62155 85240\n5680 63211\n29941 34656\n84938 95439\n3100 71707\n44677 63999\n31705 44013\n13965 61688\n72128 93723\n1336 55672\n63771 71709\n18607 67999\n909 71653\n32064 64234\n25090 33149\n44575 45577\n83698 91627\n48796 89254\n55663 72700\n30146 97701\n40178 76910\n10547 76355\n10958 82022\n70774 82457\n62438 75647\n7823 47121\n30304 34317\n40951 77411\n10108 31769\n9223 59003\n80996 91273\n8801 48710\n16707 78097\n37908 61033\n57752 67266\n40665 42661\n21352 77570\n42029 98354\n6594 74518\n31021 47934\n36340 77915\n18463 29976\n12201 42566\n57095 71270\n30029 47321\n9454 15671\n23618 63980\n17637 89573\n16222 51477\n50516 99451\n44222 61329\n26985 27411\n11382 57935\n64797 89187\n76867 78720\n17896 29983\n53728 99811\n277 31751\n89649 98267\n17150 30146\n52564 52756\n12380 55598\n23811 50828\n2263 31509\n21689 96739\n62415 89552\n87644 99286\n25044 96669\n2612 85416\n33015 69908\n24612 58809\n40573 80528\n21900 97508\n76158 79993\n30825 64749\n34489 44947\n13588 91409\n8237 65479\n42764 94008\n50234 89840\n1340 93902\n6886 39428\n40004 43308\n11242 38391\n8466 72422\n18812 19043\n24655 73320\n33187 99541\n23559 94798\n46080 95349\n75422 99281\n23145 24366\n2812 93913\n19242 64454\n27003 65802\n2701 27883\n14128 97597\n76643 84712\n49161 80836\n49819 94709\n17384 82057\n29949 37354\n48175 58690\n25564 86738\n843 40505\n21748 80552\n31807 59393\n93099 98138\n57896 76135\n427 51990\n19256 48537\n53367 95331\n55407 69650\n1424 30282\n71423 76633\n12074 27210\n15292 27864\n58584 91075\n7984 69422\n8429 32884\n38419 79773\n14045 66111\n5566 13884\n73571 81798\n73350 95601\n14256 38030\n23264 87298\n3808 13768\n28423 56343\n56969 73677\n8348 86004\n39194 50109\n13336 78411\n69049 80418\n23560 76671\n13239 28764\n32677 60167\n43186 85832\n83771 98871\n21653 23104\n34568 48832\n2624 55638\n10567 15575\n39319 70092\n28732 36311\n41229 97544\n19881 49960\n5136 16794\n12988 87739\n12563 50661\n49815 67774\n33678 94517\n24738 95039\n31953 67750\n24551 86600\n31900 49383\n2173 4689\n13420 66597\n30792 83882\n8416 97773\n77692 83200\n7710 89931\n22671 96361\n9123 90561\n27259 95272\n72711 80329\n70661 89780\n12337 85956\n30146 41961\n6574 82885\n4024 46181\n4503 90777\n49687 89661\n5451 17874\n27520 40954\n2355 74313\n1778 51287\n22454 45942\n28500 37518\n23262 64368\n67487 94346\n11515 52180\n58463 77336\n73688 80672\n10680 72938\n37026 74037\n29855 94676\n11392 29912\n33122 98991\n15553 55655\n52935 66956\n80622 97151\n53464 64696\n48239 96995\n73899 90134\n85888 87086\n14399 17473\n28730 62802\n412 75790\n24438 49015\n69887 77151\n32024 52769\n12517 83407\n19765 36291\n36544 49626\n2209 27167\n26749 52950\n3962 37059\n26466 95663\n7833 35350\n55774 88589\n33035 63829\n29526 31453\n27735 45467\n14923 88601\n47932 82195\n36380 77925\n54057 80887\n8178 51244\n41527 70694\n15443 84860\n20462 93023\n1119 11434\n33775 83839\n65881 88101\n8291 33166\n488 70578\n29670 65365\n34872 46967\n60641 81469\n11798 19034\n18935 42675\n2862 38588\n58954 63924\n7008 20781\n80344 94464\n8826 15125\n10961 94949\n65957 99559\n44350 87688\n13000 67050\n21830 39024\n47605 87883\n16504 77466\n68276 73120\n6231 71063\n55618 77437\n27549 83372\n21699 89653\n30234 68478\n36836 37359\n40545 57509\n28870 28897\n30690 46600\n5925 85216\n35185 65877\n79778 96350\n24078 54250\n25186 47877\n18190 79458\n23242 46753\n25310 55029\n25702 91371\n11968 13379\n59199 63922\n3173 54912\n62499 99610\n21274 38614\n8007 33025\n7174 89820\n39747 49825\n46608 92606\n53538 88366\n10753 50989\n28082 69277\n19278 63797\n3357 95113\n24619 93536\n41629 85525\n53580 63582\n6296 58490\n58798 97074\n70003 85164\n58036 65754\n25464 96729\n43226 59804\n29177 91722\n35914 67812\n44489 54467\n14178 46027\n50255 66288\n25607 84635\n5200 39772\n19168 39728\n25468 66684\n2979 13707\n25689 90434\n24379 98968\n15394 48311\n41093 45529\n3735 62635\n22342 26210\n57184 72435\n18928 56030\n62635 71537\n74603 97826\n12133 85726\n14965 33985\n10038 91890\n31997 76320\n74308 75255\n74579 99653\n27911 82343\n41552 49721\n23462 31861\n56774 96631\n3070 29122\n34788 87934\n23045 34881\n8049 52778\n19363 97968\n4659 45960\n67151 79617\n19909 65549\n48529 86376\n19910 75396\n22110 77023\n36826 84566\n46268 47008\n4733 30825\n36176 92231\n8543 89740\n28577 99443\n19961 98617\n13121 44263\n9708 94484\n9750 66067\n47864 87229\n18840 39760\n13488 91508\n49146 61833\n13673 21478\n71640 95081\n34049 81848\n60728 73546\n25728 27553\n4462 66023\n9584 77923\n5380 16908\n4071 32891\n52522 85250\n31463 52683\n44853 99925\n14944 74078\n29262 79351\n2961 50994\n43471 70651\n31414 92074\n34436 90203\n15015 47471\n42568 86078\n41299 76945\n4330 92988\n11008 41270\n17452 66577\n1188 3640\n19280 35513\n73355 83110\n1418 73411\n63217 98529\n4227 52779\n97117 99112\n36313 81134\n23580 56475\n24234 89014\n34391 80535\n52217 98050\n51224 56734\n10426 72833\n58025 63339\n46160 67454\n38959 70952\n12884 87022\n51752 68581\n41247 97737\n38117 41756\n51792 73306\n6405 82708\n21990 60785\n47344 89854\n10792 67928\n45295 87442\n35745 47619\n1720 60440\n28911 54795\n2512 89078\n21399 56667\n41332 88033\n8956 95503\n33947 86287\n28099 40941\n29008 76870\n5566 40519\n11044 72819\n78674 96439\n2220 48925\n2616 41828\n24953 49946\n35757 86962\n50890 69350\n21989 31237\n71831 95366\n45084 62221\n31222 51619\n82413 90209\n75383 91547\n6758 16530\n23241 49284\n26147 27559\n24343 38213\n85121 91380\n23295 39084\n73775 79027\n39979 66778\n25791 97015\n46671 63756\n29426 72498\n60331 85817\n87019 98879\n32717 34826\n51058 55204\n54289 81503\n53210 91773\n38014 83153\n73795 82190\n56954 82266\n14891 92986\n4592 63883\n31577 94259\n43641 44024\n42804 68488\n54881 63853\n84064 85121\n9964 12340\n32247 54344\n50635 97633\n65750 78970\n62303 81877\n1473 9061\n7283 56128\n2829 35648\n21920 65595\n48056 76585\n15411 96203\n94850 96167\n62656 97103\n34318 66168\n34616 57952\n43115 78061\n9314 46084\n27871 29904\n18308 46220\n26357 70403\n57094 57203\n54907 62196\n17305 47652\n26253 72920\n10567 15868\n26734 84921\n64242 89608\n12421 91890\n49128 98878\n19097 25603\n15466 59142\n75278 85393\n39303 68178\n2844 76522\n17508 41972\n45700 81221\n27674 93658\n9122 49689\n64341 87053\n17606 56195\n53318 70113\n74534 79859\n93508 97859\n85551 93776\n7988 43324\n49895 71221\n27675 97424\n74525 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74904\n1755 99827\n32875 85562\n5966 18181\n28379 52333\n74134 88305\n18008 66430\n20870 41294\n52221 68362\n68908 77440\n39837 79229\n43064 56350\n24561 93025\n36609 62780\n25426 48549\n93784 97946\n60937 90837\n77490 86999\n33554 46513\n21862 59848\n79157 82911\n5198 24958\n46318 81503\n32070 77508\n57068 90707\n29235 92455\n7063 54182\n47064 88284\n11150 81434\n21924 92484\n9991 72273\n21162 64465\n90359 95534\n46740 49784\n48441 87248\n56782 83961\n38700 72130\n5587 15504\n22098 30653\n336 64110\n65174 70034\n8190 20223\n17737 41501\n18243 90564\n33327 94632\n10439 23427\n76002 94663\n18506 32125\n52653 62865\n68533 90822\n1401 80231\n32305 43370\n76495 76873\n16131 34665\n25294 57496\n31615 79727\n11702 56350\n56173 66830\n60414 75850\n33439 62119\n40917 93459\n63219 78140\n65720 80414\n54753 83426\n40357 51678\n8404 62848\n85549 95674\n38448 84404\n11439 48379\n8302 74663\n61233 75844\n339 96715\n4236 35635\n4275 15358\n29993 52858\n14836 36637\n17051 52462\n8886 53661\n55887 90078\n8707 25756\n10890 48774\n65368 91948\n78567 89406\n11925 22670\n13270 41780\n8043 53606\n3315 62641\n20640 54929\n7593 43022\n4808 52488\n66123 88831\n819 15680\n55403 67557\n43744 72845\n5763 34933\n42646 50601\n1549 41234\n48729 99592\n39939 98095\n6295 67630\n8094 47406\n8088 78355\n62027 74224\n10952 15071\n11346 36258\n82310 91050\n16048 40580\n44240 60648\n76321 99495\n31917 85169\n25687 91904\n30623 45906\n24403 67767\n34705 80268\n23640 32009\n15443 42650\n82362 96221\n33673 50949\n8270 10477\n16746 23003\n72283 95919\n22552 62805\n57335 75265\n15105 40734\n28680 84072\n15779 87229\n18164 87111\n",
        "output": "378\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 94,
        "task_id": 541,
        "test_case_id": 27,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n44294 49292\n47765 98511\n3356 82000\n11504 35776\n37433 69276\n4893 12131\n36174 56202\n34019 39510\n18107 42493\n64822 93942\n70227 74100\n3660 67341\n53260 84815\n57015 66030\n984 75225\n5914 85951\n54601 86499\n25371 52020\n6683 42684\n35171 80518\n31951 34942\n39011 64299\n37459 53883\n7978 68973\n33560 77168\n48815 79699\n26592 48562\n43278 79542\n94355 99355\n27521 90289\n10342 80586\n60116 99148\n19325 29747\n24074 56285\n6522 67096\n10031 93059\n25156 46642\n21415 59691\n48937 52099\n29729 55915\n63918 80367\n25045 66842\n29977 41601\n44970 73947\n11178 36153\n43597 98523\n12222 15490\n47157 78882\n47358 64645\n32445 60058\n24470 90503\n15125 80701\n46802 52546\n36020 93314\n26490 46417\n31534 86265\n33753 42688\n51709 96391\n45409 70090\n60914 67431\n23659 83420\n27670 54945\n378 32290\n58718 92740\n17201 41542\n60319 75752\n41237 95309\n25217 67057\n98557 99644\n49303 99123\n36589 76797\n15136 57002\n88226 90701\n18861 39462\n14866 57213\n30029 95139\n55413 95397\n44501 72243\n29527 56274\n32318 80976\n4031 35330\n57253 95313\n21435 21844\n29988 72303\n23528 48882\n16907 92394\n44398 72897\n31572 42055\n23680 58471\n77927 98937\n2878 76629\n85785 96113\n77873 89286\n11703 23509\n294 38827\n12743 96851\n76832 96224\n42766 42819\n18519 85232\n29905 74647\n40954 69785\n14893 53443\n40526 60545\n5441 79056\n49835 55742\n4599 57063\n11200 49059\n40719 72802\n5226 96939\n6424 55076\n23392 51373\n72310 96090\n18236 61227\n25271 61332\n54402 93274\n18385 96283\n4154 54601\n57219 83454\n59058 66658\n11948 41607\n10032 50341\n25344 55440\n2728 38088\n41718 45360\n40848 56195\n2540 8607\n12771 73900\n8829 9758\n4580 80782\n57841 63898\n58117 77010\n12553 73005\n41325 69948\n8858 24938\n34139 39187\n10824 27270\n88981 90084\n42176 71270\n69727 94988\n56653 69814\n72095 95358\n81994 98351\n14202 30389\n38241 53549\n69747 87107\n52670 77846\n22094 27331\n10100 66997\n4207 47319\n37922 54728\n196 22003\n32379 64043\n26431 93695\n18674 87860\n6615 13766\n43834 89691\n37719 59393\n35571 38457\n28250 47510\n8771 45240\n59750 85166\n60300 76865\n42727 48722\n27998 47401\n49621 99904\n25129 45892\n39288 45446\n67709 74928\n48531 98060\n24692 62010\n26653 65054\n18814 81409\n12064 77367\n20308 65072\n2301 71636\n20398 32382\n5057 64409\n33482 47330\n75010 82115\n47191 78993\n52407 93807\n36881 91524\n6067 85984\n14713 14894\n61703 62458\n75959 82425\n10875 67282\n69847 95659\n71232 87260\n12657 43050\n64941 98811\n82779 96671\n48240 54403\n13030 88315\n6083 83238\n12806 19752\n43708 98686\n41447 69864\n5761 43785\n2578 61603\n31550 64727\n78674 91325\n34368 88307\n19448 93251\n3549 81842\n17207 32405\n12509 42035\n2853 39321\n37635 83356\n54171 82940\n3981 31508\n45724 98136\n49527 53039\n21594 77572\n75568 76912\n11758 77807\n32794 49397\n63775 84098\n4543 85732\n46360 98843\n44792 65845\n30967 48151\n32698 36136\n39923 95176\n32344 77826\n12088 78521\n21876 85242\n38914 44841\n32090 32875\n30927 56304\n78604 93545\n7510 99724\n45797 79396\n5409 93157\n5450 77538\n37090 44559\n53688 93507\n48215 74175\n3890 78597\n59186 92067\n18157 99407\n38807 61706\n21027 91596\n45124 91886\n27357 97781\n36922 54202\n72704 78019\n202 57860\n536 38298\n19267 45376\n76190 88765\n41064 68285\n86872 90067\n35712 56110\n13096 50863\n4971 16744\n41608 44006\n49815 68257\n64372 91328\n48 98937\n31242 81971\n41010 88204\n13267 33064\n30392 42708\n45596 58830\n2130 55730\n36677 53397\n7652 87613\n21897 28609\n72970 77938\n43136 73394\n50213 69518\n40758 44600\n13602 37763\n16398 81062\n41035 99039\n64044 94883\n22667 38768\n23331 34007\n70657 80610\n21065 85296\n28411 96792\n1733 80884\n74958 95844\n49067 57011\n52280 62402\n15550 59163\n48200 79970\n2590 76297\n19808 22435\n1919 15219\n681 58913\n30862 59427\n22411 50860\n24301 30427\n14282 49605\n7012 73316\n25272 87502\n69945 78722\n6586 39332\n76462 88285\n7754 68866\n27716 52067\n4468 66092\n338 24499\n93631 97618\n27749 49660\n46733 52966\n62684 93931\n62041 68580\n8519 47329\n44825 51709\n33878 58846\n14991 78705\n64172 76941\n56301 72745\n5646 87139\n74381 87479\n32683 54082\n18311 93099\n83074 93281\n7545 37118\n36236 47833\n72062 75801\n95325 98391\n41172 65968\n47878 81155\n27159 49119\n18157 73967\n16739 44880\n30967 71009\n20683 54781\n81994 96385\n55503 88688\n32517 92046\n38753 41350\n28530 31607\n50642 68848\n30075 83075\n37159 71552\n15284 89923\n57667 66901\n10237 67153\n9217 61609\n6504 86541\n6776 31073\n21985 74100\n8516 73554\n6625 83319\n12311 89150\n32945 88739\n14793 91939\n49130 99803\n33061 54329\n69380 75200\n28741 87331\n56370 57612\n22413 25260\n20141 34879\n39024 44551\n50522 76107\n33209 45834\n4905 73964\n23466 65132\n8701 60168\n15743 72819\n7872 29467\n6091 68968\n12545 42636\n58932 81682\n49739 85810\n59134 70793\n59338 92232\n3105 70867\n24257 78082\n16049 68552\n14422 87067\n4424 61883\n50164 56577\n27408 35434\n41890 47393\n8162 91276\n49833 75308\n80507 99669\n12823 59811\n60369 80004\n41557 92076\n2345 35608\n17207 41293\n43608 46359\n4295 9355\n29754 82247\n3926 92953\n37992 61191\n48778 84572\n36636 71544\n3825 60637\n30019 57951\n52054 61110\n45559 70856\n44583 78515\n22825 74895\n27696 65859\n64774 96604\n36848 50990\n40873 55963\n28288 74383\n33867 83764\n44740 90513\n25191 92226\n42568 89203\n60762 78494\n86077 90581\n52901 80909\n23369 60955\n37916 51213\n84907 86090\n62879 82444\n21350 29037\n24188 75577\n2000 87543\n49760 58911\n36914 84003\n31356 60818\n35815 82042\n19734 21408\n19282 30986\n40209 53900\n5644 43800\n2447 42175\n70820 89061\n5830 35475\n15443 41174\n96675 98982\n21800 26004\n17802 64984\n72642 99499\n6863 89083\n37968 44755\n32548 60693\n74447 92892\n11082 81723\n83710 84199\n25021 34090\n59969 99526\n34861 81612\n54360 54826\n33426 46263\n18032 39692\n35414 63827\n57054 93311\n706 11466\n29967 34451\n18574 42154\n12242 37452\n20335 27324\n37505 80998\n69282 86223\n24073 53248\n9000 29158\n55465 78908\n12069 22171\n35994 74879\n18154 85776\n5686 84399\n70087 70094\n8357 70428\n9337 18343\n8084 49944\n53450 88254\n4855 55560\n32545 93461\n3737 24592\n47782 90638\n30717 43461\n12153 87403\n16509 18826\n48531 69795\n6344 39392\n50359 99798\n22476 53679\n22151 22842\n5998 20088\n27932 30416\n33548 99915\n11671 55678\n12434 83937\n29193 37349\n8030 8435\n77822 90614\n68184 68518\n29687 34582\n62022 81590\n46993 68574\n9729 25414\n68265 68584\n35104 76526\n46620 89289\n22440 95478\n51589 57994\n5155 38162\n37016 58447\n2344 4400\n7057 55952\n48004 88917\n69829 77492\n30172 65482\n7317 78292\n16149 22521\n16314 69026\n15262 59067\n47618 72620\n30401 45460\n79801 93020\n792 22275\n32798 86696\n7022 28974\n21897 59402\n2920 37810\n1561 65864\n84388 87765\n39124 75416\n8298 78169\n33762 34933\n55200 84190\n73993 77943\n16078 88317\n16275 29847\n30253 93274\n27011 99997\n21346 74240\n64930 99470\n5463 75284\n9084 38185\n74217 83173\n22144 89914\n6975 90562\n26163 42435\n55183 70810\n27856 33206\n20100 94677\n7454 11744\n7144 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75759\n76359 87850\n58319 83479\n9427 10671\n46025 52653\n4944 23999\n58930 79984\n41827 97173\n37943 74364\n57924 73030\n38834 88741\n74666 84262\n27201 35437\n15754 43018\n9409 56434\n79196 82759\n32797 97365\n75837 98388\n79714 90204\n58293 94150\n6197 29478\n20486 40818\n21674 41306\n18440 55111\n53031 85248\n69581 78612\n24323 80709\n10211 79683\n16568 68720\n3041 8079\n80643 81655\n9510 65291\n64229 85103\n65853 81851\n76818 86386\n4325 68191\n4235 92145\n18663 73264\n39967 74472\n34833 75774\n24348 60038\n62120 85409\n40402 99307\n19135 63213\n22421 45350\n14190 18174\n55708 59967\n82508 95145\n35375 79109\n84652 99329\n48682 56694\n7189 22515\n55830 85124\n69474 99945\n25479 66331\n3549 61713\n4873 18357\n10452 35638\n64231 68469\n24155 74121\n33208 96117\n8467 73671\n2364 50324\n82701 98433\n74291 76591\n91587 94384\n70878 83468\n39117 88286\n43653 52090\n2185 70091\n21642 77999\n43059 90543\n14572 95665\n17707 21219\n62689 97758\n",
        "output": "362\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 95,
        "task_id": 541,
        "test_case_id": 28,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n28880 59634\n35877 72202\n4801 45897\n12889 68498\n97588 98893\n15681 59756\n38735 82453\n21394 29776\n23465 32981\n23342 41443\n11628 55666\n14896 91114\n41479 47773\n12146 48294\n55084 75568\n38664 60906\n40508 86115\n62372 65163\n27933 74041\n36539 60487\n25091 67129\n10215 68674\n4946 31121\n48602 92779\n39508 73821\n57546 96256\n36593 88442\n39699 42171\n54682 68138\n57779 65589\n18911 83084\n33841 63356\n43154 54056\n9444 27586\n36324 70777\n47045 49036\n21606 45584\n50707 58621\n7919 24717\n60669 94768\n20426 78572\n89810 91180\n32152 57455\n65505 84623\n10082 23138\n64024 96302\n50633 56907\n6582 28341\n26649 50039\n20682 59687\n48666 97706\n31359 38081\n72058 96637\n9133 62987\n39743 79869\n20855 41837\n7372 62682\n10467 43937\n9034 98796\n88082 95721\n33721 38383\n69587 75745\n4201 39728\n11557 47028\n28490 76287\n4667 59963\n28225 85635\n48999 76766\n3083 36967\n71267 88774\n71994 83323\n856 3415\n86152 90445\n32244 49797\n1034 19296\n46607 55645\n27580 43590\n56635 96899\n19481 49635\n91652 96243\n11275 77926\n56479 71859\n38213 76215\n31875 56905\n26701 64205\n60956 85096\n17749 88793\n2547 95801\n12338 80946\n25392 33819\n19621 64812\n28948 45476\n50633 86115\n20351 77716\n6486 66219\n13508 46768\n1851 5364\n8618 42985\n38979 43848\n73783 85873\n41537 67924\n23306 49208\n17679 24451\n63069 95543\n10682 47910\n44413 84693\n866 78240\n5179 68648\n55976 95681\n9562 40730\n62619 71782\n61467 78448\n33827 74678\n19363 84911\n22488 78339\n57603 66122\n20738 38708\n26389 89284\n26519 87766\n6255 50059\n46115 97375\n5137 35530\n6975 28477\n6123 88380\n91177 97342\n28077 42670\n32708 89823\n19171 83020\n38226 82159\n16413 94038\n2532 45104\n10790 54941\n17521 87702\n44851 57272\n28787 91735\n64699 87095\n47910 59696\n31714 70363\n12389 81682\n66099 91152\n12759 62747\n70274 96470\n27945 29214\n70563 96266\n32205 57756\n9048 23790\n80440 86204\n73614 89606\n81319 89598\n42969 76456\n30305 64286\n37835 52304\n62932 72988\n4849 69246\n7756 63548\n4357 41044\n8937 36624\n44012 59819\n2577 96527\n49650 95523\n64304 95358\n24207 35422\n12490 77257\n479 93002\n31098 81994\n11031 25767\n51659 70398\n21854 43906\n85879 88513\n24089 70837\n18507 93752\n56405 59419\n17589 87841\n24113 57614\n23288 73918\n21524 51919\n55114 92396\n71611 73363\n76202 79819\n20357 65952\n32098 38091\n55880 62703\n39590 90915\n16072 99439\n31063 56313\n952 47206\n9846 36909\n16593 30732\n50070 74833\n54377 65321\n59104 84187\n44600 75347\n76255 98678\n45664 60293\n15106 51150\n5679 31823\n17852 96135\n37055 58727\n81085 95554\n78031 91747\n84999 91058\n72001 85841\n75310 84827\n80386 95177\n67215 77293\n27358 44770\n56999 71294\n13477 32325\n10085 94038\n27599 94444\n56124 70314\n10056 96258\n60827 87133\n32011 41981\n50096 95271\n60670 76391\n50808 63516\n13938 93881\n59010 68054\n23974 80122\n54602 76222\n47306 63131\n15741 16841\n63946 92496\n38280 84176\n41986 93392\n29813 96410\n5141 44662\n19698 74282\n2489 70817\n13793 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94226\n8602 26659\n33045 80182\n14149 40556\n17468 56432\n41684 60123\n58877 67504\n40429 64653\n16674 67634\n273 76336\n18938 35041\n35677 38288\n3329 65740\n67648 85409\n27210 33731\n8102 66781\n13778 22692\n6318 29130\n4520 90192\n4384 96750\n302 13553\n1309 46571\n82098 84058\n56571 92683\n8910 32572\n81469 85247\n65105 93259\n80361 94132\n6156 52378\n19760 94829\n3355 20979\n2919 71397\n21159 62054\n23885 93615\n35019 84988\n2573 4436\n24351 30067\n2569 62229\n30087 78361\n21018 95325\n26062 42146\n31278 77354\n15215 28696\n25649 48900\n13193 63929\n28929 96624\n38596 90038\n715 23059\n14955 40470\n43721 64350\n10545 35701\n24370 74318\n70213 72532\n36198 72647\n12663 68673\n15801 93721\n15870 87317\n11412 17210\n40657 52304\n21592 60539\n49997 50509\n40850 95556\n6107 73750\n22269 84038\n90852 95871\n90346 93938\n33056 56416\n22763 67655\n32968 89630\n26539 31085\n7009 40577\n61502 65303\n6311 80610\n56747 60597\n22619 78730\n31557 71916\n43745 98380\n35919 40274\n70989 87226\n22879 49284\n11175 89000\n68606 92376\n30504 69259\n58989 75897\n61349 94371\n58917 86935\n14686 47321\n3325 17374\n48290 63122\n83230 92577\n67794 99789\n17432 47085\n56202 69548\n33848 63501\n91922 92893\n2442 14972\n53520 87809\n31593 98467\n5591 8951\n55019 78405\n48926 81288\n43181 74427\n4437 62558\n24474 76507\n12853 21029\n20972 62100\n99489 99958\n90224 90226\n15129 73646\n63802 64844\n46465 71604\n24940 26256\n22393 68692\n14529 41899\n35579 68574\n32509 86773\n28056 98882\n62023 87023\n46927 48214\n14997 56056\n4042 52247\n37066 50304\n19289 40142\n25834 60283\n4090 76355\n3646 8204\n30379 47003\n38902 99938\n23381 65460\n27982 90594\n50230 62401\n28093 79666\n70690 75863\n603 46545\n57184 67211\n10243 65390\n30090 32906\n14479 18059\n1707 65418\n17181 87306\n31756 46459\n10245 51453\n7128 67329\n36304 40445\n15288 52246\n81924 82678\n31972 62559\n6700 96684\n7583 86745\n76898 92971\n82598 92523\n17568 74114\n11051 14611\n30596 72980\n74557 77633\n85832 86622\n26571 38963\n18013 35455\n5952 84919\n67179 68084\n16902 24042\n39164 55618\n27405 45532\n3374 31602\n42969 64391\n7085 76758\n25738 57437\n46381 94015\n826 99837\n27631 96750\n2500 52223\n57308 80974\n53492 95113\n81032 88070\n10740 18809\n34254 38626\n57145 59956\n64894 80809\n16367 30799\n8104 70385\n34729 89748\n15915 42162\n75040 89453\n12826 84564\n12691 36626\n20563 74395\n8797 18634\n52362 86465\n43819 83417\n37718 51755\n22442 95297\n93098 99532\n18463 55850\n1873 76691\n10743 75027\n21838 85135\n4099 55711\n22151 73089\n57729 80358\n50183 95840\n4845 42683\n56802 90490\n18649 84600\n6865 79651\n14342 95662\n29807 67522\n62352 92443\n12400 82296\n49728 86020\n51892 68930\n6309 18844\n50491 87300\n43823 61031\n22618 59619\n24108 46541\n24782 30194\n51141 84682\n57546 73483\n67370 76975\n12005 73344\n3698 19249\n56943 73158\n41139 48327\n73393 89561\n26820 80392\n21260 82284\n6101 96494\n9375 73537\n18876 85082\n37174 58045\n22542 45662\n24390 47314\n69445 76163\n29895 40884\n59261 79063\n25071 42920\n2956 39474\n21180 47809\n55780 72325\n69050 97770\n29801 94501\n7421 24909\n3112 14854\n37923 44527\n41083 88598\n9188 46994\n55252 73815\n38486 79970\n10753 96946\n40778 70394\n84789 94558\n39906 59824\n61432 67762\n16000 38029\n63262 69287\n19931 28416\n52295 62311\n19074 24192\n23115 26081\n65297 76403\n4042 62336\n1009 58008\n36597 89041\n8875 10295\n59108 94050\n60390 73257\n44674 97269\n18869 41057\n97225 98410\n18385 36293\n756 47933\n50196 58219\n33581 95844\n20437 70551\n39873 69333\n60982 88562\n5976 95004\n10249 46644\n43705 64033\n9989 57431\n11576 90452\n17800 32757\n44604 53794\n63266 73050\n54138 56506\n1995 32348\n46615 57885\n68633 90324\n39729 73034\n26805 92614\n18271 80462\n20969 47488\n37973 49048\n16127 60122\n3792 10106\n50309 52521\n11475 72224\n57642 73016\n20271 21836\n49578 67611\n32286 86543\n64889 70509\n43295 61594\n23125 69836\n69713 82148\n28092 50926\n79098 86112\n79933 88720\n12312 39236\n23185 80999\n19616 73428\n59001 99606\n18111 74618\n48325 78956\n39346 55747\n14692 34945\n15273 53449\n64600 72758\n38800 88587\n75911 98798\n29555 83427\n18324 51985\n32438 67960\n30496 36866\n49662 62586\n7895 13675\n22523 57441\n48508 96814\n55134 63936\n24267 63899\n86493 93086\n30966 81267\n50246 64169\n61373 61403\n33896 36219\n76218 98987\n19149 91767\n38255 48068\n33267 39003\n23786 50285\n86637 90322\n36625 59581\n31180 81653\n43328 46201\n87990 96211\n84907 98003\n18494 35236\n32250 76145\n16351 95009\n26391 27691\n8944 12496\n44672 69770\n1351 22717\n48232 58113\n1183 76904\n60309 71858\n49861 76902\n17905 87228\n14138 92956\n82197 99677\n42873 61741\n50256 85257\n4592 98993\n68887 92754\n48035 77705\n567 17284\n55836 57716\n6328 79550\n18917 98521\n42196 97713\n4173 35841\n68901 91687\n29927 71624\n11724 18879\n23957 37723\n",
        "output": "350\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 96,
        "task_id": 541,
        "test_case_id": 29,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n18540 91050\n28511 75755\n45390 76788\n33100 52586\n49 30368\n50980 65212\n58470 71136\n33918 81419\n11885 58795\n1954 33329\n27884 38422\n25220 32602\n50306 58185\n48746 55540\n14254 84110\n43621 64254\n15287 36207\n35714 58579\n42193 85357\n10853 96362\n52929 95805\n34555 44579\n887 71846\n16161 57382\n25274 35281\n12801 24141\n45340 96431\n68805 69112\n5659 67096\n16301 59168\n51577 62968\n78325 94012\n68026 71946\n28567 62864\n8782 27843\n20518 31086\n14614 55721\n737 6095\n25002 65538\n74929 90133\n5114 47771\n4532 79270\n6847 67747\n49080 77972\n46126 67509\n62603 70482\n30032 52777\n32101 36981\n10624 86761\n20183 78625\n16422 44253\n31779 56018\n11259 79573\n22487 40860\n7966 93918\n46712 98306\n10278 80923\n806 86844\n35333 72165\n52676 85912\n22306 38718\n17443 83598\n73681 80098\n24647 54689\n53908 63938\n10675 12015\n22664 71646\n18993 58967\n35083 93247\n59770 71897\n21040 47447\n36605 99452\n63869 86759\n77609 94596\n7226 31823\n17814 33068\n16165 93253\n11921 14310\n8912 72426\n2761 34328\n21851 78895\n28401 35548\n73289 89150\n20335 86931\n6711 82038\n36345 90677\n55525 60813\n25797 72759\n26334 84233\n35331 90547\n46742 89654\n19543 79243\n11797 48727\n23122 81214\n10540 95432\n69671 76407\n48291 56496\n72763 90476\n3755 68201\n9709 65335\n79820 84064\n48640 84635\n32649 89149\n74234 85702\n43479 72766\n34669 88590\n36012 40062\n27729 30117\n21458 70806\n32708 51225\n7962 69415\n75765 97946\n16040 44171\n12850 31281\n26908 85138\n27672 50653\n23442 25771\n71306 82402\n10625 62432\n3653 87374\n2389 31917\n31822 88328\n24166 66389\n37569 72397\n65115 81101\n12552 77714\n42258 65147\n24841 27697\n12616 29364\n29318 43505\n27289 63313\n63124 78968\n7330 59120\n48494 63895\n16267 71007\n32398 80644\n70786 90712\n51479 55485\n60733 66293\n9873 43986\n67062 89203\n23895 37188\n12903 20394\n24742 69677\n56216 63078\n51978 62639\n27916 60077\n10240 63162\n5474 15091\n50125 54506\n27387 84080\n56722 89416\n78669 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31764\n39602 98064\n34844 58657\n48131 58845\n34491 98456\n8682 92298\n25037 40581\n28184 94119\n1914 26202\n34138 52930\n42163 70611\n69580 77180\n7304 96281\n27083 63830\n74923 81902\n9247 25534\n32197 83163\n35026 77132\n85325 90399\n37283 68772\n38224 66901\n1633 68679\n2857 63684\n8687 62699\n5945 7320\n47186 93155\n83753 96939\n44144 89617\n28899 68419\n61280 97525\n35205 56248\n50373 66826\n25075 32086\n70654 97533\n73507 77146\n11345 33624\n40247 56536\n43397 72986\n3943 90206\n18690 52682\n10374 11310\n17588 89706\n87691 97680\n42961 90610\n11655 76003\n971 24219\n6804 66433\n26966 70471\n33283 81397\n41662 91265\n89440 92366\n15872 30339\n39643 93555\n65170 97517\n562 38989\n96287 99352\n53193 70213\n83924 93811\n24636 44123\n657 8965\n11370 90553\n34907 70775\n3548 89422\n27811 66718\n6527 84195\n9843 63774\n1582 76992\n3161 99042\n27225 48358\n45544 89775\n27814 73426\n24674 40159\n19674 81018\n39779 95756\n25628 61770\n24228 62226\n10888 23830\n51063 55102\n28583 95272\n16901 26725\n4120 16107\n18112 44384\n21092 64473\n27397 96808\n13477 57539\n39030 89436\n72877 77213\n28789 84072\n67876 75312\n11955 25899\n2775 80182\n31660 74105\n57328 84739\n68202 93886\n53366 96857\n52025 92618\n44669 56779\n24372 42468\n66390 92020\n77846 95076\n37948 64035\n8557 85742\n29995 81274\n51850 68555\n56507 88068\n77413 94711\n11760 24244\n31448 99107\n32954 64972\n66835 83509\n3323 98795\n20336 34120\n49577 67273\n44774 95202\n2789 80120\n40245 97965\n6664 96651\n76896 99803\n20868 60461\n51519 67475\n72772 77700\n9608 97201\n11623 73812\n29254 98768\n13011 36724\n11381 68771\n23366 77867\n7014 43760\n12513 28487\n20802 60375\n31239 70772\n3689 91629\n8416 92867\n61346 81463\n37158 65505\n48108 59370\n61762 69638\n46309 96530\n89853 97325\n18044 74026\n16435 82258\n42659 48461\n48517 62506\n11611 35765\n40632 41179\n81198 88036\n54164 59686\n897 54920\n23672 66110\n60113 73253\n18905 76429\n30269 55022\n52978 65138\n4788 9048\n34457 72798\n43733 50994\n51791 64595\n58379 74899\n64262 68472\n11729 12627\n17359 20387\n58279 85639\n5951 41904\n17873 94060\n2920 21537\n70542 92786\n24375 80930\n22018 55077\n47737 94167\n4131 4555\n12331 71024\n14272 83808\n76892 97919\n37929 79265\n6845 42891\n39414 82899\n2374 19303\n4210 26717\n34606 68982\n27034 35156\n5687 51458\n69278 69314\n23289 91557\n88818 96585\n171 69480\n90488 92471\n36690 67169\n76561 78006\n10888 31839\n19503 73154\n25864 85955\n6273 45840\n13635 93599\n35167 70098\n18226 67914\n91278 94820\n46835 66307\n11031 78585\n18726 93551\n9040 59659\n31538 39119\n8261 43489\n21705 91131\n32507 67182\n17540 87464\n70685 99633\n51040 60395\n30961 46010\n29845 85647\n7112 85320\n51824 66519\n12523 13811\n19474 93782\n31423 65543\n14173 21860\n48146 51271\n8219 15856\n57170 57446\n81334 89692\n2459 18270\n34239 73063\n1534 71661\n69209 72581\n70545 77363\n18738 61605\n80853 99867\n47751 69371\n44070 85913\n33019 98163\n15565 25935\n77156 83011\n56543 70688\n293 44989\n40487 70748\n5521 81854\n33175 98014\n42579 69074\n16850 84210\n6645 98295\n61491 69893\n17884 86228\n10705 27613\n7905 23482\n3367 65180\n24978 86555\n38420 81829\n29081 95444\n9988 28141\n67513 71061\n31668 71405\n71640 91765\n5569 54463\n47628 52919\n36389 53823\n3187 17264\n45265 94008\n40927 48637\n60405 89700\n16741 28114\n54924 61599\n40400 62734\n21336 41658\n73631 90208\n26754 27641\n692 76705\n12011 78988\n6528 68036\n57484 81135\n70551 97406\n42255 71656\n4312 7445\n12296 73959\n22168 56734\n53387 98293\n35893 97981\n12029 19952\n35316 77218\n43180 74827\n45194 57394\n10655 77454\n646 52090\n20552 52088\n3538 70565\n27812 97962\n59854 64695\n14338 27069\n27722 73203\n39467 59056\n44519 61994\n51767 64204\n47524 48019\n48992 56940\n24690 57364\n6377 81944\n49301 89515\n23428 53270\n60353 78995\n64145 82258\n10279 11717\n4629 54631\n8915 67800\n40391 63565\n15941 88850\n54865 72229\n37192 85287\n42525 86363\n44696 72803\n47529 59556\n11030 58950\n39129 85752\n897 99546\n46773 47695\n73874 95230\n69110 74512\n1410 37237\n8267 68417\n28544 79991\n26435 34469\n31724 53153\n47908 68110\n7679 27840\n17655 89852\n51844 87804\n53003 73630\n45446 81906\n55822 72418\n67530 67793\n86882 93984\n26991 99928\n53231 75247\n17982 39448\n41234 79323\n19692 99922\n42222 46293\n19176 90694\n13299 39118\n53171 90175\n24353 78963\n72492 90848\n57465 79380\n53019 70345\n1197 85740\n53162 73984\n1754 79669\n52987 57660\n6257 9563\n9630 38734\n32250 53630\n60115 68712\n79879 82615\n22259 90795\n85104 87500\n19931 58354\n19425 83774\n50264 78627\n53658 95301\n17390 44498\n29420 96759\n56422 77812\n84242 95832\n31135 61919\n22215 86819\n39426 78775\n42201 62861\n77453 99597\n6599 18658\n62087 82418\n36345 85797\n918 47068\n40375 93426\n57038 78230\n32278 58611\n55956 75458\n17456 32341\n43939 98083\n28687 86194\n12311 22958\n56281 57832\n17780 97074\n69720 73813\n26104 65699\n16928 52878\n44985 74411\n30232 84075\n244 3265\n41144 95481\n11868 19967\n5780 44990\n67957 88064\n34290 75809\n9940 93866\n17140 32531\n169 77840\n41946 55280\n24096 41494\n27884 64636\n5538 83086\n21639 88020\n22775 35932\n48605 97140\n16874 22966\n28602 73608\n63134 70052\n29221 91483\n80145 93412\n41372 83666\n9786 74410\n49054 66569\n44448 77101\n36806 62150\n44719 99806\n72792 82347\n8879 59139\n6708 70488\n20756 46982\n14811 49625\n50971 95164\n79109 92078\n66426 76726\n19005 26400\n32152 45820\n46327 53693\n56767 95437\n19916 20813\n50343 97356\n48250 55431\n14266 48590\n71652 78096\n51481 64543\n230 7942\n23360 53995\n58219 58703\n51802 66719\n20402 80381\n18534 78931\n72898 89977\n41438 68588\n74838 92051\n2211 31968\n55738 57178\n35000 93080\n36336 54115\n17213 44555\n46703 47187\n43829 90023\n16844 23057\n80041 95465\n44771 71027\n20684 93844\n11968 64228\n6152 19195\n4780 9699\n281 804\n31890 45946\n415 94047\n267 77606\n59328 67942\n85117 87668\n13673 72495\n11976 35864\n3588 71135\n38911 48669\n46004 63791\n4713 79985\n55170 57099\n4143 27787\n59234 96851\n53305 90212\n1172 90490\n35216 37451\n15540 29835\n38041 47113\n40056 85147\n27336 29060\n45148 99920\n81952 95587\n1336 66442\n68171 91831\n974 37529\n23880 97267\n28214 28869\n10347 42889\n72317 76057\n39354 78742\n70 52915\n75003 82618\n86796 99640\n82588 83866\n3403 30629\n63711 94221\n4752 83164\n62644 72184\n10161 32404\n58355 87138\n19249 29654\n7082 94474\n14358 63545\n26614 34262\n50332 96735\n3197 43611\n19412 27043\n27668 34524\n53333 66102\n64037 69392\n9559 50784\n4119 99123\n13055 98416\n38911 39743\n22691 48664\n37760 89897\n68784 81665\n28025 97292\n29143 84744\n56772 81702\n25822 47904\n11109 51963\n8782 81554\n60131 76426\n13134 42895\n6365 17919\n68183 99337\n4244 83649\n2187 72476\n21637 36752\n64036 86655\n9992 42220\n54656 92489\n913 53726\n20315 84456\n61029 83536\n18569 69183\n50467 51693\n29043 33388\n26670 35553\n47637 88280\n54092 95078\n19571 95601\n3813 86628\n14867 50820\n29565 90520\n64036 65824\n29697 71686\n30482 57235\n34268 54602\n5735 35514\n11900 64372\n11910 41859\n57367 80609\n10763 17204\n83152 96605\n44307 48699\n20322 96076\n51495 54756\n51176 69267\n52072 76724\n51918 95453\n43392 60980\n5408 64163\n10315 49924\n27089 56458\n15447 42999\n29864 83814\n31158 34336\n58909 75717\n7851 89481\n3626 19763\n47480 90641\n19332 58272\n1877 21556\n54953 59149\n26360 38521\n37712 92758\n76338 78169\n7694 12200\n30030 81209\n88687 95047\n31962 33159\n11706 34405\n4384 31850\n76292 96657\n10046 62143\n60704 96453\n70967 96770\n48607 61429\n46885 98636\n2651 9173\n8279 56015\n10817 91090\n28172 55577\n",
        "output": "358\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 97,
        "task_id": 541,
        "test_case_id": 30,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n3666 30431\n37315 91068\n26597 46180\n47901 84695\n9129 93975\n30620 45498\n39459 86821\n34287 68347\n81778 83846\n52741 60798\n75320 78526\n15421 45888\n55551 94186\n36567 66022\n53592 87902\n899 33497\n11422 42018\n18473 76973\n32172 68190\n21157 77936\n32627 72232\n94211 97742\n14009 43547\n8498 32363\n47688 81788\n59379 62732\n25130 99240\n34342 58041\n29259 94138\n36056 83052\n83296 88601\n23275 59034\n6430 73415\n36629 83363\n37572 78857\n30704 67023\n81498 92672\n73323 78437\n15815 63770\n39699 83154\n39224 99418\n46355 91732\n63296 74669\n36715 89724\n47873 60483\n15821 60840\n7573 57293\n30780 98405\n16634 36691\n16860 30159\n42230 62612\n14831 46875\n16069 17193\n36776 83251\n76246 81335\n21690 94127\n70419 82300\n21220 98902\n5736 55580\n75408 98511\n42340 54823\n8694 70058\n27311 52351\n44895 48523\n79525 87794\n6121 65011\n16748 50110\n49433 68689\n34321 49436\n51360 95985\n38271 64819\n5594 43260\n56393 64349\n1076 43136\n8378 81470\n21653 38799\n4817 83735\n91173 99052\n46962 48655\n67212 77666\n19401 78402\n17834 85846\n7377 49018\n6724 7432\n9237 72000\n13320 83326\n58540 66988\n18714 39686\n220 76214\n811 37473\n61139 78398\n25166 38875\n20286 66101\n31676 34819\n21096 23528\n33823 65519\n33230 44343\n88411 93637\n11219 59588\n2332 5824\n471 94341\n58879 79349\n34218 60924\n66737 94709\n32379 45732\n24135 29334\n16296 60332\n3729 78595\n56047 93335\n19224 19867\n8479 85389\n67841 90701\n45026 49862\n36137 61346\n38279 70514\n41265 47274\n65194 74845\n8178 13626\n38901 81453\n30793 86529\n25521 95839\n43881 53231\n18592 74880\n17100 35298\n1295 34833\n18512 19006\n3025 93220\n16325 84351\n80928 86174\n22596 53962\n70389 87451\n3474 86333\n34674 52623\n52834 63330\n17830 96884\n2655 68814\n32267 43635\n675 52136\n75352 80053\n75166 95182\n21965 58820\n14377 77801\n37907 96595\n8063 17984\n34618 51592\n63890 71722\n56064 68857\n86684 95623\n4593 48428\n31560 33192\n71944 86904\n50699 92238\n59554 80111\n20558 70206\n14422 29555\n21001 80770\n1355 1767\n68561 88841\n27350 92530\n1008 48690\n57258 89602\n51511 92488\n8777 12043\n49267 73323\n30902 79451\n18171 77391\n9094 28195\n70668 90481\n15561 58185\n46500 72325\n4008 21109\n18496 77626\n1458 80150\n12501 59105\n7895 71879\n38210 96726\n72244 88013\n85673 89271\n40960 72556\n11542 44786\n20573 43506\n35824 86777\n67871 98784\n5568 44288\n20437 81167\n16075 73748\n55101 92189\n75553 87372\n14335 28122\n9940 93582\n8508 47340\n34025 70482\n61019 97539\n15946 48793\n33415 97754\n50301 90130\n80857 83883\n20299 78781\n5510 8284\n63799 98985\n14794 99149\n55463 58888\n6624 29527\n44647 54281\n45733 93298\n9182 93927\n52263 80217\n4263 47018\n8431 80138\n23683 63449\n36201 85369\n62394 82620\n10688 28328\n866 84984\n8279 31490\n6322 78473\n8750 72012\n5945 79167\n45761 75101\n79759 91001\n22504 25606\n20259 84010\n36992 58264\n2584 57826\n57325 80179\n81667 88300\n30166 72769\n39725 44424\n34328 55962\n52022 60205\n77139 90287\n35418 91608\n41760 99078\n21675 92810\n43786 73379\n34576 98192\n55438 75179\n51144 70818\n11494 47525\n54819 92857\n67581 85180\n42114 65060\n13470 58737\n19114 49962\n75137 91492\n80626 91679\n10782 40936\n9069 43082\n12729 40254\n45574 57370\n29440 48421\n41149 49110\n2991 33947\n58056 68223\n28529 48093\n10313 10476\n59507 95060\n2994 54321\n82264 89919\n246 82761\n59776 88917\n14070 21663\n27976 44226\n1155 69200\n19511 54228\n40300 42727\n10990 76378\n30381 84209\n12059 38892\n7959 20576\n85755 87564\n45811 93608\n18031 44146\n13185 76656\n13084 17250\n33434 55665\n16969 63061\n39377 84474\n28731 51030\n8489 56368\n1127 55030\n20446 58227\n23790 24024\n37837 67202\n50593 81618\n9524 88143\n32663 71365\n60889 91461\n47969 54810\n21282 42160\n3120 6624\n44094 56174\n22263 90063\n6432 85797\n51175 77209\n749 40079\n45214 76490\n11294 66125\n15730 97492\n30537 78950\n71155 74129\n42550 76821\n71355 93096\n20950 35503\n66004 76230\n5263 47765\n619 32992\n47785 72759\n36594 94915\n2979 39130\n8717 23759\n7975 44429\n6308 11418\n26715 71197\n12105 40565\n10265 50632\n15629 23373\n4061 64015\n1881 50146\n28281 72744\n20644 77606\n47314 58979\n17415 38339\n14443 55235\n43942 83701\n9019 41908\n48492 83066\n34817 69848\n46851 74013\n12634 29068\n67397 99254\n57598 80066\n14663 53508\n63819 69695\n21657 69979\n49929 72092\n48003 93650\n36850 50276\n35896 72141\n7549 83859\n23065 50712\n22547 89986\n82949 99702\n27094 54365\n78783 96758\n28369 57241\n68956 90040\n66369 84548\n36475 84590\n27272 92374\n25228 50800\n12798 43921\n357 88118\n82181 83374\n20191 36649\n56298 92615\n10837 85092\n54942 92881\n36593 53672\n24117 57880\n33324 48806\n72329 73061\n5328 27779\n27043 99136\n74794 85437\n2267 44140\n7087 51697\n64438 92352\n7785 97515\n6545 79006\n2098 47408\n26618 55491\n27060 88342\n907 77254\n28330 96467\n30553 72381\n25506 90307\n96372 98954\n207 85895\n2501 21804\n38696 91361\n50321 95181\n51627 60364\n3689 95067\n39968 71705\n3087 51357\n13565 52881\n14638 66228\n28871 94708\n7780 28439\n16606 95582\n57955 84403\n10002 15889\n27214 96664\n5542 32566\n2555 85824\n86786 87525\n63298 91000\n30214 68826\n34894 77082\n12260 75108\n40951 99492\n41534 98731\n45270 81821\n11874 43347\n62377 65916\n6020 35212\n50067 90050\n2027 95983\n86116 87602\n41552 93041\n41103 64982\n35094 79473\n63411 66909\n44509 84302\n39937 91170\n70190 72839\n1727 79317\n43317 73211\n29752 76593\n20696 96415\n21754 58770\n33185 53708\n72921 78195\n21243 54893\n2874 8596\n6850 32252\n89515 98961\n42321 85852\n45474 91814\n69643 76154\n77120 87490\n11143 24471\n49525 88597\n40559 57858\n28338 34965\n4478 16939\n26454 48948\n25993 69213\n20146 84239\n14182 54419\n2952 86445\n4695 98966\n29488 70882\n43598 92310\n74824 75973\n35953 66384\n47370 56600\n10592 13292\n35679 72950\n30456 66289\n13382 42535\n58397 84497\n33172 93896\n38467 83660\n21225 35082\n64701 76471\n66371 68282\n10360 75768\n66353 85630\n22111 22642\n35425 63727\n23485 85378\n63182 63295\n5918 20250\n20397 27164\n22648 50313\n3959 39305\n40302 96625\n76906 90094\n12416 83728\n1906 66398\n6328 78167\n8864 28291\n12328 97344\n4517 85688\n20852 22254\n3677 98275\n44871 66603\n32165 60347\n8994 74566\n21528 34745\n73979 96618\n74415 76612\n36712 69181\n929 7491\n57270 80531\n7044 25065\n38510 70566\n8079 78382\n38790 74006\n37636 43249\n43002 55545\n5453 37481\n24973 44650\n42297 77933\n37640 66556\n87005 98114\n31068 51405\n2888 10039\n14260 51510\n23934 27084\n27601 88240\n27755 29920\n11019 89649\n157 85671\n26632 98909\n3219 29600\n12702 43170\n21454 28647\n9476 92160\n44937 85520\n27063 31893\n3479 25105\n32819 69327\n11247 49319\n40227 67789\n21202 72535\n38437 48567\n158 42205\n91986 93936\n34808 43250\n19894 75591\n19891 48654\n9875 66814\n61904 74296\n23190 89290\n52224 56004\n12925 26802\n59636 69861\n19634 31079\n37732 80916\n46407 95389\n49272 55171\n5827 7679\n65145 96051\n32444 90277\n62973 81179\n75139 83654\n9844 24717\n29771 89631\n41377 81008\n18980 70539\n26398 94003\n34916 43152\n21359 62958\n9744 29435\n39659 86563\n54225 99325\n10627 80290\n6999 36418\n27613 95129\n57457 84334\n57341 72777\n15856 26910\n40829 56800\n31284 85005\n77381 91607\n5815 28447\n45381 99577\n4496 41317\n25735 32146\n30033 47829\n67341 73567\n8652 71199\n2505 4422\n5259 71499\n67317 96399\n5075 31939\n18949 46546\n9055 34347\n25974 70001\n22931 61718\n21108 41994\n20460 81274\n16131 39355\n22739 76197\n10443 42154\n52406 83586\n17915 39072\n37474 84174\n65174 68931\n13722 84014\n60227 74217\n81705 82868\n50011 98421\n245 81477\n45143 64529\n44325 64498\n33703 56604\n20312 32378\n50784 62014\n2855 74708\n38456 97167\n57332 59745\n5291 61446\n71182 96892\n48118 98273\n4261 81129\n33349 50702\n38688 85725\n3768 78095\n78306 91609\n32462 97787\n48414 48458\n9733 17427\n33996 63220\n12088 53042\n80621 84979\n33593 80028\n12196 50300\n14787 20534\n21311 88003\n47848 74356\n20873 71351\n41271 61055\n40987 43119\n9876 17463\n32779 64813\n9940 92553\n21158 48293\n16943 93981\n20301 95435\n2888 35064\n51626 88379\n17633 51370\n35003 48443\n55051 94525\n58321 96026\n7895 41594\n20288 94296\n29265 96187\n87451 91950\n820 87194\n76338 79423\n5611 28587\n9177 89769\n40522 89919\n900 54890\n1181 57280\n52818 88291\n15421 69103\n58164 96279\n37141 89982\n29143 72468\n40631 57716\n36141 64371\n12930 27547\n50012 70119\n83582 86402\n81263 87391\n46669 70280\n43460 45086\n37926 51422\n63739 94935\n60753 82968\n47376 83013\n24404 63584\n3933 41371\n41996 96292\n40631 76892\n50092 64829\n59577 78343\n17882 41827\n2262 89164\n53856 80693\n44000 82048\n3339 44908\n62088 95589\n42321 87602\n5895 42679\n60381 82205\n20377 58313\n22463 77345\n70129 83016\n7564 84069\n36902 88657\n66482 86828\n37338 41604\n30761 60357\n21010 35383\n9002 69318\n89087 96257\n86136 87065\n33401 49483\n9744 40079\n8209 8592\n15669 86081\n58784 63954\n28886 53344\n56247 72288\n46450 82333\n45203 65046\n40302 73252\n17438 28970\n10701 63454\n74875 89423\n10376 74105\n42068 69664\n44018 66368\n14744 51187\n25362 35008\n58473 77412\n9584 14203\n68327 86018\n26981 83502\n62569 63004\n10204 80840\n26418 91881\n77790 80960\n61955 70964\n16747 79046\n59391 97038\n59131 87282\n50604 58338\n40150 42514\n40613 53228\n13434 27753\n39292 50191\n22503 36348\n75001 76102\n19908 46774\n73545 79995\n6933 61219\n40285 81069\n11234 28555\n29910 62740\n25735 49730\n41969 90410\n37395 76670\n89161 92839\n6255 33498\n1795 62191\n11505 85517\n28159 69784\n5406 53190\n69869 89743\n74000 96834\n2538 6054\n5799 12318\n19829 51427\n64985 80895\n10725 26905\n8252 31518\n37191 73620\n24922 51670\n19425 98979\n60921 72770\n32957 82395\n94246 95074\n2084 56553\n18453 79632\n26324 47301\n17581 61866\n30939 91781\n80050 86376\n39695 54430\n7940 30046\n53069 71724\n30108 30665\n20849 34670\n43285 79416\n29724 64477\n27209 36612\n76145 93497\n52457 56566\n98 50887\n35547 64835\n46766 67197\n5931 57726\n12573 50407\n17331 79531\n22496 88598\n4238 30404\n387 99073\n24821 56943\n12877 95481\n1864 84919\n79510 80155\n34175 52345\n91901 92842\n30359 36013\n43926 76284\n102 36669\n40273 73494\n86766 92653\n6590 65840\n37213 42404\n72943 93076\n36939 68282\n7364 67273\n82077 89038\n21220 67158\n10569 38816\n36940 65939\n69748 92940\n60488 65785\n24360 63153\n22579 67983\n1598 75375\n70452 75257\n14084 28505\n67805 84227\n38594 92209\n28133 39866\n39449 79016\n79764 95480\n971 18264\n64835 73078\n16722 73187\n93424 98735\n81363 87798\n6503 35841\n22097 60772\n7579 66935\n50810 97959\n16574 66081\n16030 88756\n15278 39216\n40336 75681\n20181 76576\n40803 66365\n54955 67177\n2771 12561\n32982 37269\n81976 84863\n48230 65936\n32870 49179\n11331 99016\n72545 83113\n41494 44870\n19041 40870\n18763 79997\n13196 57384\n43199 78407\n50803 96927\n2286 97934\n39947 81457\n20550 81026\n39520 70194\n2792 78373\n17463 78728\n44092 83715\n16178 96597\n79852 88267\n7083 81870\n18821 75904\n87708 88174\n47104 61502\n18162 72056\n66780 83097\n42708 44311\n40668 42315\n52961 91144\n21229 95264\n70253 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95631\n43993 83557\n9246 22218\n38369 88666\n76564 87291\n28645 44496\n17958 25629\n24061 85766\n38425 48273\n19685 26588\n31341 58851\n220 8276\n59251 88840\n46409 82919\n27793 56858\n38199 74418\n64072 72774\n3031 69665\n7004 69700\n62895 87084\n23967 51810\n25555 26493\n9706 84957\n54287 54488\n51602 88932\n59226 59819\n63915 78610\n50234 61805\n75712 93876\n41839 61529\n59951 79139\n3293 56825\n45039 51012\n66844 80800\n23482 64276\n68315 93837\n6985 20689\n23510 86188\n9768 47281\n22666 41340\n19481 80975\n34628 97969\n28257 52605\n76583 84412\n77389 79626\n19933 23686\n28132 47947\n11643 56904\n15389 27075\n60304 62991\n33721 79936\n844 88528\n17957 23296\n69765 79918\n16587 35276\n67622 82982\n76933 98880\n74832 82622\n47826 89804\n31363 78508\n72528 80261\n37529 97272\n59774 60468\n70561 78976\n56469 62851\n55586 70523\n30111 87304\n11091 89628\n16772 49651\n11970 91870\n33002 63750\n34174 49892\n43578 75538\n22078 64079\n62379 81985\n45139 76027\n14120 67416\n17935 80107\n44766 66063\n4649 89691\n29620 34911\n28358 89472\n8120 63962\n27927 34293\n14105 35396\n20234 58991\n55490 76314\n66078 94110\n4350 9179\n42094 90905\n32586 72056\n5788 75942\n12292 54884\n48298 50740\n74855 75514\n1960 34307\n38065 44018\n24169 80412\n4049 53719\n60718 87042\n59067 82567\n10687 16311\n49957 99714\n4410 49605\n11740 63732\n4850 17157\n89759 98843\n43269 67840\n38082 92117\n3282 92390\n28926 31925\n52986 55736\n24212 27580\n58310 61567\n22477 22584\n21448 30978\n13550 19478\n4215 29633\n47190 95539\n21283 47934\n3483 15088\n9183 52096\n63375 83286\n10217 19718\n62176 99817\n63903 92339\n7393 91546\n2618 87571\n5582 86054\n14673 79543\n73283 84016\n3810 98878\n1630 99168\n44270 59264\n86431 89981\n39538 53620\n19299 86555\n32794 45447\n435 25424\n68884 86374\n73125 73163\n25871 33153\n23420 94673\n13614 32007\n71164 96975\n23763 92724\n49187 58663\n42823 57838\n62451 63066\n13679 48817\n28042 62202\n20463 62879\n26026 80254\n44795 51307\n60748 73744\n8178 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89158\n23638 96180\n15953 88919\n17401 40626\n3912 7837\n19144 81913\n24753 53867\n83156 88136\n56790 77917\n28774 59622\n52042 61329\n8041 97549\n54404 78613\n1019 24369\n35606 39047\n33930 39503\n43612 57832\n40320 78565\n29506 54784\n24199 32699\n18446 38224\n13990 90487\n19498 93077\n44891 51671\n19348 72070\n75246 98567\n62978 68488\n29512 60530\n7620 15414\n34248 98638\n80167 96100\n61913 97399\n24046 26922\n57305 64657\n61418 83221\n68828 93507\n61176 92186\n45670 67545\n1833 4126\n31962 36207\n38364 46351\n77102 83189\n40933 69034\n23766 35823\n10140 79866\n11783 74629\n26597 57434\n40073 42633\n41444 91914\n25627 25952\n12271 28871\n35447 82719\n18386 27500\n11158 98738\n30011 40002\n44437 71405\n35118 94754\n37634 71968\n27000 66105\n29379 54902\n10537 89090\n18029 65116\n62264 84684\n21252 44656\n40408 82081\n49977 86947\n11391 77524\n2652 49201\n8163 20108\n21103 53016\n59457 66073\n35697 55724\n17032 89896\n33142 37980\n24169 94462\n13435 33026\n69016 79115\n26373 27367\n54863 93166\n12807 27451\n58780 60010\n65304 79479\n18431 94678\n41914 73923\n30908 44239\n22426 61786\n28790 94332\n7890 93503\n11533 77194\n29735 43891\n40933 60690\n2536 5026\n22952 28417\n61526 62236\n427 50018\n41885 87316\n71199 98873\n16840 68646\n14596 80455\n40783 80178\n32554 51523\n32413 95417\n34831 36740\n18715 50741\n29743 96519\n52919 87919\n28430 63341\n62925 71325\n27820 85336\n7121 18636\n45337 94860\n12820 80843\n10886 43627\n28701 36998\n75797 96944\n57483 69568\n757 66191\n65596 91539\n30787 42166\n32141 70064\n9353 79647\n64505 89204\n32505 82048\n57524 96090\n442 44143\n51467 57915\n2106 39046\n24572 31119\n48234 54284\n12432 55506\n37484 86559\n31185 87896\n50937 88653\n81884 99320\n87785 92204\n69742 99479\n50844 71207\n12798 70588\n12157 40205\n99330 99883\n22791 54112\n37651 62167\n5946 28708\n26148 68183\n5991 43905\n27587 56356\n24657 98041\n70617 78656\n16003 17420\n18134 77778\n30076 75083\n54293 94589\n38747 40801\n46541 56063\n25738 39294\n31461 79782\n3021 90102\n67990 98567\n21632 45259\n42886 96018\n54610 94129\n47081 85984\n8890 54260\n56978 68917\n12879 34344\n16379 69261\n50160 65571\n26870 53170\n82695 98369\n15984 22880\n6340 84460\n49448 84581\n17471 86311\n40844 99967\n10718 74714\n17036 74853\n43991 67741\n51425 54088\n11615 96229\n64907 84581\n60935 76121\n14922 60514\n51846 54163\n35802 80085\n15119 19122\n9117 38963\n36190 42732\n80067 94367\n15088 80155\n8406 51293\n8238 91703\n30649 70863\n30122 60713\n69675 81330\n46676 57198\n81381 82088\n11495 42207\n12246 63705\n4668 14292\n2017 51772\n7130 77718\n42095 46669\n8154 51876\n59399 91234\n71099 90832\n74588 94471\n23463 28879\n15461 88416\n20349 93156\n3932 14636\n2072 16373\n26927 91611\n49414 88320\n32100 94306\n52747 93551\n13768 33828\n66772 72899\n53943 77810\n33493 54960\n37238 96855\n32406 36091\n3304 10439\n3229 18945\n43748 66775\n24249 95205\n8218 76321\n90832 92091\n7749 80031\n16400 63101\n34266 72479\n32269 43957\n47268 67765\n40336 64974\n35293 51558\n59411 94124\n54602 79770\n10477 66839\n23500 86914\n45200 76451\n36644 97720\n36603 86315\n12535 49373\n51395 93424\n13643 29953\n35488 69919\n12740 42012\n36308 81873\n30 17724\n35052 76804\n39529 63138\n19636 46042\n15494 57714\n60637 99723\n11845 14372\n32580 38570\n50633 92904\n8071 66172\n47625 99277\n24138 41737\n62040 79101\n15534 70877\n54272 67367\n46131 84223\n",
        "output": "343\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 98,
        "task_id": 541,
        "test_case_id": 31,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n39039 45713\n36321 66646\n43196 83009\n18951 92859\n9554 76692\n94505 99582\n12896 83426\n77749 79862\n21002 30445\n10287 28848\n5403 65586\n13948 48815\n36517 41908\n13205 30101\n40977 52189\n52306 60002\n5134 81576\n40974 72098\n10679 20083\n71188 85550\n90106 98917\n63718 96777\n36732 61569\n32192 36314\n85995 95013\n55212 63764\n33342 75768\n8523 92439\n12536 59110\n30551 99454\n77210 95154\n26390 34654\n10621 87663\n39410 53853\n25859 98193\n43174 48467\n17068 80691\n69383 84448\n1365 89055\n33525 67381\n6917 72737\n9952 92373\n92 28275\n72297 92955\n18920 54592\n3189 33014\n790 99671\n18335 39024\n21101 65823\n90476 96251\n149 6854\n67358 95522\n4585 81183\n28964 71187\n13431 96196\n5559 6627\n4771 46837\n48588 77437\n23644 77145\n24409 66448\n8406 33402\n54401 94975\n51443 64236\n69105 93021\n93204 98321\n37337 62685\n16933 81407\n20670 47633\n41259 71044\n19238 79815\n2513 4904\n31266 71493\n43090 68868\n17901 67435\n30028 53693\n32350 81631\n25316 75678\n66945 69145\n28698 76027\n48208 86112\n32928 52806\n75981 93250\n30579 90897\n46528 55153\n54021 59026\n12934 83838\n9242 10977\n29079 44690\n95013 95273\n89877 91668\n15751 77888\n39655 79521\n21911 91628\n9961 72846\n50477 92846\n64314 77483\n11475 59648\n10237 35535\n22934 82564\n37096 39706\n18117 18986\n33229 60164\n67455 72696\n27163 91668\n34820 78096\n38714 88478\n36927 77898\n48730 63519\n2532 63826\n3186 54018\n45243 87052\n28994 76617\n33522 59506\n35726 53301\n24719 59828\n9240 82495\n57248 91691\n47117 51301\n67704 73698\n17936 95180\n2408 86148\n38358 77750\n43612 68318\n28313 63254\n11486 89293\n7018 60746\n15825 51438\n4089 33926\n28415 39127\n9944 15105\n73518 79337\n5243 23255\n425 49294\n20083 62182\n9523 86126\n76460 78457\n30654 53064\n10085 37091\n50920 91852\n45994 69875\n40862 97755\n69432 87273\n39055 63485\n23474 32372\n12837 33178\n12394 26919\n11797 76453\n16702 74947\n86500 91068\n41867 78356\n61931 62002\n41122 47005\n74133 81009\n42205 98185\n69530 87419\n71349 92210\n36615 89254\n13264 86606\n46719 79886\n16136 69578\n26835 86503\n39587 95698\n8390 77626\n25884 87215\n165 6098\n9864 12072\n14408 30857\n23552 48697\n24057 62043\n18756 91202\n65714 98961\n63484 88091\n1367 5037\n62582 74564\n9749 32524\n5250 70003\n4904 21509\n64874 72491\n47131 90615\n41816 95475\n34614 81940\n5449 60069\n54039 79069\n13934 21269\n50901 56953\n22874 72814\n43593 97857\n20047 48981\n35697 74805\n37674 44401\n40295 96023\n21451 62711\n1435 71795\n29680 35261\n56176 59849\n20587 57314\n12368 47199\n36346 57286\n68138 93108\n56941 73682\n63967 72891\n69797 71067\n46832 65249\n19921 31481\n21138 22002\n30292 64997\n29123 64975\n51509 52206\n35370 76885\n33676 43165\n31153 32539\n3131 66280\n3133 13470\n2686 32771\n26995 42702\n31798 92430\n28230 99202\n48769 57467\n58729 62395\n83387 89855\n19019 21183\n14461 34451\n45278 47876\n17941 54617\n74459 96159\n40743 81534\n69317 74628\n14090 56510\n43931 66667\n46546 66204\n46229 97314\n47964 77374\n46422 56319\n46171 91654\n18644 67391\n20749 79841\n20542 39218\n50888 59906\n22265 90949\n32040 44912\n64257 74038\n54234 63976\n11915 83786\n63089 90881\n37323 61952\n45639 95784\n48395 73983\n9985 24752\n50911 64073\n14173 66711\n14159 81939\n3888 59893\n6191 59256\n54092 63254\n3472 12306\n4620 6138\n1572 40028\n50161 86709\n61323 76484\n21018 99879\n40036 50266\n46205 73728\n21938 79361\n41533 78726\n47337 88603\n40479 75100\n64365 82549\n2995 63041\n16741 67581\n2805 44894\n56457 67555\n2243 38866\n12446 62616\n42863 54089\n20753 81955\n16987 45575\n9433 71102\n38647 87996\n63337 82843\n73603 80469\n44195 97965\n13357 72003\n17629 67923\n4094 88097\n4044 66477\n47120 67834\n42596 79689\n49711 53602\n40928 85023\n7747 84500\n2229 85083\n12050 86426\n24188 49050\n4851 45494\n9414 52984\n1587 53470\n67049 77323\n44915 49924\n17621 55106\n448 96366\n4152 92876\n44728 46143\n5916 7641\n46132 69844\n26367 35250\n57938 93315\n16893 21544\n37803 73938\n39764 41426\n40472 87291\n27246 61698\n6308 65223\n56723 93504\n18889 73362\n27382 75934\n59252 73017\n41122 52163\n8054 39960\n48777 76108\n24780 88817\n28368 90261\n5362 33147\n54596 68540\n8792 37334\n49560 93295\n44814 82523\n59892 75533\n12127 74569\n1809 49958\n36340 90325\n54068 91828\n1451 52399\n76299 92011\n38311 90662\n19695 20852\n58857 98193\n21557 77815\n1914 6623\n3636 92538\n24873 52225\n54213 85630\n9482 82753\n51515 88261\n76574 82548\n11259 50151\n52781 84848\n26562 92375\n39032 92584\n37234 61685\n38947 50107\n26948 80270\n7769 32397\n34061 99953\n2741 88463\n30939 43059\n22344 66696\n18102 34717\n76927 89244\n19778 81904\n26546 38783\n4850 60882\n34580 78261\n24842 30384\n65802 85916\n7693 69341\n17757 74642\n63806 66138\n42131 85550\n31257 89648\n30569 51409\n42250 53703\n2657 70153\n29471 95081\n16340 75729\n17526 21770\n38848 71566\n2179 42392\n13387 52891\n54085 60489\n58858 84360\n12082 50543\n78272 95600\n50515 63700\n1192 46074\n6609 61970\n44349 83385\n1291 80375\n27390 80699\n95209 98217\n15063 61174\n63299 90227\n89979 91643\n21448 66887\n48075 85328\n3348 82536\n4961 59267\n2727 8121\n8779 31052\n14890 68897\n42810 61333\n63620 70246\n3003 77008\n4758 45948\n3476 44241\n25856 72655\n66881 68747\n80276 94148\n2033 78690\n26244 51093\n39783 43669\n13844 96546\n56837 98996\n36676 45157\n47893 99852\n20884 36781\n33124 33562\n77961 99160\n21315 69287\n7839 12507\n5960 66463\n38313 51450\n2721 66521\n42054 55672\n47455 76821\n21955 72772\n5978 30956\n37804 86319\n58294 96947\n37407 83682\n18993 92997\n25592 33038\n34103 55217\n32493 97418\n53186 62841\n3212 11652\n30157 83340\n47916 63395\n14526 73404\n47004 72408\n53898 98519\n26829 56209\n3206 37181\n99479 99919\n29759 32560\n33378 44352\n75450 77591\n8215 36204\n85184 94606\n41671 74891\n32425 32632\n11913 47193\n11778 21435\n50383 88368\n32971 82440\n2420 43120\n29866 55320\n24858 83779\n71778 92925\n28693 62894\n66128 86509\n20819 40448\n38961 62023\n21222 36214\n20351 94903\n17721 75472\n72182 86720\n81075 93124\n63184 98361\n66047 77614\n21475 44395\n26848 66518\n21182 68824\n16125 32636\n44490 88626\n69440 84150\n41230 41810\n33046 87517\n3562 57548\n20221 55576\n7027 36161\n5054 73752\n6013 77077\n19169 80974\n47915 94987\n11508 97382\n24299 99747\n8870 10360\n25533 97387\n16249 72420\n17166 81485\n65851 79482\n37054 46241\n24206 64532\n70437 80307\n54091 95445\n2857 41400\n15486 90098\n2752 18569\n62667 68292\n10953 39445\n63084 85395\n23873 55103\n39085 95987\n23742 96990\n19535 39940\n12897 26565\n29996 51339\n31527 79682\n54164 56131\n21568 25707\n53607 99220\n48793 75761\n33683 96379\n41152 78562\n15753 62362\n13465 26453\n751 93225\n36140 63399\n9801 28514\n38641 83365\n1710 86497\n42575 61213\n68470 80235\n57780 66259\n49341 83446\n13558 32253\n26933 53997\n10366 39999\n56099 60785\n892 76854\n29951 75900\n126 45134\n8814 32105\n45609 95058\n31848 45380\n31953 35098\n68757 97245\n74351 93615\n48687 94641\n80982 91435\n9492 65266\n36337 80565\n2692 83745\n38943 64231\n29404 73717\n12977 66019\n53632 63194\n95907 98099\n52218 70394\n50734 56057\n6743 29066\n23165 94149\n15044 86882\n954 48424\n25741 79685\n4571 44965\n41236 81006\n21135 32055\n5259 85781\n59670 98455\n59151 60553\n57520 91076\n45765 65732\n28635 30690\n3027 64961\n21967 44078\n50568 70825\n11136 31078\n10792 43577\n5483 44161\n54460 60613\n40678 64911\n12901 95491\n20758 71168\n5521 48395\n23974 91227\n49329 96342\n27955 66244\n1945 21864\n20602 52350\n16269 99165\n42449 58943\n25269 46311\n19451 95846\n79441 81288\n32829 49024\n89028 98901\n10920 40378\n2919 98126\n73084 75802\n69652 75133\n48053 97242\n58312 77002\n34376 34615\n32146 34486\n14990 65326\n87484 90776\n4790 96088\n20193 86476\n40134 92141\n30808 56298\n7666 10904\n31511 89423\n53561 83385\n47370 61021\n29235 75607\n74716 99362\n42262 90526\n12678 54958\n10471 73343\n86959 87026\n7208 26531\n29214 49293\n27860 57616\n15372 27558\n19695 94122\n62901 66065\n62495 94695\n11668 54682\n39852 60807\n48241 50688\n50568 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92387\n58684 83966\n25960 81905\n22668 85573\n40869 60127\n58989 99427\n57072 87116\n30656 50623\n11897 79871\n11322 26528\n39401 45840\n48378 72767\n55507 95044\n62241 62431\n28722 74694\n22416 49011\n50251 79556\n72533 87515\n38902 96560\n27327 53553\n10293 21352\n66779 94809\n76259 86245\n51190 77752\n42599 59036\n54114 61845\n50191 60781\n46177 57552\n27285 73495\n28120 65796\n47066 52965\n25399 57957\n35136 85109\n16655 64720\n2801 18738\n7134 82432\n12237 49999\n17657 59810\n67267 67458\n61232 84901\n6016 22254\n59221 97964\n29694 50858\n",
        "output": "340\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 99,
        "task_id": 541,
        "test_case_id": 32,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n15075 67129\n40925 74589\n14795 60798\n39504 73262\n69273 88005\n9694 68748\n79104 86863\n11079 87835\n15925 33347\n40797 73757\n39303 81413\n9186 89007\n27804 63658\n58073 98153\n25235 28051\n42288 46439\n29256 51600\n38073 98777\n17159 29340\n41100 64848\n40526 62736\n77345 92797\n3263 57884\n78833 87795\n39943 87671\n6225 23495\n41880 83807\n23931 28440\n60679 68897\n13864 45203\n44031 93482\n51569 65719\n5059 38285\n32163 77165\n77049 82372\n33895 67589\n38980 56258\n42873 94864\n49137 51488\n62362 67411\n30597 54530\n948 58529\n44842 71264\n89539 98122\n2780 54855\n52712 67290\n21487 53281\n34471 44076\n32921 70117\n26294 30324\n50168 96832\n27170 31988\n24928 62504\n55345 70853\n21973 85899\n12307 73632\n14332 89412\n69473 89221\n27278 63784\n28581 39066\n38182 97878\n33692 52946\n32162 67044\n43135 44135\n42274 70335\n1399 96570\n11265 86553\n17827 83626\n8299 76146\n35473 97713\n64570 94479\n51325 93272\n58027 81302\n21643 96266\n78548 79916\n47469 75080\n28331 55478\n57774 95486\n3055 30439\n29864 42441\n39608 85607\n5146 14925\n27986 99159\n52863 64041\n30198 84746\n43812 52450\n18906 57139\n32166 66690\n55769 72858\n43929 50235\n40788 80550\n20465 90578\n55186 78588\n41849 90499\n17209 52893\n6919 57327\n46995 69023\n1844 97181\n13542 58443\n18528 81758\n39907 41349\n65575 78202\n43109 76147\n13045 51908\n76377 76914\n59513 80029\n51550 81661\n14362 25661\n999 82350\n18642 18903\n2301 39877\n3175 11589\n39681 94041\n48915 92936\n33315 50745\n31492 98096\n13524 77960\n65595 77305\n59874 61482\n65921 94533\n20273 59405\n33779 49549\n9659 43328\n53956 94831\n74774 96220\n55728 78605\n20681 51797\n65017 89909\n39480 40248\n63971 73306\n29951 63688\n54140 80849\n42759 60997\n59029 90591\n53019 58832\n1371 10355\n66338 67664\n20201 62395\n56402 68212\n45494 64675\n74437 94718\n76053 99845\n37039 63076\n74487 75399\n18081 35506\n9227 89621\n15270 15285\n9090 17634\n15653 18115\n1184 95426\n55854 93965\n84379 88513\n41634 64919\n17005 18366\n25012 90162\n42553 60819\n40506 89533\n32227 72416\n154 16501\n24955 37513\n19164 73617\n23878 77771\n16915 65332\n35085 89083\n88383 88992\n41108 80967\n44675 49996\n3540 59000\n19330 51143\n28647 50807\n26664 94065\n5372 38268\n2945 56821\n58638 60057\n19327 89087\n61516 79966\n5388 98695\n20030 20408\n19020 94959\n12838 21676\n27907 59174\n58258 97144\n12634 29313\n67411 86616\n49511 77102\n17770 94734\n15785 74895\n9439 32739\n1490 93901\n8623 51367\n16329 98361\n40244 50614\n33041 37127\n58605 95528\n16640 79694\n31022 66895\n5223 38845\n4803 87740\n16232 69865\n3829 95178\n19184 39818\n15116 82911\n20924 45587\n499 20784\n51443 72714\n29029 92834\n5429 97233\n16824 62662\n92649 94660\n19686 34954\n5410 94573\n47675 77207\n25884 45016\n32751 42166\n5477 8222\n62208 73099\n46656 56779\n56980 91025\n26328 50560\n9020 28948\n48544 98234\n26697 80936\n16356 54395\n48709 79625\n4677 21561\n10963 55223\n39910 45772\n9311 82697\n80794 96383\n1258 50261\n21009 87591\n3374 39966\n396 30146\n22041 92935\n48270 53400\n19976 92488\n6161 95222\n44073 46708\n52495 88765\n48092 49302\n36136 47456\n30754 94146\n33878 76093\n1216 45025\n49132 67742\n56036 71850\n7247 38963\n6496 35019\n18284 52660\n38062 64692\n1686 52680\n41222 64348\n95549 99321\n24939 89911\n66821 97529\n12196 73578\n79502 81310\n35853 69620\n31034 45917\n31967 48993\n203 60772\n12645 35098\n2761 8075\n27490 76720\n12114 34451\n34151 94869\n7491 19416\n48524 71227\n11869 93650\n78116 83363\n12692 74392\n21774 75960\n49025 73672\n38443 76408\n17074 82466\n55449 69081\n1475 6936\n18750 50069\n50792 73895\n541 45858\n57566 91769\n46033 56703\n12917 40852\n29578 59846\n25520 70393\n71395 74104\n5938 95270\n44937 94570\n27630 47659\n28910 99795\n63965 78920\n24088 62093\n31570 96812\n42719 66723\n48227 66472\n6470 84058\n39571 57941\n4823 43634\n2803 78015\n75610 79875\n15291 63265\n69838 74984\n26453 95820\n45001 64400\n4068 48112\n18217 77717\n65114 78675\n17499 95625\n45833 63167\n53794 70961\n22451 53875\n23583 57901\n17681 48469\n25255 59806\n50526 88775\n6449 46383\n63439 69832\n29226 58977\n85393 87659\n20097 67619\n25527 59776\n48203 88909\n15667 52344\n21635 54872\n80618 81508\n25810 77215\n18168 92932\n6033 47770\n29588 32372\n28196 68100\n38404 88082\n13732 84623\n9641 20149\n18401 79338\n81726 91185\n22106 46789\n71917 88560\n4136 82070\n5584 14853\n52146 81361\n36307 71959\n35713 54966\n2589 88617\n55671 92058\n30903 43815\n33567 69260\n21640 67641\n20250 83227\n7361 83438\n15955 82432\n37926 75848\n13011 49049\n33407 84605\n68223 85271\n52569 56458\n35328 52952\n21633 72522\n33887 83700\n10097 85145\n49702 55927\n4347 51406\n66720 97290\n27953 36690\n6386 35763\n23792 84041\n34107 69983\n51695 70611\n49441 84248\n21039 73998\n29104 37641\n9312 49985\n22693 62380\n46147 57670\n40437 71957\n57058 62924\n59813 71251\n16143 53524\n16612 67291\n33586 74484\n35795 81389\n15225 85712\n56891 76753\n52059 76204\n5412 29265\n9878 44145\n44818 50411\n61915 67512\n3330 29748\n48005 94662\n51461 70448\n65840 99671\n48681 64689\n80430 89489\n19545 68892\n5421 10138\n36699 84723\n25184 71622\n11119 51503\n1998 97737\n14612 53268\n30080 61523\n34480 49909\n66421 81196\n63033 75974\n89772 98577\n2468 13888\n532 25330\n43871 56679\n48304 55608\n2014 9565\n3693 79201\n22992 28123\n51884 98033\n67148 70883\n48369 67841\n55911 93071\n65831 71222\n29380 31231\n59719 67122\n1434 27399\n44665 70331\n70981 93768\n24779 68909\n29356 81855\n11022 19738\n70347 80958\n16489 88534\n7659 66031\n16829 55236\n42600 98634\n2114 28778\n58055 93824\n36174 77205\n25928 63797\n24450 32277\n25726 76146\n59601 83097\n12029 83699\n43096 61370\n48025 85007\n28980 86090\n56067 78660\n27308 27758\n24191 39872\n21734 39848\n31538 82298\n66376 68437\n4864 71026\n42144 76100\n45775 84708\n1555 98309\n4878 10879\n74778 85719\n7378 42091\n76290 95542\n26365 39415\n14814 77736\n55150 82906\n9863 42370\n14531 91977\n26935 77434\n28647 93682\n40162 96695\n2229 81796\n23419 54426\n75280 90822\n44262 53629\n21814 38952\n11759 68108\n19948 33386\n10297 93004\n3664 96797\n18773 64614\n3440 92612\n15601 98095\n56644 65366\n44397 89015\n28985 83108\n27162 99478\n58752 73204\n6369 81428\n10608 69937\n23033 30846\n52706 88904\n41774 67369\n14115 22042\n45323 74268\n68954 79796\n59508 94967\n7181 26010\n21754 80798\n70849 71175\n88826 90663\n76998 90973\n54645 80521\n15814 77422\n29340 87209\n4899 14357\n80744 93925\n93525 99533\n1857 60088\n9668 51158\n2547 72759\n53415 78704\n8293 99578\n20510 47639\n73758 94467\n54926 63544\n57975 92706\n23663 27596\n2715 97206\n1197 16107\n9078 80493\n69015 73206\n11480 45682\n67773 92485\n15183 45364\n65927 83083\n23794 46486\n7186 88796\n82871 95702\n26104 80118\n28975 39729\n20078 53582\n9773 55355\n12454 39694\n71501 79158\n18720 23867\n26927 38307\n26963 52266\n9861 89256\n4217 30257\n8700 86733\n26266 71586\n44109 58957\n3225 32258\n42182 84516\n38548 55865\n32292 51469\n39490 51721\n7766 87685\n25587 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42750\n48357 93557\n28013 55057\n11402 21864\n72496 93269\n41344 59377\n4551 39963\n75183 86384\n45179 85843\n51862 62471\n61657 94272\n20157 43889\n27639 56882\n46418 95651\n84856 87573\n31405 62959\n25064 28665\n12391 33221\n48186 75951\n6723 69307\n28697 74477\n26108 65888\n12047 89398\n93828 98577\n35227 36604\n72631 92912\n3958 78537\n24266 37962\n36850 75590\n59777 89895\n79888 90196\n15936 57306\n14323 70013\n49388 72317\n40140 54651\n3831 47051\n9049 21238\n95819 96207\n26441 31839\n31835 50825\n73888 90192\n39927 64239\n6134 10798\n6717 76033\n10888 31499\n24172 97927\n47887 88637\n2052 85248\n47603 96989\n84845 90274\n40303 58408\n54506 89395\n59941 98390\n34369 71753\n",
        "output": "355\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 100,
        "task_id": 541,
        "test_case_id": 33,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n12235 22384\n80629 82168\n40625 54348\n37560 47670\n74493 92066\n11110 63641\n23518 55697\n4498 70459\n27228 78652\n36202 59282\n12601 68014\n70279 80015\n21439 93731\n21515 77446\n54229 94251\n44529 96098\n68701 87332\n71163 98922\n64210 73176\n18500 59122\n31185 45412\n35394 66460\n55622 96558\n89070 99290\n60379 75998\n8506 40158\n30361 64088\n13571 62274\n71213 99326\n28579 42461\n15731 44343\n30469 33716\n54612 93988\n18140 32530\n30576 31520\n15097 34220\n20246 53712\n25770 90732\n31194 94159\n28966 59969\n45927 69521\n51965 96501\n36024 79879\n12278 87612\n48760 77068\n14058 15141\n30419 51075\n12886 96746\n5890 6270\n40963 88149\n52109 78995\n46513 60536\n11766 73195\n2692 52415\n16643 49764\n21177 76076\n3571 57465\n52419 68409\n19303 48127\n53004 91454\n38780 43846\n13876 26343\n3551 51802\n50944 98654\n9039 73663\n8374 78664\n11753 19801\n62186 74349\n80450 82616\n176 5533\n29141 97031\n6820 69129\n35096 80864\n2367 73527\n38562 59262\n5967 57544\n49407 68067\n3841 44407\n11915 33891\n14593 64525\n2286 89285\n23733 89604\n25836 27526\n13135 36154\n41856 73904\n51235 94453\n60622 93436\n27624 98737\n11105 20978\n16816 32140\n54226 90926\n33189 71264\n2239 82965\n18596 82647\n53622 91282\n37966 44382\n24146 76267\n30243 39191\n30636 33671\n731 68650\n70650 87838\n86684 88870\n8246 11276\n21531 35589\n39766 92047\n15682 54477\n30693 66816\n28930 31432\n62893 88572\n17018 51982\n81386 84712\n930 80841\n17877 67006\n58258 60285\n32743 78031\n14945 42614\n37002 56030\n17504 20688\n240 1589\n78730 95786\n74882 82492\n43070 53489\n29536 90590\n35597 51621\n7839 28724\n19368 94951\n2779 55199\n8096 34259\n8295 19807\n32463 96701\n78381 80964\n15273 95941\n59137 83875\n13821 27930\n84550 85017\n25026 73951\n22813 51018\n25483 76386\n11213 11445\n27816 71650\n65539 84448\n16117 84671\n46548 76411\n59596 64018\n56358 60040\n30937 42181\n53528 86043\n74773 79666\n53256 65680\n17567 72873\n78305 90531\n62236 68518\n49232 49872\n25734 33697\n23908 92820\n46098 79415\n50671 69189\n35750 72938\n20312 99772\n25704 82584\n29809 84455\n2709 39444\n46477 54114\n35072 96270\n13090 39903\n55037 78240\n41998 92612\n91130 98348\n82113 96714\n1787 41209\n58836 98282\n22322 44417\n18503 40642\n20397 54585\n62932 91874\n1514 54014\n30387 46607\n19689 43479\n72734 78849\n8717 15567\n75430 83764\n61758 94871\n506 2059\n76388 96566\n64771 78753\n17107 72336\n34216 81743\n36924 97932\n583 18276\n23120 95975\n14570 66311\n57471 72307\n29784 60335\n43199 79732\n28750 91868\n14292 45563\n26995 93852\n7557 30012\n76308 83787\n26262 63638\n54950 69027\n41760 96332\n16489 71975\n50355 66850\n5251 41728\n31886 55909\n18457 99504\n13045 62883\n86122 89192\n79945 92880\n91604 99947\n47502 64085\n78111 89858\n45802 91687\n61255 91920\n35176 94044\n44682 84118\n21646 66788\n36498 69596\n55454 83274\n77223 86294\n53079 89882\n15154 40808\n80147 83821\n7216 19483\n57340 99493\n845 31421\n1950 9023\n57841 88022\n26109 66295\n23422 88585\n4599 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71798\n18041 18667\n56284 90252\n25206 82377\n57154 78191\n67563 79184\n21941 58684\n3671 31029\n23053 31682\n15354 28828\n11486 73194\n11458 23709\n58769 92987\n50978 92140\n60105 81835\n26568 31141\n12595 90282\n33986 61219\n77279 89343\n81774 86515\n4188 62525\n36634 88013\n91166 97167\n47374 99234\n11996 78756\n9726 57868\n8059 16728\n50634 61162\n14939 28329\n26289 34624\n2041 86862\n21216 33903\n4683 91741\n61004 98416\n39501 49621\n25100 78328\n87095 95563\n65871 70644\n23064 31654\n34816 50389\n14998 83717\n31085 73149\n11047 82318\n12464 46308\n76779 97660\n8095 98145\n14653 61799\n33900 40658\n39535 98185\n77357 82536\n24083 87983\n10236 36225\n31563 54332\n31612 44603\n58680 70480\n32821 82608\n62734 88061\n52704 78828\n41178 76550\n51797 91051\n33288 95452\n30272 77137\n6155 88476\n55383 57478\n68676 78298\n48104 54028\n71407 88641\n61906 66734\n43114 50490\n26969 77709\n30778 31738\n33132 98797\n65301 81029\n23836 26060\n20255 32300\n46391 85264\n16247 70256\n92995 94861\n30377 49561\n26168 97843\n29208 76852\n11014 29626\n8055 87519\n68595 70145\n9534 91618\n7155 60439\n58317 63991\n42522 44323\n6944 95319\n25792 47250\n18738 32427\n44287 66255\n4478 77250\n57093 68992\n64178 75311\n70669 85752\n18206 97484\n36315 72308\n4000 95241\n1103 76768\n74537 80967\n73616 82767\n54652 87306\n662 4073\n15227 77647\n1385 5844\n61889 77197\n924 57956\n906 3728\n13338 72317\n25822 90932\n53440 85314\n49798 71710\n60929 66293\n21900 41018\n14991 22482\n85170 89817\n1775 45384\n25466 87327\n13053 44822\n69530 93829\n33106 35036\n11928 32001\n67287 84603\n26321 50673\n3706 47819\n30852 47393\n52441 78583\n49483 76258\n19848 55718\n23429 44321\n60349 86863\n9552 99597\n53640 56840\n51721 79970\n7666 28163\n40213 58411\n72748 87185\n44383 94636\n63879 97326\n25740 95176\n498 69497\n11925 99198\n11499 66163\n13691 60086\n5969 71275\n15726 91504\n26510 52544\n5872 99090\n5149 62128\n29451 39359\n86255 91427\n3916 68814\n87899 99660\n24269 58549\n35515 78462\n2051 45458\n4918 34044\n39530 64588\n35940 45383\n56121 75835\n7957 30381\n74800 92310\n12812 98115\n174 26788\n58168 80866\n44233 99882\n1198 73694\n7556 9733\n37532 85410\n70039 84125\n92882 99055\n42003 85293\n18422 36006\n7883 70041\n22324 49950\n66061 76284\n12636 21776\n63381 95038\n72938 94530\n4484 89716\n733 46010\n43833 68139\n41489 80635\n6247 8210\n17018 73118\n12356 73119\n35407 38532\n10188 34944\n10859 45009\n1364 25786\n8791 36022\n833 6944\n42255 77620\n68302 81801\n24746 61748\n12390 67007\n60038 91145\n17010 52246\n28409 69349\n39372 53284\n57340 88937\n31313 92098\n23631 40306\n21170 52717\n82577 84471\n9954 18129\n15303 29656\n90757 98437\n55871 62926\n8383 72334\n4193 50288\n8473 29670\n9142 91586\n92014 92291\n35470 46463\n21723 42506\n13631 29870\n25974 95238\n65829 65970\n39571 56535\n55658 85786\n26935 91003\n74266 77990\n16844 86863\n25223 60743\n30925 98818\n44445 44470\n10183 46925\n24677 59074\n540 18561\n78804 94884\n35963 36231\n51915 95716\n39624 51986\n11896 12777\n7052 25394\n26209 49535\n25336 56340\n10039 79073\n13004 99694\n52270 82416\n21694 83285\n3401 45293\n77287 92284\n53504 67352\n33825 36520\n9029 86989\n22642 60013\n22950 48979\n57110 72170\n73482 73733\n56854 58978\n820 58804\n21223 24381\n58008 63021\n57028 87033\n44234 54067\n30096 85575\n42660 98965\n73307 82287\n25325 50414\n27822 53520\n69148 87072\n4368 65214\n11611 40604\n10560 26561\n5901 59731\n38289 77617\n3423 20078\n4318 85695\n51904 72328\n15131 83914\n28885 80614\n80879 95583\n33185 33201\n11812 74341\n41511 64860\n33195 37626\n22924 33011\n34766 37075\n13523 15733\n39208 98140\n9270 63434\n23059 76049\n9541 12566\n70722 94431\n42170 82927\n16322 94395\n45464 53031\n3559 11222\n31202 74354\n37606 39486\n29632 69436\n27831 92501\n64355 69980\n15830 22141\n42027 55659\n18719 57921\n17501 72625\n35443 44063\n50370 97479\n21803 90652\n34714 85714\n47397 94594\n42600 76498\n6723 89059\n10886 62624\n58970 62899\n5046 44997\n29559 57244\n47261 88659\n33376 66055\n34334 90116\n17627 72330\n1545 45184\n11333 42015\n49229 55096\n35137 89488\n18872 52432\n29336 44956\n26471 59254\n38140 67020\n41840 79874\n14913 63800\n34023 57977\n59585 90607\n15421 86057\n10367 25139\n22678 33244\n5370 97326\n54499 79406\n15147 75720\n32125 78019\n79278 81780\n44379 79596\n3823 41608\n13656 20706\n50389 75712\n26498 47359\n53067 96963\n12783 43947\n52005 99728\n46362 65786\n34967 38536\n56600 56851\n39787 42552\n15286 94391\n28273 74191\n19320 31415\n4325 94004\n93258 99453\n15577 95165\n10138 44608\n17532 81275\n9444 93034\n13392 70814\n81005 89595\n24522 32526\n43316 82990\n48739 58144\n1470 34141\n44821 94381\n46976 47159\n2536 20101\n60811 85582\n2751 10847\n10425 70728\n15382 77238\n20828 38846\n",
        "output": "350\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 101,
        "task_id": 541,
        "test_case_id": 34,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 100000\n65685 79664\n48772 63387\n65341 71703\n50457 93012\n29003 29777\n31312 96301\n50913 89517\n33608 52742\n50592 82037\n25459 35970\n26674 80932\n43864 49628\n76799 82243\n12953 67920\n6055 94957\n78161 87111\n84580 89980\n46817 76356\n64388 95050\n37844 53925\n40567 53543\n50006 61151\n22949 28101\n7150 46645\n50073 57697\n762 33913\n4590 75605\n14403 33180\n6922 93043\n41577 84367\n45967 60199\n31786 72980\n14150 65922\n23959 60922\n90737 99849\n42417 98491\n69491 88010\n25403 26123\n18673 51788\n33735 55163\n30010 74118\n39677 48372\n47162 64461\n6783 10894\n5387 76829\n26731 77254\n28062 50311\n45174 86638\n8473 94955\n53506 65193\n37693 51484\n51208 82450\n87594 91089\n39707 89069\n3176 69740\n50272 86685\n32765 68167\n94754 95475\n83152 92539\n41944 97430\n56825 63616\n57065 98608\n20153 48946\n44427 79304\n90887 99298\n58943 67775\n49123 58468\n25000 50677\n8365 18377\n55867 97105\n6959 85045\n2246 91348\n8616 83798\n843 90900\n20322 29439\n23799 32699\n9817 95085\n55350 66498\n21254 80958\n80559 85452\n51346 99172\n16731 76949\n29831 86103\n31688 75737\n21485 62394\n11348 47898\n36685 68400\n43929 59712\n72454 88526\n34392 48420\n47359 96420\n7033 57667\n43307 43888\n12213 25120\n49985 67640\n66821 91966\n35055 86361\n14227 29241\n90580 97968\n35063 52126\n17721 69264\n27711 36938\n31499 32850\n91194 98789\n168 54825\n40637 90871\n40685 85838\n42597 46879\n4149 48676\n1889 3559\n15554 94416\n49869 69609\n28642 63803\n13650 98568\n32855 36442\n7016 70562\n39333 85102\n2832 34519\n64933 84433\n7399 92946\n5904 28508\n37835 56407\n42024 81635\n18742 75868\n11407 69589\n64728 82442\n9000 44641\n31744 81329\n13375 36736\n44901 51184\n14452 41963\n17697 46241\n37173 43651\n68911 93347\n47822 98884\n11556 75911\n3987 28379\n3987 71350\n6462 30379\n70887 94647\n56014 95829\n48450 90083\n54580 98353\n34070 53640\n12756 17444\n21296 86481\n71604 99760\n51270 99027\n79265 98899\n18775 82611\n12742 55246\n92213 96962\n31888 40165\n51600 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74217\n54211 81159\n43436 86725\n2533 85872\n10336 96020\n47110 87791\n38757 68205\n47079 51226\n20567 71045\n13660 34032\n643 83932\n15506 74779\n14535 75381\n24021 55485\n59229 78177\n23768 36463\n1239 37391\n2479 90586\n128 46732\n29403 47936\n12106 77062\n4613 30936\n53990 65505\n12080 63765\n16698 38143\n25787 62030\n88861 92339\n68224 89963\n88857 95240\n63879 96996\n9871 88694\n51338 58291\n10424 21583\n16739 68057\n60486 72123\n8170 90331\n41000 75795\n22262 65069\n53797 76893\n20275 80755\n44606 85260\n3559 78513\n62044 95375\n14237 66816\n20922 52006\n21735 78118\n1445 1781\n9227 74217\n28825 29826\n38098 66542\n98354 99418\n43296 51964\n38898 43586\n4208 82757\n5281 75310\n55604 74843\n78354 80046\n67046 77215\n3438 92582\n46272 90388\n26233 84994\n54136 84963\n14468 70385\n46637 80838\n34221 61430\n27669 91130\n14283 25171\n73576 91850\n30079 69695\n20782 54442\n36274 40438\n12482 60155\n3972 34823\n52790 55315\n2528 26976\n10416 24992\n51352 62383\n20699 68354\n46994 98357\n26691 76238\n19636 26215\n46237 70453\n29404 94944\n34171 71297\n15958 99885\n40550 54758\n19874 94111\n6518 29052\n14216 61616\n1310 27583\n45051 60404\n20860 70765\n20830 79073\n30808 94552\n40112 51597\n39744 79728\n24016 37179\n18695 76524\n48907 87770\n67479 67927\n29907 56324\n64523 72563\n63794 83235\n50053 60001\n12943 58929\n87703 89150\n62869 81800\n14726 59713\n23823 90413\n4946 70589\n4533 64967\n30049 55456\n22278 51682\n32059 86070\n278 638\n79631 89243\n33048 38682\n26357 99528\n74755 99586\n2423 63882\n68427 80888\n72646 85517\n43438 84536\n25210 76206\n45147 99162\n7684 7797\n4461 13642\n5213 7695\n35810 56815\n49091 60813\n4303 45111\n44314 66886\n24857 44721\n11931 95778\n2444 69509\n51770 79379\n77800 98045\n5039 55047\n21830 21858\n39031 58381\n19685 65279\n10083 45586\n24854 37203\n18353 78791\n60282 63047\n48845 75986\n14503 30149\n70973 75305\n18615 34303\n25484 53673\n85275 91346\n53301 55673\n68682 87780\n47575 89044\n83230 83770\n74421 87723\n15431 33242\n3666 43257\n28638 67122\n19161 24213\n52263 76999\n40316 67844\n2425 5516\n1445 93855\n49394 88410\n1497 83565\n9929 28991\n2677 14602\n65284 80909\n46906 88311\n82281 94531\n11504 34122\n10650 95362\n63548 93995\n20145 33228\n34814 46308\n76459 93535\n48754 81199\n20499 28812\n16527 45253\n41407 89871\n41408 69000\n41142 60801\n52681 64285\n6942 87203\n30492 89572\n35051 61668\n8140 79724\n10454 98607\n54250 91438\n9392 47479\n210 10593\n9932 74409\n22426 94469\n19904 42394\n56533 61275\n55463 94836\n591 52273\n75215 75866\n1017 14795\n79841 90547\n43373 71815\n30458 62247\n32418 33577\n14080 94162\n60329 64270\n17922 20581\n77736 91534\n82316 89603\n1011 96845\n34046 77696\n53787 87784\n37914 38706\n36305 81027\n55083 98427\n68586 89949\n8073 82622\n27746 95521\n52115 72833\n669 62833\n8873 68507\n8268 75299\n47940 64982\n8156 58376\n1661 89328\n53648 72689\n9180 93367\n9370 97332\n10395 17578\n26895 88614\n18866 68278\n40074 51172\n15286 76240\n37158 73399\n69159 89718\n9541 41449\n33755 35928\n39862 87486\n23204 59942\n10631 80022\n32794 84551\n15247 75972\n40988 99756\n31077 99290\n46741 98101\n64315 81108\n39366 74403\n16497 41079\n6106 64455\n59369 90199\n32114 84551\n8125 82795\n54364 64154\n9163 21729\n36554 93204\n3399 82693\n76016 91663\n13256 22552\n3315 74913\n9004 35342\n25068 64311\n60224 82646\n43572 47085\n71652 92070\n51064 84425\n8887 74290\n684 44322\n77210 82077\n18117 47507\n19085 32543\n61323 65299\n69205 70806\n26794 73135\n21272 92895\n16195 72014\n4998 9364\n23119 83556\n11064 50285\n39252 61816\n58824 95697\n26430 59415\n683 38708\n271 21219\n12522 82149\n18756 42994\n59435 66939\n55347 92052\n36230 85024\n23695 78681\n70049 85948\n2742 17801\n67854 68437\n67594 92242\n26153 72615\n21208 81270\n48264 89883\n27504 46831\n46527 95090\n33771 90629\n49509 59430\n25327 48912\n28041 95176\n34672 95436\n11231 20410\n69578 85783\n74943 99087\n27641 77935\n39473 52887\n6244 13954\n5453 8251\n10104 39419\n29386 61682\n5374 43288\n52667 69709\n7201 31987\n36112 90628\n38943 98333\n73977 98103\n37364 95661\n68152 90631\n40473 65099\n13959 96859\n1182 1466\n41150 96683\n53565 60698\n58296 93721\n68048 68603\n377 10584\n61498 69106\n58513 75792\n15588 60817\n60836 99760\n1489 50372\n74228 94339\n50097 83139\n52140 64737\n26436 29681\n5413 48927\n25525 47251\n4705 32902\n63562 82646\n25295 44934\n22998 75886\n7420 25958\n37856 83807\n46304 72285\n39431 69865\n16805 43669\n28208 51585\n25268 80587\n3537 71513\n34657 40526\n6418 41573\n29926 33350\n20682 94221\n60871 83133\n21236 61036\n1679 93948\n259 10685\n44013 52686\n32892 81377\n36885 57224\n11481 89002\n62973 73214\n22687 85044\n7155 87076\n65945 78442\n25371 63165\n47331 93744\n1811 21854\n2430 91486\n25403 39344\n60882 99471\n96183 97132\n40101 97551\n15204 30279\n4211 73788\n89150 99522\n56463 75235\n19897 49813\n29923 36718\n23224 73067\n48688 52472\n23779 48746\n39864 57014\n20891 70859\n48952 98245\n76699 79169\n45936 82054\n28899 79546\n59340 77693\n79509 91793\n37792 70364\n17915 81446\n44503 84255\n75712 80975\n6670 7274\n30406 72232\n6122 68811\n706 31507\n5103 35333\n18952 74114\n6864 55408\n11866 34839\n13985 16588\n39737 98394\n23497 39528\n47019 60977\n52833 72014\n78623 82958\n31692 79222\n59441 73379\n55269 93141\n11938 13315\n85413 94882\n54006 67370\n87971 94474\n40530 82903\n68596 89156\n6984 81027\n22201 50523\n76697 88427\n11774 37456\n20685 29759\n34743 56137\n6735 20404\n80296 82357\n36209 87351\n24492 47487\n35066 47482\n43926 51528\n21203 75207\n22864 91926\n22361 44073\n67562 75831\n27766 95932\n280 77819\n4716 80745\n38947 48333\n82471 97989\n61417 84715\n36934 54268\n5692 11374\n27041 59243\n4234 85331\n86496 95049\n49605 69066\n52397 69600\n6846 91610\n55020 71581\n22170 44594\n62519 95876\n27183 97203\n75462 88429\n57329 86659\n8038 68513\n11819 81253\n17419 67876\n58445 59206\n12803 97081\n31938 90705\n82592 82616\n3664 79737\n190 52571\n30626 31148\n26521 70736\n66302 82833\n33946 44213\n72454 89511\n85 9497\n7365 95760\n24091 30089\n67587 97487\n38582 75156\n13701 24255\n41777 50409\n47796 95818\n20093 34899\n15658 78439\n13566 96770\n39580 48294\n11438 48247\n8983 14468\n76112 81866\n88977 91520\n9975 63130\n5278 62178\n57493 73751\n60040 70800\n79683 95531\n55326 56500\n19700 23667\n80855 85633\n27937 47424\n5244 60617\n27983 82601\n37262 92299\n22756 74586\n90364 93167\n24126 34558\n49293 94077\n51911 84921\n21095 36115\n26570 65060\n12299 77276\n35760 57323\n93448 93837\n33668 90815\n25517 47551\n4990 31947\n18906 79282\n20178 75186\n27816 45129\n48193 79861\n76724 86830\n25919 35681\n27890 39900\n18301 76581\n66155 74270\n43102 64482\n1573 64441\n38687 57090\n23701 63206\n86759 88077\n28543 84982\n16651 48479\n24700 36582\n90300 90965\n32502 95765\n65637 80994\n32418 55204\n7400 16206\n36460 41222\n29361 86816\n16588 42814\n74612 91350\n14857 54552\n12930 45622\n7646 33261\n11525 79775\n56740 93455\n17003 31664\n58852 96175\n16443 96517\n20659 25712\n26722 52394\n49999 63351\n74913 85458\n24778 67834\n18707 30734\n38922 92219\n36326 70185\n2798 67751\n6440 12462\n24749 66787\n25729 81642\n45912 88362\n4780 41782\n39904 44068\n25614 27223\n1597 66937\n45186 59765\n18067 83174\n8924 90766\n45502 59294\n34237 91346\n22331 76523\n40226 75658\n19583 48990\n4074 69680\n10155 22143\n15970 94602\n9064 13807\n89171 95397\n5838 52898\n34003 80905\n5739 56813\n32566 69882\n81225 96585\n15105 94179\n90041 93981\n33896 95891\n39487 69410\n2762 97395\n19457 33115\n67971 73370\n654 5010\n27328 29447\n115 30116\n10805 89437\n28086 30361\n19333 65092\n28054 41219\n67859 84629\n4815 92363\n22566 30663\n3404 48006\n31225 97512\n17532 41868\n83439 83744\n25834 52725\n82475 92417\n26574 85063\n43444 70087\n1100 55696\n10400 77904\n20420 67877\n",
        "output": "365\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 102,
        "task_id": 541,
        "test_case_id": 35,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n21030 31526\n56512 84755\n93090 100000\n92698 100000\n28396 42568\n52169 78264\n52391 78590\n37822 56684\n44665 66939\n37750 56578\n56449 84661\n65179 97772\n49481 74210\n23744 35623\n43740 65539\n6838 10325\n50524 75780\n88081 100000\n27647 41448\n35065 52588\n50836 76263\n67951 100000\n13103 19705\n51748 77627\n79534 100000\n1759 2635\n77377 100000\n61510 92288\n54156 81241\n32142 48198\n43658 65416\n77570 100000\n22021 33051\n43745 65545\n18510 27738\n42592 63834\n64396 96611\n1556 2343\n28790 43154\n31870 47786\n93591 100000\n98449 100000\n29811 44696\n90256 100000\n91502 100000\n11376 17129\n3421 5143\n42849 64201\n52230 78354\n11769 17706\n24280 36407\n51107 76680\n43730 65522\n94425 100000\n34584 51876\n20060 30087\n94080 100000\n62798 94212\n3348 5029\n34884 52320\n29148 43697\n50849 76283\n76783 100000\n37209 55783\n63114 94709\n88091 100000\n66070 99104\n93780 100000\n48889 73320\n43263 64830\n85058 100000\n35729 53578\n6292 9505\n733 1096\n63541 95334\n30211 45277\n35893 53824\n60704 91074\n82228 100000\n24435 36636\n2313 3475\n98834 100000\n39998 59939\n88445 100000\n60131 90225\n60345 90537\n25739 38596\n27877 41794\n43828 65671\n90951 100000\n85368 100000\n42042 63017\n41662 62448\n26306 39449\n40014 59960\n23545 35320\n64983 97484\n8963 13483\n79354 100000\n8644 13017\n22536 33817\n6466 9763\n57242 85875\n26406 39601\n73761 100000\n36561 54834\n68852 100000\n5573 8408\n44533 66742\n81668 100000\n56487 84720\n70032 100000\n79856 100000\n67744 100000\n9028 13586\n53051 79576\n23667 35510\n53910 80876\n84789 100000\n65037 97565\n96519 100000\n41296 61887\n66598 99899\n63764 95667\n4574 6880\n44516 66712\n44658 66928\n1446 2175\n73945 100000\n78159 100000\n57368 86070\n81441 100000\n4050 6079\n68918 100000\n43532 65227\n92322 100000\n13508 20285\n18721 28069\n95587 100000\n93286 100000\n83601 100000\n99153 100000\n6435 9719\n33898 50833\n32910 49358\n10059 15157\n29360 44017\n85471 100000\n31544 47291\n1332 2003\n54124 81195\n51396 77113\n8622 12987\n5193 7836\n5404 8155\n93877 100000\n47076 70594\n27925 41863\n48370 72533\n96409 100000\n53176 79772\n91082 100000\n46604 69881\n51511 77273\n24213 36310\n71373 100000\n64318 96496\n36917 55362\n21433 32139\n88810 100000\n57397 86113\n76687 100000\n73965 100000\n8012 12068\n49025 73523\n1860 2783\n46882 70305\n26383 39563\n27200 40770\n53642 80476\n84863 100000\n72397 100000\n48447 72651\n60197 90324\n10671 16072\n62649 93992\n97242 100000\n62498 93758\n77383 100000\n92667 100000\n85611 100000\n66447 99671\n50914 76386\n62309 93474\n87402 100000\n40495 60677\n1241 1867\n20530 30785\n12624 18997\n70130 100000\n31253 46852\n95488 100000\n28367 42523\n40637 60891\n94098 100000\n75197 100000\n48209 72296\n19820 29719\n53023 79534\n72343 100000\n36793 55180\n42926 64314\n63167 94792\n6118 9237\n18156 27213\n95557 100000\n72550 100000\n1557 2345\n74349 100000\n3935 5910\n62459 93699\n99787 100000\n1814 2715\n91088 100000\n14209 21324\n54312 81476\n61818 92742\n8131 12242\n87311 100000\n95358 100000\n12510 18828\n81133 100000\n2422 3635\n40447 60610\n55662 83475\n25608 38395\n21366 32035\n43599 65327\n50720 76082\n35424 53125\n33623 50427\n80152 100000\n96028 100000\n73068 100000\n87071 100000\n11350 17087\n15325 23000\n47644 71456\n56026 84023\n41963 62898\n63763 95666\n22326 33511\n31721 47563\n95501 100000\n73574 100000\n90259 100000\n82382 100000\n22149 33245\n76708 100000\n35395 53081\n16965 25445\n54184 81282\n75152 100000\n63066 94634\n21938 32922\n16983 25475\n3327 5001\n38531 57745\n6289 9500\n53397 80092\n36149 54209\n86861 100000\n49731 74594\n91051 100000\n70729 100000\n52812 79216\n11807 17759\n27934 41877\n10665 16061\n88430 100000\n78726 100000\n47926 71875\n49488 74221\n14966 22455\n81581 100000\n45471 68135\n6418 9693\n69261 100000\n98976 100000\n27505 41228\n62717 94090\n56126 84170\n62780 94186\n72287 100000\n79891 100000\n89571 100000\n90521 100000\n5454 8231\n58584 87881\n53309 79965\n74554 100000\n41399 62041\n91723 100000\n72711 100000\n76012 100000\n78589 100000\n54219 81334\n10017 15091\n64584 96887\n56191 84278\n5811 8763\n61701 92568\n61406 92133\n51245 76888\n86892 100000\n78809 100000\n6512 9840\n52773 79154\n30391 45539\n200 296\n3662 5497\n97507 100000\n9734 14644\n12757 19197\n85069 100000\n23108 34670\n85056 100000\n6684 10098\n20751 31116\n87507 100000\n86057 100000\n31990 47967\n77904 100000\n80844 100000\n25206 37790\n61629 92458\n53780 80683\n55460 83177\n9258 13926\n71459 100000\n51002 76526\n19849 29760\n6089 9196\n67628 100000\n47577 71351\n46790 70169\n73231 100000\n91091 100000\n62103 93170\n79236 100000\n58127 87209\n98155 100000\n98649 100000\n45265 67827\n43009 64441\n34908 52358\n40166 60191\n70413 100000\n15778 23673\n4187 6291\n35078 52605\n84282 100000\n11744 17673\n4269 6421\n31781 47651\n98595 100000\n46477 69689\n85590 100000\n4453 6703\n55850 83759\n9355 14072\n46285 69400\n14036 21065\n11452 17247\n1851 2772\n56287 84419\n69653 100000\n65192 97794\n80263 100000\n56482 84713\n958 1438\n10417 15690\n23898 35841\n64999 97509\n64462 96710\n93306 100000\n12952 19471\n67647 100000\n60300 90470\n48112 72145\n17045 25573\n16840 25256\n81256 100000\n28563 42819\n97769 100000\n37538 56270\n47811 71706\n77969 100000\n50803 76209\n60776 91171\n35111 52652\n24229 36334\n63587 95397\n43375 64991\n62905 94382\n64085 96146\n15859 23787\n46061 69049\n70034 100000\n50632 75938\n99187 100000\n7403 11156\n91308 100000\n59648 89494\n23806 35709\n86199 100000\n82882 100000\n81562 100000\n70282 100000\n93897 100000\n11912 17921\n54185 81283\n34096 51132\n53140 79716\n58917 88373\n76356 100000\n3566 5354\n59339 89025\n42027 62995\n75324 100000\n38223 57278\n84932 100000\n72605 100000\n27408 41076\n61502 92275\n75267 100000\n13541 20334\n77500 100000\n46143 69170\n75527 100000\n4227 6353\n25003 37485\n47496 71232\n16248 24383\n43782 65599\n29564 44328\n46328 69462\n90131 100000\n66990 100000\n76199 100000\n3392 5096\n95098 100000\n67232 100000\n3552 5331\n20086 30126\n77520 100000\n43428 65072\n7741 11673\n75801 100000\n8934 13440\n74635 100000\n18508 27735\n97404 100000\n49205 73786\n78505 100000\n74369 100000\n18930 28376\n6731 10169\n71369 100000\n69472 100000\n74678 100000\n84977 100000\n30743 46085\n88681 100000\n42395 63547\n18285 27401\n59552 89347\n47868 71788\n57856 86792\n97195 100000\n14615 21935\n43153 64655\n18836 28234\n41868 62755\n3117 4684\n61216 91845\n12647 19032\n12518 18840\n58518 87783\n70502 100000\n2538 3814\n43549 65253\n60979 91488\n87019 100000\n68816 100000\n51356 77057\n46138 69164\n2096 3143\n91563 100000\n80943 100000\n40811 61160\n77422 100000\n37390 56059\n65500 98250\n72947 100000\n27644 41442\n94982 100000\n89699 100000\n3058 4596\n70802 100000\n42176 63217\n83232 100000\n43673 65440\n44111 66100\n87764 100000\n85989 100000\n12716 19142\n24758 37114\n88177 100000\n24728 37073\n98253 100000\n3038 4568\n2111 3166\n74606 100000\n15506 23270\n94975 100000\n91468 100000\n10614 15986\n80359 100000\n94284 100000\n34126 51175\n50113 75155\n26433 39638\n62134 93218\n44017 65951\n34561 51839\n73307 100000\n33082 49629\n25041 37549\n72146 100000\n59107 88667\n62031 93061\n422 624\n33497 50244\n22005 33026\n11383 17140\n24255 36370\n54042 81074\n36244 54347\n20205 30306\n87147 100000\n82093 100000\n64220 96345\n92663 100000\n89616 100000\n27860 41769\n6579 9937\n82391 100000\n46415 69598\n89204 100000\n77655 100000\n16423 24650\n77119 100000\n39536 59229\n89585 100000\n27197 40764\n35953 53917\n12379 18629\n83736 100000\n10266 15465\n78313 100000\n56002 83986\n84569 100000\n43563 65272\n58494 87748\n47978 71945\n15145 22729\n41814 62671\n33350 50018\n46194 69247\n38552 57774\n33578 50360\n13650 20493\n48933 73386\n90499 100000\n90039 100000\n36933 55387\n49020 73513\n83938 100000\n79702 100000\n43411 65045\n88752 100000\n33631 50439\n83170 100000\n79331 100000\n21375 32048\n73581 100000\n37467 56165\n914 1372\n46362 69518\n67935 100000\n64180 96285\n25218 37807\n98320 100000\n61392 92110\n41043 61523\n13552 20353\n85293 100000\n97447 100000\n35406 53096\n71925 100000\n94393 100000\n4265 6415\n79297 100000\n41225 61786\n85877 100000\n6716 10146\n71911 100000\n43688 65460\n84066 100000\n66031 99045\n55572 83341\n89731 100000\n15525 23301\n33998 50986\n27376 41029\n38503 57704\n61716 92595\n45333 67931\n52291 78445\n406 597\n51674 77524\n35774 53647\n15250 22889\n49168 73731\n8477 12763\n67940 100000\n51176 76783\n43192 64718\n69210 100000\n85233 100000\n60643 90980\n35461 53177\n90576 100000\n87720 100000\n75948 100000\n72665 100000\n43335 64937\n39215 58752\n79012 100000\n17895 26845\n44871 67241\n17408 26117\n27893 41818\n52949 79419\n81331 100000\n39932 59838\n27336 40972\n28436 42626\n51073 76629\n5753 8673\n51340 77034\n94638 100000\n19844 29753\n90491 100000\n58097 87163\n62458 93698\n42536 63751\n31497 47223\n12738 19172\n51664 77507\n17151 25734\n19417 29111\n25980 38960\n66759 100000\n85899 100000\n48127 72168\n97946 100000\n88787 100000\n13939 20927\n92458 100000\n88281 100000\n85916 100000\n87394 100000\n90334 100000\n89536 100000\n1305 1964\n55479 83205\n87597 100000\n75667 100000\n59658 89510\n96828 100000\n72615 100000\n39030 58478\n51343 77040\n97065 100000\n97085 100000\n53068 79602\n65838 98745\n59688 89555\n60938 91425\n71939 100000\n45931 68846\n25284 37904\n42255 63335\n59312 88983\n95052 100000\n6569 9925\n96567 100000\n4503 6774\n80239 100000\n32647 48962\n29050 43554\n82026 100000\n62485 93741\n1158 1748\n25672 38490\n7104 10708\n84794 100000\n22924 34397\n53700 80564\n11451 17245\n17526 26295\n14906 22363\n73328 100000\n28445 42639\n94936 100000\n28075 42094\n2416 3626\n73381 100000\n14874 22314\n72725 100000\n46205 69264\n66420 99629\n10364 15612\n45198 67733\n56326 84481\n66978 100000\n64065 96119\n6033 9114\n10844 16334\n55139 82683\n8337 12543\n74235 100000\n63995 96017\n7802 11763\n90051 100000\n29153 43704\n41884 62781\n72680 100000\n76515 100000\n75571 100000\n23903 35849\n54789 82158\n15652 23493\n91626 100000\n44305 66390\n16843 25259\n30474 45675\n98220 100000\n74433 100000\n73664 100000\n19085 28621\n19276 28904\n13981 20986\n13208 19851\n67545 100000\n68532 100000\n62169 93267\n33083 49631\n23670 35514\n43286 64866\n1030 1548\n75853 100000\n88492 100000\n64055 96105\n3615 5429\n39230 58776\n26436 39642\n54345 81528\n33655 50478\n45595 68329\n71955 100000\n96192 100000\n65051 97582\n55458 83173\n76150 100000\n71672 100000\n62806 94226\n81991 100000\n83795 100000\n90998 100000\n26707 40044\n63373 95083\n3088 4641\n3325 4998\n52825 79234\n39035 58483\n96966 100000\n54505 81751\n21170 31740\n11003 16572\n84200 100000\n78170 100000\n32234 48335\n45450 68106\n50401 75594\n79604 100000\n16079 24127\n90241 100000\n64872 97317\n47206 70790\n59843 89790\n60900 91369\n88085 100000\n3494 5252\n89596 100000\n66477 99716\n23869 35798\n62469 93716\n57653 86491\n47635 71444\n79440 100000\n36980 55456\n9683 14562\n15669 23517\n46601 69876\n8916 13415\n41687 62485\n84275 100000\n57714 86587\n13633 20469\n22345 33539\n3207 4818\n64857 97291\n77070 100000\n85796 100000\n89037 100000\n46379 69544\n69768 100000\n651 974\n83506 100000\n52252 78388\n4153 6237\n93073 100000\n11971 18016\n410 605\n93567 100000\n94403 100000\n54631 81927\n45372 67992\n70411 100000\n29558 44319\n24188 36275\n5274 7960\n85123 100000\n7299 11002\n862 1294\n54691 82016\n86121 100000\n65811 98707\n65356 98034\n56522 84773\n3822 5736\n85414 100000\n1926 2878\n75175 100000\n24882 37305\n61677 92529\n55955 83920\n59758 89662\n74800 100000\n3469 5217\n15405 23121\n31985 47960\n78096 100000\n62521 93790\n37971 56905\n35241 52853\n54683 82004\n64859 97294\n25797 38681\n29507 44244\n43401 65029\n96572 100000\n7652 11532\n72706 100000\n89987 100000\n74131 100000\n30935 46382\n99968 100000\n80417 100000\n89361 100000\n62392 93603\n98353 100000\n18010 27004\n99989 100000\n28149 42202\n61553 92356\n48826 73224\n67276 100000\n3112 4677\n8942 13454\n34142 51199\n62426 93654\n65864 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11911\n89288 100000\n93701 100000\n59884 89849\n88447 100000\n5933 8959\n88731 100000\n46524 69761\n7448 11226\n76862 100000\n26037 39047\n93550 100000\n77203 100000\n95155 100000\n71238 100000\n45662 68441\n18326 27464\n96348 100000\n44768 67086\n38463 57641\n18075 27097\n28650 42947\n34340 51498\n78770 100000\n72065 100000\n41893 62795\n6364 9618\n15348 23039\n40312 60407\n97890 100000\n21561 32327\n42808 64138\n24619 36907\n23617 35432\n70315 100000\n58751 88129\n4511 6783\n48863 73282\n74529 100000\n40196 60235\n40944 61363\n78948 100000\n59930 89918\n55046 82534\n97273 100000\n43007 64438\n20840 31241\n95276 100000\n23828 35736\n58604 87909\n28605 42879\n36279 54404\n99130 100000\n69631 100000\n6693 10111\n54428 81639\n32016 48013\n60336 90522\n86901 100000\n46771 70137\n8280 12457\n25915 38861\n37431 56115\n35455 53167\n65133 97709\n38158 57180\n46054 69039\n12381 18631\n865 1300\n39826 59675\n61815 92738\n39478 59140\n97924 100000\n62414 93637\n10991 16553\n37627 56399\n78972 100000\n9 14\n25817 38714\n9306 14000\n14264 21402\n67905 100000\n14033 21061\n59798 89722\n54285 81434\n86640 100000\n33817 50716\n6620 9998\n59595 89415\n84728 100000\n14397 21612\n15041 22565\n79224 100000\n90595 100000\n52124 78195\n36603 54897\n32270 48390\n98384 100000\n51324 77008\n70482 100000\n32929 49387\n25141 37697\n98453 100000\n9072 13653\n71998 100000\n62302 93463\n30012 44996\n17201 25806\n3103 4661\n76036 100000\n87860 100000\n92511 100000\n9681 14559\n56221 84321\n14444 21680\n44672 66950\n67136 100000\n81523 100000\n85175 100000\n59317 88990\n46973 70442\n81854 100000\n75219 100000\n73982 100000\n4555 6853\n55628 83425\n88814 100000\n50764 76152\n14950 22431\n96005 100000\n45420 68062\n9404 14147\n77413 100000\n41782 62626\n63716 95590\n74734 100000\n98880 100000\n31312 46943\n48612 72911\n27162 40714\n35356 53020\n81272 100000\n52997 79492\n77011 100000\n60787 91185\n13616 20441\n56256 84369\n54328 81501\n73226 100000\n55637 83440\n39514 59196\n75891 100000\n13314 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6894\n5216 7868\n41429 62090\n35787 53664\n398 586\n59563 89364\n93145 100000\n69420 100000\n40498 60681\n35100 52635\n29362 44020\n3653 5484\n27757 41608\n81885 100000\n3847 5773\n48715 73062\n96871 100000\n24862 37273\n97122 100000\n13000 19546\n55646 83454\n23280 34928\n96662 100000\n84023 100000\n41226 61788\n42221 63284\n34510 51757\n85709 100000\n50259 75375\n32601 48896\n99101 100000\n57757 86649\n76238 100000\n54250 81381\n67356 100000\n59642 89485\n61286 91946\n93945 100000\n1048 1576\n26264 39389\n8651 13026\n44027 65969\n61141 91734\n20338 30493\n45576 68297\n17366 26054\n32241 48346\n93223 100000\n25263 37872\n42795 64121\n72263 100000\n83916 100000\n91421 100000\n37435 56120\n78894 100000\n49557 74332\n86193 100000\n1867 2794\n8760 13182\n66675 100000\n70306 100000\n92330 100000\n68327 100000\n94986 100000\n74390 100000\n43327 64925\n12972 19504\n37714 56525\n90793 100000\n58181 87284\n91481 100000\n38238 57302\n79092 100000\n72543 100000\n28986 43455\n20255 30377\n57212 85826\n30562 45814\n65521 98282\n15773 23666\n88393 100000\n33687 50525\n10697 16109\n25185 37759\n9144 13756\n28915 43351\n18292 27409\n52821 79229\n58126 87207\n76172 100000\n63352 95051\n41287 61873\n29561 44323\n77186 100000\n21843 32773\n13383 20112\n80693 100000\n98200 100000\n6318 9546\n56385 84565\n35102 52638\n52819 79225\n19587 29369\n51347 77046\n56228 84334\n69540 100000\n21323 31966\n39918 59816\n21966 32963\n82788 100000\n41309 61903\n41533 62251\n10895 16407\n1992 2983\n65555 98331\n78059 100000\n96732 100000\n75944 100000\n80831 100000\n99612 100000\n10054 15150\n94261 100000\n19635 29440\n34784 52178\n42886 64253\n75505 100000\n10030 15111\n68037 100000\n33579 50362\n93952 100000\n77481 100000\n44556 66780\n49985 74968\n76240 100000\n2188 3279\n97824 100000\n53452 80181\n86457 100000\n73309 100000\n626 936\n84735 100000\n98459 100000\n20827 31219\n53229 79851\n65732 98595\n80641 100000\n23530 35299\n50929 76409\n25693 38526\n30122 45154\n52509 78764\n96489 100000\n87305 100000\n88238 100000\n80822 100000\n74345 100000\n29140 43683\n19126 28682\n1898 2842\n13778 20684\n86849 100000\n65233 97852\n64082 96143\n94434 100000\n25433 38128\n86857 100000\n55088 82602\n2145 3215\n33231 49846\n88527 100000\n5435 8201\n77171 100000\n4152 6236\n7242 10919\n81106 100000\n27880 41799\n73137 100000\n60931 91414\n57340 86024\n86762 100000\n39601 59327\n11791 17734\n34767 52150\n97208 100000\n96035 100000\n18113 27150\n22978 34482\n63510 95289\n47018 70517\n16234 24361\n37699 56504\n35364 53033\n40243 60304\n87716 100000\n52791 79184\n17259 25892\n4926 7427\n39505 59181\n8904 13397\n67259 100000\n52915 79372\n60124 90214\n42281 63376\n92496 100000\n48002 71982\n4061 6092\n69649 100000\n66431 99645\n50287 75420\n33408 50108\n5411 8164\n8508 12811\n66817 100000\n37342 55988\n14522 21795\n94119 100000\n71917 100000\n61225 91860\n59242 88875\n60461 90711\n56696 85038\n49512 74259\n26183 39266\n69103 100000\n47304 70936\n2623 3938\n14167 21261\n81702 100000\n67014 100000\n75143 100000\n41903 62810\n93422 100000\n78486 100000\n39544 59241\n20114 30166\n56587 84879\n82839 100000\n78848 100000\n28582 42844\n20518 30767\n24051 36072\n820 1231\n23912 35866\n25703 38542\n53008 79510\n25122 37672\n41260 61834\n18044 27055\n72748 100000\n82336 100000\n73139 100000\n10028 15107\n85569 100000\n90123 100000\n44212 66245\n73237 100000\n30650 45941\n11508 17325\n59593 89412\n10104 15228\n8201 12344\n76743 100000\n40648 60908\n23076 34625\n27204 40777\n57562 86355\n54850 82253\n21498 32233\n94611 100000\n33624 50428\n7744 11678\n50563 75838\n2148 3221\n64823 97238\n62186 93289\n40403 60545\n98250 100000\n1390 2092\n3602 5410\n50264 75384\n54382 81576\n90794 100000\n58717 88079\n42445 63623\n41067 61558\n17885 26831\n18462 27665\n93387 100000\n35739 53596\n57827 86748\n11782 17721\n11481 17285\n12161 18309\n35860 53775\n20872 31288\n87184 100000\n15237 22870\n75469 100000\n9275 13952\n63506 95283\n80131 100000\n24419 36612\n51323 77006\n34801 52201\n98225 100000\n22099 33166\n98469 100000\n94361 100000\n64976 97474\n45004 67433\n48822 73218\n18016 27013\n83144 100000\n94161 100000\n95890 100000\n65961 98931\n60329 90512\n80168 100000\n14685 22039\n37632 56407\n75856 100000\n38181 57218\n29554 44314\n35029 52534\n44819 67158\n90466 100000\n90099 100000\n40322 60422\n45156 67669\n51711 77580\n78643 100000\n44001 65929\n80232 100000\n33710 50559\n70607 100000\n80527 100000\n4382 6589\n93717 100000\n38840 58192\n95139 100000\n29369 44029\n92819 100000\n49448 74159\n3183 4781\n15624 23451\n53429 80145\n66939 100000\n59066 88605\n29434 44134\n50386 75570\n89763 100000\n50211 75308\n22049 33095\n85425 100000\n56095 84123\n65824 98726\n90363 100000\n53744 80628\n5267 7947\n91276 100000\n85568 100000\n36253 54362\n4293 6456\n68969 100000\n95755 100000\n58566 87857\n98034 100000\n44946 67348\n64404 96623\n34558 51834\n99030 100000\n47031 70535\n22804 34217\n48348 72500\n98008 100000\n53908 80873\n71832 100000\n25465 38175\n76091 100000\n4361 6559\n7573 11413\n88977 100000\n52178 78274\n11506 17323\n48706 73051\n10992 16554\n7458 11242\n90523 100000\n34475 51702\n45574 68293\n13655 20500\n5607 8456\n20796 31179\n97245 100000\n99425 100000\n93636 100000\n34524 51782\n74977 100000\n15206 22825\n94831 100000\n5142 7755\n69337 100000\n71944 100000\n28095 42122\n55872 83794\n69465 100000\n93867 100000\n11645 17527\n69614 100000\n97488 100000\n22585 33891\n9517 14315\n62658 94005\n83175 100000\n17174 25767\n627 938\n67163 100000\n32853 49272\n41263 61838\n16272 24418\n47705 71548\n4634 6974\n96892 100000\n60636 90969\n38724 58016\n73116 100000\n20339 30494\n85436 100000\n81090 100000\n74188 100000\n14146 21229\n41618 62381\n10184 15345\n85166 100000\n81147 100000\n42738 64038\n43285 64864\n20506 30749\n34498 51739\n92641 100000\n42675 63952\n10124 15257\n56880 85322\n53254 79887\n73080 100000\n35250 52869\n63893 95864\n28826 43212\n97144 100000\n82546 100000\n14406 21624\n67480 100000\n27516 41248\n42629 63889\n48739 73098\n82817 100000\n37097 55621\n20381 30559\n27409 41077\n2860 4295\n52880 79318\n7311 11020\n83936 100000\n7783 11731\n39608 59338\n5813 8766\n83026 100000\n51968 77953\n65154 97739\n37378 56042\n21189 31768\n38701 57986\n47127 70669\n50676 76009\n33412 50114\n77573 100000\n18730 28083\n99146 100000\n92708 100000\n88790 100000\n23190 34791\n75069 100000\n59490 89249\n29407 44092\n4430 6668\n40721 61018\n68335 100000\n21046 31554\n39329 58919\n30825 46214\n52059 78094\n2290 3438\n14624 21949\n18934 28382\n5058 7629\n57842 86771\n50225 75326\n74033 100000\n39437 59079\n15821 23735\n94765 100000\n36547 54814\n49162 73720\n13145 19762\n72178 100000\n43822 65659\n93597 100000\n97521 100000\n15555 23345\n18662 27973\n39081 58546\n13842 20782\n72627 100000\n36682 55008\n96416 100000\n30828 46219\n93027 100000\n85745 100000\n83289 100000\n16856 25277\n72519 100000\n4481 6743\n223 330\n11141 16775\n56414 84608\n1535 2312\n15402 23115\n65831 98734\n49596 74393\n54539 81795\n39597 59321\n41886 62784\n65490 98234\n15816 23727\n14389 21602\n67292 100000\n66192 99283\n49330 73981\n24521 36762\n60021 90056\n46525 69763\n56061 84075\n56833 85248\n2525 3793\n3427 5153\n72174 100000\n90036 100000\n9394 14129\n60283 90445\n38969 58389\n98704 100000\n12552 18891\n38449 57622\n1210 1820\n98385 100000\n25354 38007\n1520 2289\n98076 100000\n47640 71451\n17231 25848\n5045 7609\n64719 97097\n19039 28549\n35191 52778\n70162 100000\n29019 43508\n1913 2861\n65311 97962\n89364 100000\n13949 20942\n39384 59003\n37181 55743\n34747 52121\n92369 100000\n14928 22396\n43603 65333\n64555 96847\n30817 46203\n58216 87341\n44620 66871\n14856 22287\n7842 11821\n52645 78970\n254 373\n13889 20857\n11990 18043\n33309 49957\n81630 100000\n99910 100000\n24018 36022\n48029 72024\n6652 10047\n",
        "output": "27\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 103,
        "task_id": 541,
        "test_case_id": 36,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n35632 53587\n17790 26804\n65225 97834\n81739 100000\n16536 24911\n27927 42050\n75467 100000\n36899 55496\n18352 27657\n32467 48888\n93531 100000\n39907 60031\n48270 72485\n91354 100000\n26835 40425\n97679 100000\n89570 100000\n22155 33397\n71374 100000\n75665 100000\n72651 100000\n12288 18486\n26600 40071\n82226 100000\n36983 55624\n58091 87142\n92323 100000\n69421 100000\n18821 28362\n78153 100000\n35359 53189\n33948 51114\n21180 31924\n65345 98007\n98108 100000\n37858 56944\n78018 100000\n95446 100000\n358 521\n37661 56632\n72975 100000\n16974 25567\n48092 72225\n7792 11704\n1215 1816\n84409 100000\n11904 17908\n61682 92541\n26633 40120\n89056 100000\n55238 82885\n72061 100000\n14962 22534\n61242 91886\n36358 54686\n56352 84537\n53789 80717\n47047 70684\n34175 51444\n20083 30247\n64816 97217\n94470 100000\n90909 100000\n46581 69975\n77314 100000\n88846 100000\n73789 100000\n67757 100000\n1800 2717\n5887 8847\n85322 100000\n70975 100000\n59088 88644\n64286 96419\n46225 69439\n61820 92740\n70885 100000\n19204 28927\n96359 100000\n49778 74742\n17023 25642\n34393 51764\n17218 25948\n20332 30612\n36349 54673\n41493 62406\n76037 100000\n983 1469\n82593 100000\n57222 85842\n59884 89843\n10178 15310\n97540 100000\n60162 90267\n24888 37523\n54960 82460\n70995 100000\n66569 99847\n26342 39684\n41344 62186\n13121 19766\n71058 100000\n14329 21563\n47592 71490\n77382 100000\n31986 48174\n90904 100000\n23771 35829\n56431 84656\n1017 1518\n7162 10761\n62075 93120\n25369 38233\n5856 8802\n11896 17895\n64068 96093\n62481 93720\n20134 30320\n5394 8098\n26530 39968\n6474 9723\n20925 31530\n71092 100000\n74925 100000\n68321 100000\n37197 55945\n94417 100000\n98326 100000\n62898 94329\n12754 19199\n40406 60773\n93291 100000\n24245 36540\n57993 86996\n33978 51154\n53920 80909\n36633 55104\n52404 78670\n99552 100000\n97418 100000\n45892 68937\n77054 100000\n71406 100000\n60992 91509\n84954 100000\n36651 55130\n43841 65888\n49449 74251\n76946 100000\n13303 20038\n47713 71665\n46287 69538\n25819 38925\n57585 86371\n99223 100000\n54326 81508\n80369 100000\n2627 3973\n41456 62352\n70364 100000\n5889 8851\n6979 10477\n99857 100000\n3997 6030\n42849 64412\n81571 100000\n29958 45131\n25040 37740\n16043 24174\n92385 100000\n72606 100000\n95244 100000\n45248 68000\n68450 100000\n37080 55770\n74078 100000\n27813 41882\n30177 45467\n74090 100000\n52553 78901\n15514 23374\n73078 100000\n18431 27775\n61584 92390\n38771 58325\n2356 3562\n46795 70291\n84864 100000\n55092 82659\n41684 62690\n87362 100000\n83922 100000\n82977 100000\n20692 31170\n66683 100000\n27432 41309\n4351 6561\n40083 60291\n12023 18082\n79056 100000\n34387 51755\n12985 19558\n63521 95270\n40015 60190\n89471 100000\n77621 100000\n38393 57765\n50805 76273\n81969 100000\n91310 100000\n23401 35262\n25356 38212\n41390 62256\n4312 6501\n6447 9684\n11064 16650\n85493 100000\n50176 75336\n67959 100000\n61536 92321\n51215 76876\n92710 100000\n56497 84756\n36998 55646\n502 742\n91908 100000\n24587 37050\n13671 20584\n41079 61787\n38127 57363\n65885 98809\n36694 55190\n67798 100000\n69013 100000\n68512 100000\n13341 20095\n66221 99328\n47952 72020\n55582 83410\n52954 79494\n51737 77668\n66498 99742\n34753 52293\n15346 23123\n85221 100000\n38772 58327\n57580 86364\n22550 33977\n87876 100000\n49049 73644\n19429 29262\n43113 64808\n79116 100000\n99016 100000\n44026 66169\n9388 14111\n29274 44084\n9215 13845\n70206 100000\n57768 86653\n67491 100000\n43802 65833\n87359 100000\n66940 100000\n7164 10764\n96234 100000\n9461 14221\n31320 47168\n88043 100000\n69896 100000\n34389 51759\n30225 45540\n429 633\n98426 100000\n68725 100000\n90100 100000\n81543 100000\n91521 100000\n75452 100000\n35885 53969\n27949 42079\n96680 100000\n2541 3843\n9310 13990\n86792 100000\n23170 34922\n8921 13401\n52477 78777\n8226 12356\n51216 76878\n18260 27516\n45197 67928\n89786 100000\n83308 100000\n25566 38532\n3941 5947\n62908 94342\n4494 6776\n54585 81900\n84063 100000\n45823 68838\n39739 59784\n54644 81982\n56335 84513\n96586 100000\n44174 66386\n34585 52043\n73000 100000\n77698 100000\n85961 100000\n74497 100000\n66405 99601\n42473 63864\n52022 78091\n69304 100000\n27332 41162\n4360 6574\n47474 71317\n27306 41123\n57083 85632\n94875 100000\n38659 58153\n98330 100000\n71787 100000\n34155 51413\n84819 100000\n70247 100000\n22082 33292\n72698 100000\n33542 50497\n71188 100000\n25101 37833\n77279 100000\n72948 100000\n4391 6620\n13849 20855\n4100 6186\n24875 37503\n81862 100000\n34953 52579\n11881 17873\n5315 7985\n58652 87965\n18081 27238\n95205 100000\n98185 100000\n9204 13828\n80223 100000\n2601 3934\n25410 38297\n66834 100000\n33958 51128\n20183 30394\n93910 100000\n29179 43944\n85847 100000\n17117 25789\n45064 67725\n59299 88959\n84140 100000\n17911 26984\n17381 26182\n20378 30682\n93027 100000\n47516 71380\n78397 100000\n31367 47240\n28914 43536\n96707 100000\n97046 100000\n47024 70648\n13052 19658\n10487 15770\n41670 62668\n7509 11286\n17436 26269\n32812 49404\n60224 90358\n28614 43082\n36081 54265\n95596 100000\n61004 91528\n35257 53036\n79139 100000\n96823 100000\n11803 17761\n2120 3208\n63573 95354\n25290 38111\n62289 93440\n48423 72711\n48530 72877\n52151 78287\n5864 8813\n24090 36312\n33055 49783\n58114 87176\n86826 100000\n47765 71741\n10501 15791\n40245 60524\n53043 79630\n67616 100000\n35694 53683\n24923 37575\n63316 94966\n45483 68342\n43361 65188\n72805 100000\n45235 67984\n81835 100000\n57583 86368\n48225 72422\n83769 100000\n41279 62089\n21818 32888\n50687 76093\n72307 100000\n39788 59859\n68681 100000\n28690 43197\n4286 6461\n25943 39106\n76151 100000\n60819 91257\n23112 34836\n48108 72244\n94952 100000\n87662 100000\n76803 100000\n25180 37945\n22261 33556\n92766 100000\n89967 100000\n43294 65086\n93373 100000\n87584 100000\n76675 100000\n65523 98288\n81821 100000\n49439 74238\n10795 16233\n97222 100000\n23678 35691\n25800 38897\n83237 100000\n34019 51215\n16256 24498\n39140 58884\n81815 100000\n31116 46856\n73928 100000\n48206 72390\n90110 100000\n70809 100000\n68101 100000\n25663 38689\n82578 100000\n67174 100000\n26937 40579\n37395 56237\n53262 79953\n3904 5887\n23339 35171\n339 490\n74343 100000\n69149 100000\n43095 64784\n19788 29795\n21891 33005\n52853 79339\n57809 86716\n3307 5002\n28122 42344\n61892 92852\n15957 24044\n71598 100000\n5960 8959\n6621 9934\n3273 4955\n34583 52041\n8124 12203\n64772 97151\n14110 21251\n88435 100000\n84641 100000\n99969 100000\n54239 81378\n94179 100000\n8176 12284\n51401 77148\n98655 100000\n34004 51192\n75773 100000\n14784 22255\n26407 39786\n72441 100000\n16450 24777\n23829 35918\n95564 100000\n14093 21223\n58874 88316\n24138 36384\n41414 62291\n41950 63085\n92401 100000\n8806 13230\n22126 33357\n21102 31804\n75672 100000\n92732 100000\n90248 100000\n56572 84863\n35663 53629\n44862 67426\n2215 3355\n52488 78793\n41545 62483\n26698 40217\n60899 91369\n98352 100000\n88815 100000\n83367 100000\n63090 94619\n2902 4399\n33380 50255\n27226 41007\n71513 100000\n43391 65234\n46965 70553\n30276 45615\n96381 100000\n22839 34407\n44931 67522\n92175 100000\n77321 100000\n83536 100000\n56988 85492\n59562 89356\n79692 100000\n40954 61591\n56033 84068\n36549 54973\n38062 57261\n94751 100000\n28536 42959\n6926 10395\n7887 11851\n90047 100000\n49653 74563\n62322 93490\n1961 2959\n8928 13412\n25711 38762\n98442 100000\n86066 100000\n2653 4010\n39353 59209\n95911 100000\n22146 33384\n66183 99274\n96636 100000\n83995 100000\n42135 63361\n83102 100000\n5770 8665\n26721 40251\n35123 52840\n14281 21491\n64386 96571\n16091 24248\n96852 100000\n31649 47662\n97988 100000\n29231 44018\n44217 66449\n56488 84743\n97542 100000\n5853 8797\n56074 84131\n55931 83913\n3042 4601\n49865 74870\n58032 87050\n38103 57328\n39644 59641\n79407 100000\n13429 20228\n12424 18689\n94899 100000\n75130 100000\n57118 85687\n99688 100000\n82203 100000\n14069 21189\n74770 100000\n74759 100000\n79917 100000\n93042 100000\n21029 31689\n70991 100000\n34133 51383\n27109 40828\n2484 3757\n45927 68986\n11485 17287\n78867 100000\n53482 80269\n1296 1944\n52335 78566\n88326 100000\n62352 93534\n76072 100000\n40624 61100\n97997 100000\n45003 67632\n39811 59891\n15570 23458\n14559 21916\n47365 71151\n1475 2218\n80577 100000\n36440 54809\n5234 7875\n53511 80310\n45828 68846\n59139 88719\n30522 45976\n85055 100000\n81826 100000\n64566 96839\n1747 2633\n31499 47443\n34703 52220\n98243 100000\n99160 100000\n22630 34091\n4705 7092\n96069 100000\n14297 21517\n4716 7110\n11869 17856\n48658 73060\n23685 35701\n54351 81547\n68409 100000\n40930 61557\n91535 100000\n59085 88639\n82675 100000\n5247 7888\n95690 100000\n75312 100000\n80381 100000\n88306 100000\n58818 88232\n95826 100000\n39403 59281\n4797 7234\n19798 29809\n78801 100000\n46675 70112\n34652 52146\n5693 8551\n51720 77639\n96314 100000\n45354 68157\n93682 100000\n15475 23313\n45274 68039\n48348 72604\n84461 100000\n96456 100000\n82926 100000\n58805 88214\n38937 58580\n76919 100000\n50756 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        "output": "29\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 104,
        "task_id": 541,
        "test_case_id": 37,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n22225 33389\n83449 100000\n64120 96171\n129 185\n16424 24662\n81015 100000\n46752 69997\n51906 77749\n93086 100000\n61300 91905\n4583 6921\n4591 6933\n87027 100000\n50230 75255\n76350 100000\n96066 100000\n17508 26288\n13293 20014\n47898 71725\n50164 75156\n38307 57346\n49123 73594\n19468 29254\n93321 100000\n97295 100000\n26472 39709\n73736 100000\n84136 100000\n71553 100000\n58134 87135\n88208 100000\n26315 39479\n9243 13905\n67355 100000\n36284 54330\n52964 79330\n76002 100000\n83653 100000\n68306 100000\n90958 100000\n2761 4179\n10496 15791\n90002 100000\n68378 100000\n97804 100000\n30068 45051\n96038 100000\n31674 47453\n55795 83590\n85945 100000\n8488 12766\n53152 79611\n45305 67821\n36134 54099\n82916 100000\n48026 71916\n26120 39185\n81271 100000\n12946 19491\n65403 98111\n24694 37058\n87473 100000\n99620 100000\n9565 14383\n8128 12232\n86815 100000\n9617 14459\n60786 91136\n79979 100000\n12303 18519\n90448 100000\n11230 16925\n50992 76398\n32638 48886\n66373 99553\n56509 84672\n36576 54773\n21271 31943\n70239 100000\n17467 26225\n50233 75259\n65358 98046\n99715 100000\n87983 100000\n26040 39065\n61316 91927\n96476 100000\n91163 100000\n67827 100000\n91512 100000\n79541 100000\n38992 58370\n58139 87144\n97412 100000\n82673 100000\n88527 100000\n59589 89340\n98191 100000\n42300 63350\n98757 100000\n16284 24459\n83128 100000\n36794 55094\n69736 100000\n94997 100000\n81651 100000\n1697 2549\n91789 100000\n38744 57982\n69135 100000\n85287 100000\n24007 36026\n33664 50444\n1531 2291\n96211 100000\n6805 10280\n14208 21386\n67309 100000\n16495 24771\n93527 100000\n25401 38101\n40787 61066\n52709 78946\n54198 81193\n93315 100000\n35772 53547\n32580 48795\n30908 46309\n54822 82125\n8358 12580\n45298 67813\n80951 100000\n39325 58863\n95534 100000\n71294 100000\n7929 11943\n98192 100000\n5817 8781\n48994 73395\n56998 85420\n46781 70040\n28225 42326\n37097 55541\n82054 100000\n12912 19438\n74487 100000\n5028 7588\n56142 84122\n42444 63566\n56944 85333\n76154 100000\n15489 23283\n2672 4045\n46718 69951\n98615 100000\n37030 55437\n48518 72668\n90442 100000\n92511 100000\n43045 64452\n94092 100000\n72867 100000\n41367 61943\n62232 93327\n61642 92426\n69695 100000\n64794 97189\n78490 100000\n81246 100000\n59195 88725\n89167 100000\n97632 100000\n14331 21568\n5638 8499\n83066 100000\n77177 100000\n19287 28981\n36255 54283\n69147 100000\n41576 62260\n42214 63222\n41168 61647\n36944 55310\n46304 69327\n10052 15123\n31138 46647\n98868 100000\n47867 71674\n7308 11011\n8771 13194\n39786 59547\n34081 51063\n55634 83351\n44035 65910\n12963 19515\n40374 60447\n70315 100000\n83018 100000\n41279 61818\n87015 100000\n48918 73285\n2798 4228\n81698 100000\n71133 100000\n31559 47276\n66258 99381\n73802 100000\n68832 100000\n24579 36885\n51037 76465\n21808 32752\n20561 30894\n81226 100000\n31721 47524\n14235 21424\n16998 25518\n42964 64335\n94454 100000\n19776 29703\n83206 100000\n5646 8511\n91060 100000\n71689 100000\n54361 81438\n47956 71809\n52708 78944\n476 711\n95108 100000\n22157 33279\n80959 100000\n82142 100000\n9749 14661\n83613 100000\n12101 18207\n54003 80900\n87570 100000\n53207 79689\n64454 96672\n48922 73290\n4718 7124\n70241 100000\n9646 14504\n27533 41282\n74298 100000\n38635 57826\n50138 75118\n74842 100000\n95873 100000\n1244 1864\n55711 83464\n71885 100000\n67017 100000\n34508 51694\n39941 59794\n77861 100000\n70296 100000\n72151 100000\n64965 97454\n42031 62942\n63705 95543\n540 807\n34760 52056\n18519 27800\n30732 46057\n49423 74058\n80603 100000\n94032 100000\n82192 100000\n59345 88961\n99553 100000\n31660 47429\n31867 47741\n77147 100000\n42133 63096\n17914 26893\n71007 100000\n71577 100000\n41971 62853\n60280 90374\n59989 89942\n47445 71042\n64119 96170\n36268 54303\n51362 76959\n59654 89436\n2160 3267\n92532 100000\n2488 3771\n32205 48236\n99342 100000\n79166 100000\n81473 100000\n30230 45296\n39478 59083\n84341 100000\n96782 100000\n59731 89557\n85583 100000\n64651 96971\n14128 21269\n74237 100000\n50869 76210\n51239 76773\n29092 43607\n78378 100000\n2108 3184\n51487 77143\n13394 20163\n39723 59447\n45332 67864\n19803 29745\n61002 91451\n1956 2954\n49554 74245\n36334 54404\n14478 21776\n82281 100000\n90508 100000\n1886 2848\n16714 25086\n35563 53247\n53758 80529\n29434 44108\n11218 16905\n11268 16980\n3514 5302\n95403 100000\n75033 100000\n86191 100000\n70460 100000\n2268 3432\n87793 100000\n9984 15018\n34440 51595\n60507 90721\n47977 71842\n49374 73977\n70329 100000\n65151 97739\n74162 100000\n52809 79103\n81924 100000\n34621 51849\n92079 100000\n66581 99873\n2660 4027\n97371 100000\n70677 100000\n41897 62749\n28567 42831\n79715 100000\n20945 31466\n49889 74757\n566 848\n73793 100000\n68720 100000\n93788 100000\n16143 24241\n3311 5006\n2378 3605\n57835 86679\n35001 52407\n84993 100000\n53468 80087\n48431 72540\n58685 87953\n11123 16754\n38944 58293\n3891 5858\n96218 100000\n87126 100000\n48072 71991\n84974 100000\n29276 43871\n46822 70099\n65426 98145\n54871 82196\n41353 61924\n95190 100000\n9474 14246\n40728 60976\n95058 100000\n37531 56183\n71738 100000\n25672 38515\n74458 100000\n4848 7321\n29116 43641\n10731 16155\n29536 44254\n5380 8120\n49098 73556\n84560 100000\n25780 38680\n81400 100000\n84344 100000\n51729 77491\n53764 80541\n33693 50480\n5730 8640\n1172 1758\n26432 39650\n85129 100000\n53335 79885\n76948 100000\n52368 78436\n46051 68938\n63075 94591\n70309 100000\n3157 4780\n19178 28816\n71348 100000\n41255 61783\n77551 100000\n76101 100000\n35430 53044\n32385 48499\n66248 99368\n59108 88592\n90165 100000\n42878 64204\n15562 23391\n84437 100000\n29779 44618\n92237 100000\n76731 100000\n55822 83632\n56255 84290\n84471 100000\n30529 45748\n55100 82542\n9134 13732\n45753 68495\n16919 25400\n55638 83358\n11999 18056\n34962 52353\n51591 77294\n98962 100000\n64262 96389\n36787 55084\n46116 69036\n31963 47885\n165 241\n59073 88537\n89850 100000\n29235 43807\n53203 79683\n15126 22747\n17116 25688\n21627 32485\n40598 60786\n42014 62915\n62997 94480\n15702 23594\n90810 100000\n22346 33564\n4290 6478\n68119 100000\n79720 100000\n97481 100000\n87623 100000\n24242 36374\n83210 100000\n49562 74255\n24901 37358\n58107 87093\n82465 100000\n37120 55575\n81823 100000\n33281 49862\n89615 100000\n89162 100000\n8645 13005\n31579 47302\n39288 58804\n44545 66681\n4590 6931\n72828 100000\n55009 82398\n32331 48424\n60109 90117\n58657 87909\n62170 93235\n66225 99335\n38368 57444\n94209 100000\n48329 72381\n3689 5556\n1867 2818\n69056 100000\n21876 32856\n9649 14508\n68640 100000\n22015 33061\n49543 74231\n16507 24789\n47015 70387\n92278 100000\n94781 100000\n67794 100000\n97137 100000\n20398 30651\n89049 100000\n16675 25025\n62249 93354\n11221 16910\n42641 63851\n24170 36273\n39629 59306\n91459 100000\n61629 92408\n5166 7802\n99436 100000\n58045 87000\n60496 90704\n17169 25773\n36419 54539\n11173 16838\n3429 5178\n80652 100000\n46027 68904\n73811 100000\n94321 100000\n58260 87322\n28666 42977\n27003 40476\n7159 10792\n24787 37184\n88597 100000\n26485 39726\n53597 80280\n67046 100000\n5751 8672\n97555 100000\n84713 100000\n78396 100000\n56204 84215\n70867 100000\n62444 93655\n92088 100000\n43099 64534\n83304 100000\n71266 100000\n1625 2435\n75189 100000\n96940 100000\n5853 8837\n99545 100000\n66470 99701\n53019 79412\n21478 32257\n69335 100000\n5080 7672\n28986 43448\n69140 100000\n65201 97816\n88040 100000\n93136 100000\n53968 80847\n6505 9818\n15280 22975\n7810 11763\n87625 100000\n38788 58056\n72366 100000\n21787 32719\n94939 100000\n77962 100000\n67758 100000\n8971 13494\n73722 100000\n9183 13810\n82543 100000\n46996 70357\n86277 100000\n78968 100000\n9590 14418\n79578 100000\n62089 93111\n28616 42906\n58230 87274\n76783 100000\n33654 50428\n56164 84155\n5269 7953\n9084 13648\n52875 79201\n18267 27426\n18036 27077\n87085 100000\n14223 21408\n57448 86091\n50145 75130\n2040 3080\n75321 100000\n59297 88886\n36501 54666\n79840 100000\n16354 24557\n70159 100000\n35199 52690\n47117 70540\n4994 7540\n95760 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        "output": "29\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 105,
        "task_id": 541,
        "test_case_id": 38,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n9660 14492\n39218 58792\n7097 10672\n471 721\n47512 71200\n29187 43767\n19659 29556\n59043 88558\n70154 100000\n47561 71275\n56682 85011\n52940 79344\n392 602\n63273 94906\n32157 48246\n2137 3205\n76159 100000\n89991 100000\n99644 100000\n66945 100000\n91481 100000\n3339 5038\n26852 40266\n72371 100000\n55470 83184\n81327 100000\n65427 98144\n23836 35763\n49766 74607\n4937 7429\n83337 100000\n68025 100000\n98872 100000\n1551 2348\n50174 75209\n15076 22687\n73917 100000\n13267 19922\n21137 31770\n25330 38008\n80239 100000\n66042 99079\n59106 88648\n16643 25026\n81516 100000\n47738 71544\n81903 100000\n24095 36160\n15318 23049\n60383 90590\n26442 39670\n71619 100000\n56247 84361\n87418 100000\n69485 100000\n64244 96356\n61510 92267\n46262 69361\n91177 100000\n93248 100000\n17196 25846\n5170 7772\n44284 66416\n86940 100000\n14073 21163\n33355 50012\n28495 42740\n29018 43526\n83503 100000\n22156 33273\n56321 84473\n30487 45735\n7182 10802\n73911 100000\n47021 70482\n2323 3495\n9881 14831\n7822 11749\n45182 67766\n22176 33305\n6224 9372\n77422 100000\n93966 100000\n70062 100000\n11340 17023\n88509 100000\n29476 44207\n86547 100000\n79695 100000\n45340 68005\n58039 87044\n30847 46289\n84591 100000\n23761 35651\n83831 100000\n28035 42046\n60144 90240\n29186 43766\n17099 25689\n16507 24826\n7040 10585\n13459 20222\n96199 100000\n38612 57899\n53392 80032\n3443 5196\n59679 89537\n56511 84757\n29711 44553\n43730 65596\n16455 24743\n88646 100000\n79069 100000\n23331 35011\n18249 27418\n9563 14349\n86866 100000\n91778 100000\n30308 45450\n87447 100000\n12405 18614\n15515 23344\n73813 100000\n91821 100000\n11983 17986\n94981 100000\n73624 100000\n32663 48993\n52832 79183\n43773 65655\n71523 100000\n70297 100000\n38708 58045\n64925 97378\n3480 5249\n49715 74525\n21409 32179\n32039 48070\n89521 100000\n97490 100000\n52270 78335\n29470 44197\n17764 26692\n41309 61967\n19869 29872\n18264 27441\n35118 52669\n44486 66716\n24542 36823\n11339 17021\n89347 100000\n71456 100000\n82302 100000\n3074 4640\n15847 23828\n12974 19474\n59401 89094\n61767 92652\n5427 8156\n59158 88733\n17572 26406\n86430 100000\n15423 23209\n93344 100000\n60859 91298\n34800 52197\n37023 55515\n14200 21351\n64612 96906\n62258 93394\n87313 100000\n2153 3232\n38466 57683\n85385 100000\n23165 34766\n48556 72773\n15895 23903\n83378 100000\n99504 100000\n84247 100000\n30121 45170\n6657 10014\n74555 100000\n88447 100000\n46257 69355\n18574 27913\n5948 8940\n71683 100000\n44379 66560\n11325 17000\n59201 88796\n15799 23760\n56927 85377\n59479 89224\n9842 14768\n22709 34085\n33331 49980\n63133 94709\n37550 56298\n15549 23397\n62295 93451\n16529 24854\n39349 58998\n23533 35308\n60086 90154\n74917 100000\n68849 100000\n15925 23945\n32983 49467\n54946 82380\n1956 2943\n95486 100000\n51542 77245\n38527 57779\n39828 59719\n73524 100000\n42789 64175\n24835 37266\n25639 38457\n23414 35138\n56089 84121\n19815 29793\n40260 60372\n59997 90021\n63140 94717\n90825 100000\n68250 100000\n58886 88322\n80749 100000\n32176 48272\n54468 81659\n5660 8508\n96849 100000\n77196 100000\n57331 85989\n20098 30210\n29624 44418\n84678 100000\n12668 19014\n64202 96293\n11775 17676\n10479 15724\n41038 61548\n54150 81161\n35614 53395\n10219 15339\n4611 6940\n96982 100000\n51172 76716\n33212 49807\n94708 100000\n77255 100000\n45860 68768\n81757 100000\n54085 81062\n26255 39392\n68732 100000\n74340 100000\n84287 100000\n27464 41185\n23569 35365\n39115 58630\n78363 100000\n38121 57162\n98381 100000\n78006 100000\n79792 100000\n55936 83886\n47029 70495\n64502 96735\n83576 100000\n31481 47232\n98226 100000\n1337 2027\n36295 54419\n97787 100000\n33901 50840\n86865 100000\n93084 100000\n57898 86828\n17287 25985\n35787 53653\n57660 86483\n90556 100000\n41406 62104\n30215 45315\n86962 100000\n84331 100000\n79208 100000\n35508 53241\n69570 100000\n27997 41986\n48533 72737\n26890 40317\n37822 56713\n22316 33501\n75401 100000\n34559 51827\n17888 26873\n48926 73335\n4097 6164\n76057 100000\n48181 72200\n83780 100000\n2792 4212\n66114 99192\n84435 100000\n92484 100000\n63808 95680\n42358 63534\n28968 43454\n81755 100000\n17469 26255\n9675 14517\n57882 86803\n92532 100000\n81435 100000\n85178 100000\n17087 25673\n27454 41170\n16267 24456\n13472 20241\n9101 13641\n77335 100000\n436 665\n22322 33510\n12168 18265\n37647 56452\n59601 89414\n84356 100000\n17054 25619\n28801 43200\n35683 53499\n69887 100000\n29022 43533\n92353 100000\n27393 41070\n56608 84903\n43904 65847\n56503 84745\n2248 3376\n66620 99942\n94197 100000\n15698 23617\n9743 14620\n85272 100000\n79920 100000\n75770 100000\n63935 95878\n35102 52643\n2619 3947\n20267 30467\n30358 45527\n28822 43234\n23425 35154\n41053 61572\n64872 97294\n86791 100000\n50191 75237\n23571 35369\n6991 10512\n93620 100000\n66592 99898\n25476 38223\n64915 97362\n88111 100000\n61194 91800\n51268 76856\n62822 94251\n32796 49193\n39574 59341\n63372 95047\n21672 32556\n59138 88700\n57338 86000\n42567 63845\n6427 9683\n70616 100000\n9129 13683\n27387 41059\n56473 84701\n22350 33548\n30422 45635\n41663 62493\n46056 69066\n81150 100000\n19115 28739\n52047 78012\n6989 10508\n97686 100000\n54670 81959\n63862 95768\n54460 81646\n36343 54493\n7698 11566\n42319 63476\n38040 57045\n68830 100000\n81669 100000\n61605 92409\n60166 90269\n39148 58679\n4009 6022\n96273 100000\n80243 100000\n61472 92215\n65187 97770\n78456 100000\n95790 100000\n28390 42578\n92017 100000\n81338 100000\n62781 94188\n10819 16228\n86455 100000\n75736 100000\n9908 14877\n62250 93383\n72567 100000\n56715 85059\n72889 100000\n8699 13053\n50212 75269\n42499 63744\n34314 51450\n46203 69273\n80522 100000\n94763 100000\n76361 100000\n87343 100000\n25719 38580\n73086 100000\n44398 66589\n33186 49766\n56440 84653\n12589 18888\n92358 100000\n53687 80461\n58882 88315\n6185 9313\n44305 66448\n52513 78701\n79975 100000\n39135 58659\n72212 100000\n99572 100000\n5709 8580\n27878 41811\n49193 73731\n35861 53767\n58053 87067\n96384 100000\n15611 23488\n48167 72178\n24976 37477\n93858 100000\n3482 5252\n76676 100000\n6833 10271\n75070 100000\n14199 21350\n1190 1800\n24109 36184\n13932 20948\n11750 17637\n35001 52498\n97935 100000\n28509 42761\n8183 12286\n47343 70967\n8907 13366\n33222 49820\n4908 7380\n69459 100000\n4693 7064\n63452 95162\n28779 43170\n27152 40705\n91900 100000\n42351 63521\n62915 94383\n25471 38216\n28868 43302\n30437 45662\n93639 100000\n37738 56586\n21877 32868\n80602 100000\n95454 100000\n22716 34094\n45797 68675\n12687 19043\n12845 19274\n68006 100000\n27670 41488\n94686 100000\n85683 100000\n34444 51654\n20799 31264\n89152 100000\n17566 26396\n14493 21787\n85747 100000\n41810 62722\n41058 61581\n55270 82883\n27060 40566\n82330 100000\n30459 45694\n98307 100000\n81187 100000\n96549 100000\n44671 66990\n25596 38392\n19772 29729\n629 963\n44416 66614\n35511 53246\n14631 22002\n66749 100000\n1842 2773\n62689 94047\n94477 100000\n58265 87391\n2396 3600\n97 152\n47688 71469\n73183 100000\n51690 77463\n54496 81696\n17958 26980\n79872 100000\n71902 100000\n59122 88675\n91663 100000\n14336 21557\n83667 100000\n94091 100000\n58593 87880\n89513 100000\n12394 18600\n42163 63244\n63116 94684\n77504 100000\n4224 6358\n46978 70415\n54958 82397\n79722 100000\n40297 60423\n98912 100000\n6731 10124\n97433 100000\n86044 100000\n36520 54755\n85892 100000\n92191 100000\n31052 46606\n58572 87850\n56054 84065\n20489 30794\n69425 100000\n4460 6713\n68101 100000\n86806 100000\n26107 39171\n76224 100000\n72662 100000\n86967 100000\n67072 100000\n59965 89974\n4202 6326\n73850 100000\n77696 100000\n45661 68483\n13398 20123\n30777 46189\n3242 4892\n82079 100000\n24201 36316\n64634 96940\n87509 100000\n51821 77667\n21411 32182\n94957 100000\n53348 79972\n40022 60009\n2834 4277\n64418 96612\n7670 11527\n79260 100000\n3462 5223\n91733 100000\n1023 1546\n44140 66205\n99168 100000\n23492 35247\n75885 100000\n15851 23835\n75680 100000\n96497 100000\n80865 100000\n91000 100000\n39098 58606\n97616 100000\n13613 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        "output": "25\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 106,
        "task_id": 541,
        "test_case_id": 39,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n28588 42741\n96186 100000\n94298 100000\n35373 52923\n6935 10339\n22035 32968\n78523 100000\n74473 100000\n82107 100000\n49423 74086\n31616 47308\n77702 100000\n70404 100000\n21162 31647\n73570 100000\n76159 100000\n49197 73743\n93680 100000\n76954 100000\n57003 85439\n74802 100000\n1821 2719\n69620 100000\n69106 100000\n61570 92344\n94918 100000\n44102 66091\n54720 82019\n69341 100000\n64180 96245\n49630 74401\n14695 21954\n45148 67632\n69926 100000\n66031 99041\n91612 100000\n48795 73128\n50185 75228\n31956 47819\n17904 26769\n5299 7890\n78419 100000\n66167 99248\n90078 100000\n18297 27350\n9918 14805\n92637 100000\n3369 5007\n41191 61740\n40118 60098\n13227 19780\n84388 100000\n33933 50762\n81349 100000\n87945 100000\n62478 93701\n53631 80398\n75342 100000\n14272 21323\n31332 46878\n96564 100000\n36655 54895\n42258 63323\n77781 100000\n47564 71291\n51680 77467\n26024 38949\n34493 51611\n84986 100000\n84903 100000\n75739 100000\n23575 35286\n83728 100000\n74123 100000\n27206 40713\n78558 100000\n70288 100000\n11608 17350\n9448 14094\n43502 65198\n76460 100000\n99900 100000\n40729 61039\n8024 11942\n9168 13670\n75794 100000\n12003 17958\n20821 31136\n11296 16863\n23299 34882\n8807 13130\n27775 41541\n83476 100000\n12095 18100\n7957 11847\n34733 51962\n44769 67055\n20021 29926\n26333 39422\n47492 71181\n77807 100000\n34270 51273\n63460 95173\n39522 59217\n202 300\n25512 38184\n62211 93316\n34062 50951\n69705 100000\n4251 6323\n66526 99784\n91464 100000\n59844 89720\n74625 100000\n77740 100000\n43140 64643\n61453 92173\n92883 100000\n47743 71554\n89408 100000\n76069 100000\n41839 62697\n29831 44620\n10112 15094\n95850 100000\n87594 100000\n80271 100000\n97812 100000\n88381 100000\n19445 29076\n76046 100000\n3032 4521\n54380 81517\n75835 100000\n99111 100000\n23543 35239\n68021 100000\n70542 100000\n31019 46405\n24302 36373\n38516 57697\n35365 52911\n49764 74600\n92676 100000\n50077 75072\n28852 43138\n69612 100000\n61332 91993\n15124 22594\n71043 100000\n76823 100000\n61422 92128\n65028 97513\n98249 100000\n72088 100000\n4735 7038\n52608 78859\n90068 100000\n75776 100000\n76433 100000\n86376 100000\n89238 100000\n1543 2301\n99371 100000\n88494 100000\n86872 100000\n74197 100000\n84750 100000\n10702 15963\n32027 47926\n71557 100000\n13602 20336\n51005 76460\n41454 62123\n96375 100000\n23895 35763\n10748 16034\n32248 48257\n52909 79329\n9892 14767\n21055 31483\n51538 77256\n54762 82083\n52529 78740\n21869 32723\n3622 5380\n27038 40459\n78058 100000\n40925 61338\n12731 19040\n8821 13151\n49435 74105\n9654 14401\n87094 100000\n569 852\n31855 47668\n69030 100000\n12233 18300\n72204 100000\n68621 100000\n67225 100000\n61443 92158\n45128 67605\n86156 100000\n35846 53655\n50243 75313\n81806 100000\n28039 41936\n24859 37210\n39740 59530\n28717 42939\n36579 54780\n10432 15580\n22554 33756\n28860 43153\n59312 88905\n84557 100000\n8139 12114\n10277 15330\n91951 100000\n92727 100000\n437 651\n70844 100000\n61799 92696\n19372 28973\n80667 100000\n61282 91911\n81790 100000\n12839 19202\n36336 54408\n96463 100000\n60073 90070\n4121 6125\n80419 100000\n78505 100000\n86731 100000\n37224 55747\n92710 100000\n56509 84705\n59555 89274\n96743 100000\n30605 45780\n4811 7154\n23763 35558\n93879 100000\n80855 100000\n50609 75851\n1007 1508\n40949 61374\n92882 100000\n42897 64276\n78131 100000\n98905 100000\n64139 96183\n53260 79847\n61480 92211\n50671 75949\n86070 100000\n22397 33524\n59781 89625\n15791 23606\n75460 100000\n84065 100000\n93259 100000\n20509 30665\n13448 20109\n75643 100000\n88049 100000\n89858 100000\n59286 88868\n19819 29637\n55543 83243\n72563 100000\n68572 100000\n57723 86525\n4127 6135\n39246 58786\n33453 50038\n6566 9784\n38586 57798\n19363 28959\n7592 11319\n48545 72752\n31439 47044\n33752 50489\n78013 100000\n24840 37185\n79365 100000\n79163 100000\n29429 44000\n72670 100000\n29661 44359\n66207 99308\n81825 100000\n94767 100000\n92314 100000\n6052 9018\n83577 100000\n9998 14925\n2975 4436\n12820 19175\n82484 100000\n9413 14039\n88281 100000\n44990 67392\n55152 82653\n15391 22993\n96709 100000\n90315 100000\n95065 100000\n63316 94963\n86334 100000\n4271 6351\n89120 100000\n88870 100000\n53286 79884\n24510 36696\n44356 66455\n64751 97094\n32428 48518\n64423 96609\n50336 75457\n89404 100000\n85134 100000\n89818 100000\n73788 100000\n29361 43899\n35142 52576\n79828 100000\n40183 60192\n51571 77306\n20018 29921\n16063 24017\n98722 100000\n5248 7815\n64925 97361\n46858 70224\n61649 92466\n39825 59660\n85252 100000\n4148 6169\n30508 45628\n84725 100000\n33285 49788\n25620 38345\n37129 55605\n41525 62232\n22014 32938\n62473 93693\n9150 13644\n91259 100000\n80077 100000\n11818 17673\n6922 10319\n66025 99032\n64739 97077\n9055 13505\n27294 40837\n40147 60141\n17311 25865\n87076 100000\n41458 62130\n70763 100000\n46555 69757\n45766 68569\n76995 100000\n3893 5783\n76770 100000\n94205 100000\n30242 45235\n77243 100000\n31381 46952\n23897 35766\n90399 100000\n11750 17571\n56763 85081\n35960 53828\n16106 24081\n34627 51803\n18662 27898\n62070 93107\n27608 41298\n87109 100000\n3615 5370\n9979 14895\n42529 63727\n54668 81938\n40470 60625\n12310 18416\n59581 89311\n99693 100000\n79793 100000\n20465 30597\n55174 82692\n90231 100000\n83029 100000\n93228 100000\n79771 100000\n50029 75002\n21143 31621\n5159 7682\n65800 98694\n12830 19188\n31940 47797\n74985 100000\n63861 95773\n58936 88340\n68773 100000\n60961 91421\n61317 91967\n57891 86773\n99565 100000\n82068 100000\n27352 40921\n75443 100000\n96432 100000\n26170 39174\n31087 46505\n8940 13333\n26032 38960\n24758 37062\n91447 100000\n54348 81468\n39229 58762\n64670 96976\n45684 68441\n73202 100000\n47899 71795\n27554 41216\n63960 95923\n15002 22417\n31947 47808\n57303 85875\n42241 63299\n34398 51474\n32471 48583\n44172 66198\n11755 17578\n15688 23450\n38300 57361\n75330 100000\n10394 15518\n84272 100000\n74337 100000\n68355 100000\n31365 46931\n47958 71886\n77969 100000\n43583 65319\n26806 40126\n77601 100000\n45115 67583\n3596 5342\n36095 54042\n84589 100000\n62360 93533\n28487 42600\n20745 31025\n54484 81670\n93158 100000\n603 900\n56143 84147\n4637 6894\n92920 100000\n99204 100000\n1095 1640\n57451 86106\n93005 100000\n45207 67726\n95235 100000\n54701 81990\n2906 4339\n79576 100000\n30890 46224\n42322 63414\n92629 100000\n34858 52143\n47928 71840\n91424 100000\n13304 19893\n72631 100000\n27782 41552\n9282 13840\n86659 100000\n32378 48444\n16093 24064\n43783 65615\n53946 80872\n33111 49532\n59061 88527\n66604 99904\n51984 77925\n90375 100000\n6909 10301\n86644 100000\n6209 9260\n26601 39821\n55671 83426\n2878 4296\n19725 29494\n64231 96317\n8455 12589\n94223 100000\n2446 3660\n40954 61382\n21728 32504\n76628 100000\n6359 9479\n76379 100000\n46874 70248\n52108 78103\n1182 1766\n75563 100000\n17243 25759\n77867 100000\n55338 82936\n14295 21358\n81772 100000\n67732 100000\n27408 41009\n25850 38692\n76068 100000\n74844 100000\n89756 100000\n55856 83711\n21405 32013\n31278 46794\n77133 100000\n83557 100000\n7748 11549\n87455 100000\n25644 38380\n41859 62725\n96090 100000\n3245 4835\n81768 100000\n23664 35419\n54636 81890\n17255 25779\n97725 100000\n33243 49725\n41046 61524\n2611 3907\n97015 100000\n3336 4959\n8118 12081\n20327 30388\n4425 6582\n14596 21803\n60909 91341\n69784 100000\n65326 97983\n97313 100000\n9356 13951\n84432 100000\n3409 5065\n37701 56469\n55196 82725\n98391 100000\n1631 2426\n53580 80321\n2331 3492\n87874 100000\n17215 25719\n88030 100000\n544 815\n84379 100000\n30784 46054\n40184 60193\n88614 100000\n63401 95082\n62170 93256\n5732 8534\n7716 11509\n52020 77971\n3918 5817\n20365 30447\n57123 85614\n53597 80348\n38143 57126\n30407 45476\n7702 11489\n98276 100000\n12274 18369\n25739 38522\n58531 87737\n31418 47008\n85878 100000\n79278 100000\n12982 19411\n45584 68286\n21965 32862\n69219 100000\n82829 100000\n25187 37697\n26080 39032\n10688 15942\n38323 57398\n38613 57838\n57743 86553\n47305 70904\n56725 85027\n46271 69323\n66628 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        "output": "28\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 107,
        "task_id": 541,
        "test_case_id": 40,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n58824 88280\n16745 25090\n56223 84348\n94625 100000\n2156 3231\n85280 100000\n69277 100000\n99070 100000\n34062 51160\n29198 43841\n92449 100000\n20025 30039\n78078 100000\n95191 100000\n59353 89067\n75547 100000\n20478 30739\n27639 41479\n55121 82689\n77849 100000\n37089 55657\n51940 77944\n15989 23940\n43296 65038\n54657 81983\n27536 41330\n87795 100000\n72712 100000\n84451 100000\n84985 100000\n44842 67333\n27105 40674\n60703 91068\n31457 47235\n71450 100000\n87671 100000\n42352 63610\n92255 100000\n38036 57082\n78372 100000\n6764 10156\n94454 100000\n92270 100000\n38575 57887\n94446 100000\n81626 100000\n96565 100000\n73904 100000\n36368 54579\n44653 67048\n29193 43832\n64521 96789\n22239 33406\n17339 26008\n15900 23805\n73114 100000\n91829 100000\n53135 79735\n83144 100000\n40206 60335\n15151 22681\n22145 33265\n71977 100000\n34244 51413\n67240 100000\n43081 64716\n1786 2682\n74685 100000\n51962 77981\n92068 100000\n56943 85429\n18024 27039\n36635 54975\n86749 100000\n61223 91840\n71560 100000\n74178 100000\n44323 66568\n41735 62676\n91664 100000\n90152 100000\n8257 12384\n99114 100000\n31685 47560\n31813 47763\n6320 9492\n94385 100000\n65609 98416\n41095 61692\n62703 94073\n44487 66807\n14880 22274\n26608 39919\n98083 100000\n63714 95567\n46483 69817\n86926 100000\n60609 90933\n90012 100000\n59663 89529\n6185 9293\n40209 60338\n47948 72011\n47314 71063\n53621 80463\n57170 85769\n51972 77997\n58014 87031\n39827 59775\n70230 100000\n96253 100000\n40078 60149\n65997 99005\n62749 94139\n21517 32292\n24103 36190\n22546 33858\n89832 100000\n1324 1965\n53482 80254\n45865 68863\n38089 57160\n68650 100000\n12227 18306\n26692 40046\n21670 32537\n93907 100000\n55119 82686\n84864 100000\n38296 57465\n69730 100000\n93331 100000\n30211 45356\n43095 64737\n5929 8912\n11929 17874\n78909 100000\n94074 100000\n60711 91079\n17472 26209\n251 382\n77578 100000\n32899 49390\n68770 100000\n19511 29283\n19194 28798\n10415 15571\n95452 100000\n94246 100000\n48393 72674\n45909 68933\n16715 25043\n41504 62324\n12191 18256\n81608 100000\n94372 100000\n43332 65093\n31709 47593\n19993 29990\n73581 100000\n53380 80087\n11020 16498\n69010 100000\n45899 68916\n7968 11954\n1316 1952\n83756 100000\n23931 35921\n44925 67462\n8467 12689\n16309 24424\n44460 66766\n25957 38926\n17247 25869\n49113 73758\n68632 100000\n30801 46249\n97510 100000\n25115 37703\n66824 100000\n31690 47567\n22133 33248\n94673 100000\n97686 100000\n97447 100000\n80877 100000\n2138 3201\n14977 22420\n3563 5364\n81897 100000\n62334 93513\n5714 8597\n16406 24563\n91767 100000\n36697 55063\n40393 60618\n56457 84709\n49275 73996\n96779 100000\n23507 35292\n95737 100000\n40171 60283\n52682 79059\n93856 100000\n7477 11234\n19645 29483\n60759 91150\n33540 50354\n40729 61134\n80973 100000\n47256 70979\n41721 62655\n28610 42956\n7192 10799\n76834 100000\n37880 56854\n43798 65775\n42331 63578\n12904 19339\n39346 59051\n12882 19304\n45310 68029\n15779 23628\n92725 100000\n3313 4982\n21958 32984\n68510 100000\n17680 26526\n34701 52098\n22452 33713\n36899 55368\n55912 83878\n16498 24708\n81078 100000\n16256 24340\n75522 100000\n80021 100000\n72186 100000\n5138 7719\n40620 60965\n73992 100000\n12626 18918\n63921 95875\n71569 100000\n77173 100000\n58666 88053\n93238 100000\n50110 75211\n32505 48803\n61994 92993\n90438 100000\n4600 6920\n97684 100000\n15816 23679\n34990 52530\n56825 85251\n56870 85315\n57889 86848\n18467 27715\n2361 3546\n27601 41423\n34773 52207\n9850 14732\n51812 77761\n93107 100000\n18076 27117\n76975 100000\n52734 79137\n36411 54641\n88367 100000\n29689 44562\n41843 62841\n41571 62424\n81742 100000\n16892 25318\n55946 83930\n74870 100000\n3669 5523\n15734 23555\n83050 100000\n94479 100000\n50071 75152\n82259 100000\n21202 31817\n26938 40417\n56624 84960\n81877 100000\n53006 79543\n93934 100000\n43564 65426\n63492 95235\n49267 73984\n29620 44459\n83856 100000\n71854 100000\n70093 100000\n49328 74067\n32434 48697\n4760 7158\n79346 100000\n35577 53406\n2186 3277\n73382 100000\n26590 39893\n99219 100000\n5053 7591\n4945 7433\n13469 20176\n94196 100000\n40219 60354\n55983 83988\n47400 71193\n78072 100000\n31598 47442\n76960 100000\n80874 100000\n39521 59316\n76908 100000\n72576 100000\n65475 98218\n48826 73324\n42474 63800\n43890 65915\n19147 28730\n36085 54158\n13870 20756\n23886 35850\n64549 96829\n70737 100000\n75113 100000\n46684 70118\n78765 100000\n40876 61362\n96244 100000\n74978 100000\n56244 84381\n28183 42313\n65546 98319\n5373 8075\n98555 100000\n26669 40010\n47688 71626\n70938 100000\n13629 20401\n76419 100000\n15176 22720\n59779 89707\n20816 31238\n36748 55136\n31134 46754\n25040 37594\n76397 100000\n39578 59404\n69787 100000\n86167 100000\n93983 100000\n93412 100000\n42524 63875\n78708 100000\n45151 67799\n89109 100000\n89134 100000\n45621 68497\n98698 100000\n77510 100000\n30432 45692\n47906 71951\n72461 100000\n51991 78024\n59994 90020\n31121 46736\n88988 100000\n13143 19690\n9480 14195\n81818 100000\n75190 100000\n71507 100000\n88734 100000\n35068 52648\n17689 26539\n20633 30970\n95986 100000\n50424 75676\n4301 6473\n63150 94733\n26578 39876\n87755 100000\n93011 100000\n75431 100000\n42387 63667\n19440 29173\n55792 83701\n12132 18172\n13039 19539\n35175 52804\n69196 100000\n23481 35252\n58055 87097\n2103 3148\n90299 100000\n66908 100000\n83279 100000\n32844 49309\n72397 100000\n3150 4735\n9094 13611\n21054 31597\n56249 84388\n95182 100000\n43906 65938\n64620 96931\n5297 7963\n67187 100000\n57946 86932\n49801 74765\n17251 25876\n45831 68809\n57373 86064\n35878 53852\n11676 17481\n13104 19635\n56123 84199\n40289 60461\n10976 16430\n14821 22188\n25378 38085\n62913 94377\n55595 83409\n4673 7027\n29624 44465\n46752 70217\n87148 100000\n56935 85417\n33412 50154\n13598 20361\n83776 100000\n57964 86959\n9538 14278\n62078 93127\n81983 100000\n69960 100000\n98823 100000\n95851 100000\n27590 41407\n85626 100000\n91046 100000\n45172 67828\n68320 100000\n50518 75812\n36568 54878\n42110 63237\n3212 4832\n2788 4187\n1094 1630\n30562 45891\n57451 86181\n61211 91820\n63831 95737\n94395 100000\n72857 100000\n76166 100000\n24012 36051\n66184 99286\n37051 55602\n66239 99367\n99979 100000\n68606 100000\n24651 37015\n56867 85311\n24489 36773\n61457 92192\n11133 16664\n11487 17193\n12995 19471\n56799 85209\n70378 100000\n83659 100000\n83598 100000\n83687 100000\n5142 7724\n21364 32063\n55612 83435\n67650 100000\n99877 100000\n19095 28650\n93583 100000\n93163 100000\n94609 100000\n68138 100000\n52707 79095\n68865 100000\n30838 46305\n73297 100000\n84801 100000\n42016 63099\n83743 100000\n12379 18541\n95547 100000\n14894 22296\n31157 46788\n5060 7603\n87215 100000\n57856 86797\n17629 26445\n3620 5449\n45490 68305\n57090 85655\n8487 12720\n60773 91174\n26970 40464\n40952 61471\n75492 100000\n46194 69359\n62120 93188\n3683 5543\n66919 100000\n14661 21944\n76295 100000\n88118 100000\n50900 76393\n543 819\n20115 30177\n24702 37092\n41503 62322\n45997 69063\n78554 100000\n49300 74026\n51613 77452\n66334 99503\n95029 100000\n23991 36018\n55644 83485\n22612 33957\n5184 7785\n24415 36653\n30543 45863\n60712 91080\n96030 100000\n23697 35567\n34069 51171\n12323 18454\n16240 24317\n36952 55451\n60772 91173\n57855 86796\n83554 100000\n92486 100000\n65079 97615\n97916 100000\n62371 93572\n54453 81695\n25522 38294\n35903 53890\n4937 7419\n15492 23209\n41562 62412\n27792 41716\n12258 18354\n78059 100000\n71350 100000\n99790 100000\n21072 31622\n10662 15950\n8508 12748\n35267 52946\n52626 78974\n17528 26291\n24218 36354\n9871 14766\n96634 100000\n60962 91450\n68696 100000\n71210 100000\n37109 55682\n17719 26586\n60698 91060\n82382 100000\n88827 100000\n1212 1802\n73135 100000\n4253 6398\n92988 100000\n45010 67594\n69393 100000\n35868 53836\n32011 48061\n33473 50246\n44382 66656\n60989 91488\n97582 100000\n7289 10946\n78948 100000\n49391 74154\n1486 2226\n81844 100000\n87071 100000\n71113 100000\n1283 1904\n69240 100000\n15042 22519\n16004 23962\n99805 100000\n16794 25161\n53227 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        "output": "28\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 108,
        "task_id": 541,
        "test_case_id": 41,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n60122 90186\n99323 100000\n89674 100000\n56831 85188\n86209 100000\n4662 7009\n51761 77564\n8055 12060\n37648 56294\n8591 12858\n15118 22631\n83256 100000\n12278 18417\n53679 80468\n33285 49758\n78279 100000\n21800 32593\n16845 25194\n92229 100000\n64886 97318\n76429 100000\n51552 77245\n81224 100000\n43168 64587\n80133 100000\n58985 88457\n76295 100000\n75656 100000\n10391 15591\n3340 5024\n36264 54214\n76784 100000\n82312 100000\n20955 31323\n85355 100000\n47079 70483\n14258 21362\n11664 17489\n90912 100000\n10801 16203\n82980 100000\n33149 49562\n1598 2421\n70462 100000\n88937 100000\n52784 79115\n44428 66487\n97659 100000\n34510 51594\n96031 100000\n8485 12700\n12507 18750\n76003 100000\n49937 74813\n8201 12280\n73102 100000\n18744 28039\n81988 100000\n37979 56798\n552 837\n8602 12876\n90533 100000\n23532 35191\n15915 23830\n66111 99177\n52833 79186\n19371 28959\n6225 9317\n31876 47662\n39534 59165\n8405 12583\n36324 54308\n22490 33616\n29363 43859\n94876 100000\n94454 100000\n94760 100000\n59241 88839\n85164 100000\n72122 100000\n64093 96129\n89962 100000\n76040 100000\n70336 100000\n91531 100000\n97531 100000\n92445 100000\n16875 25242\n44853 67117\n30012 44859\n36880 55138\n3219 4853\n90415 100000\n58018 87022\n76663 100000\n89595 100000\n17251 25811\n39015 58386\n74030 100000\n31695 47407\n76902 100000\n53418 80061\n1878 2826\n75777 100000\n61125 91687\n25282 37773\n17343 25949\n63967 95946\n48326 72369\n21535 32199\n5797 8679\n5306 7962\n69925 100000\n52013 77951\n60475 90721\n29421 43947\n57345 85990\n97204 100000\n10920 16377\n11675 17508\n6 10\n71883 100000\n92727 100000\n12745 19107\n28661 42820\n28949 43257\n21964 32830\n96497 100000\n45861 68647\n79062 100000\n6521 9748\n93388 100000\n94546 100000\n33060 49429\n88602 100000\n85123 100000\n38739 57968\n86886 100000\n89616 100000\n43481 65057\n96205 100000\n4735 7122\n28669 42832\n79932 100000\n87065 100000\n90647 100000\n97421 100000\n83692 100000\n3508 5281\n67384 100000\n5883 8803\n65924 98889\n27554 41166\n32594 48736\n6814 10192\n65264 97892\n34223 51154\n70724 100000\n37877 56646\n74781 100000\n17968 26893\n53870 80745\n2863 4315\n53973 80902\n21184 31672\n70228 100000\n68725 100000\n47917 71763\n17482 26155\n28546 42641\n16709 24995\n17589 26310\n3813 5737\n20910 31256\n93677 100000\n88604 100000\n72203 100000\n51861 77724\n53616 80368\n9610 14406\n39335 58880\n28923 43216\n59552 89324\n71045 100000\n80132 100000\n16342 24462\n39953 59796\n31022 46382\n67541 100000\n39862 59663\n92340 100000\n40052 59941\n1444 2186\n8780 13157\n94625 100000\n54288 81376\n91264 100000\n86985 100000\n26850 40120\n66839 100000\n32481 48563\n33612 50242\n67052 100000\n19528 29189\n69394 100000\n71905 100000\n87215 100000\n21222 31728\n1329 2017\n61239 91873\n43297 64784\n35767 53469\n44432 66495\n25666 38341\n44286 66276\n43678 65362\n8314 12445\n77111 100000\n4124 6206\n48518 72655\n31223 46681\n18842 28182\n69982 100000\n12145 18218\n88059 100000\n92406 100000\n4448 6684\n87978 100000\n26319 39344\n73897 100000\n1198 1824\n87233 100000\n52941 79344\n49734 74513\n92478 100000\n90908 100000\n38520 57632\n65527 98289\n61228 91853\n70328 100000\n39 54\n40394 60456\n38386 57426\n13765 20615\n27769 41488\n9498 14246\n9538 14301\n49618 74339\n93355 100000\n42277 63258\n6338 9488\n88517 100000\n52809 79152\n42509 63601\n38752 57989\n99056 100000\n54726 82045\n81774 100000\n83584 100000\n49684 74436\n64329 96482\n59335 88980\n90714 100000\n63466 95197\n95447 100000\n6046 9051\n79541 100000\n90917 100000\n70230 100000\n46215 69183\n60833 91252\n45933 68760\n48118 72061\n74324 100000\n98484 100000\n72826 100000\n41694 62387\n38282 57267\n20139 30118\n40793 61052\n28823 43068\n6882 10293\n46175 69123\n62120 93202\n58757 88126\n18011 26959\n34420 51444\n50273 75317\n20863 31190\n66558 99865\n21883 32711\n79583 100000\n61235 91865\n10627 15944\n9835 14755\n3676 5526\n75722 100000\n73027 100000\n68454 100000\n33413 49944\n21851 32667\n81356 100000\n72864 100000\n30135 45036\n34012 50831\n98740 100000\n8096 12121\n37139 55535\n3055 4605\n45285 67776\n73831 100000\n60776 91165\n23248 34766\n10642 15967\n82830 100000\n36752 54939\n3872 5830\n9589 14376\n99497 100000\n12546 18812\n68346 100000\n24617 36798\n66214 99337\n96246 100000\n91353 100000\n93774 100000\n38493 57590\n45750 68476\n63810 95705\n70096 100000\n43393 64925\n17676 26445\n99884 100000\n39784 59547\n74594 100000\n56315 84420\n10033 15052\n83629 100000\n47699 71429\n74743 100000\n4347 6535\n30282 45264\n32602 48746\n14778 22121\n29357 43852\n13520 20260\n76244 100000\n23813 35611\n90199 100000\n30757 45984\n35659 53306\n92290 100000\n7856 11758\n3037 4573\n84432 100000\n68360 100000\n69362 100000\n55687 83483\n57336 85977\n78511 100000\n34808 52040\n72125 100000\n95617 100000\n87812 100000\n32178 48120\n92545 100000\n67568 100000\n79459 100000\n20357 30442\n5773 8648\n67271 100000\n3245 4893\n14445 21637\n25532 38146\n4140 6232\n34133 51015\n59974 89960\n76524 100000\n76225 100000\n46662 69869\n8215 12298\n24354 36414\n91317 100000\n45119 67521\n1234 1877\n48520 72658\n8255 12354\n44818 67064\n79809 100000\n67939 100000\n87357 100000\n83577 100000\n29727 44424\n58346 87517\n86178 100000\n65251 97875\n93256 100000\n76544 100000\n92047 100000\n78137 100000\n46645 69842\n72208 100000\n21249 31768\n66730 100000\n81547 100000\n65183 97768\n66793 100000\n85370 100000\n27133 40548\n27394 40930\n29198 43621\n33735 50420\n59940 89905\n15772 23619\n16789 25111\n97737 100000\n97783 100000\n53388 80015\n90244 100000\n28689 42865\n88480 100000\n52398 78536\n82339 100000\n47439 71044\n12750 19113\n66360 99554\n27653 41319\n89874 100000\n20358 30443\n18536 27731\n72186 100000\n32391 48435\n56380 84521\n83032 100000\n17472 26140\n57756 86625\n13253 19858\n59110 88640\n67529 100000\n80678 100000\n48746 73002\n96196 100000\n23162 34632\n23485 35127\n38132 57035\n62155 93256\n10523 15787\n7907 11838\n16434 24594\n47065 70462\n58420 87631\n7115 10641\n40222 60196\n73985 100000\n55327 82943\n35142 52529\n70473 100000\n96437 100000\n66773 100000\n80844 100000\n84586 100000\n18098 27084\n74292 100000\n87702 100000\n63480 95216\n34374 51377\n75013 100000\n33594 50217\n89517 100000\n56059 84039\n88034 100000\n42871 64144\n65821 98732\n38064 56933\n93 142\n437 660\n61802 92709\n27213 40658\n19014 28433\n30896 46187\n71173 100000\n4399 6612\n45850 68632\n51186 76684\n16890 25265\n63302 94955\n40386 60443\n93547 100000\n95122 100000\n45000 67339\n15919 23834\n19313 28876\n36093 53964\n47934 71787\n24378 36445\n87006 100000\n5990 8966\n97505 100000\n89913 100000\n37145 55545\n70134 100000\n22775 34056\n9327 13995\n43537 65142\n60704 91059\n30677 45856\n71755 100000\n52867 79235\n66581 99901\n94916 100000\n28222 42179\n92688 100000\n72471 100000\n66756 100000\n90881 100000\n87051 100000\n90794 100000\n79868 100000\n40075 59976\n52411 78552\n37055 55408\n83096 100000\n41806 62549\n89414 100000\n2533 3818\n43633 65296\n11628 17432\n32880 49157\n51909 77791\n40065 59960\n20637 30864\n72632 100000\n8671 12988\n71153 100000\n27338 40846\n56621 84881\n56948 85373\n49696 74455\n94574 100000\n21318 31864\n18546 27744\n23292 34828\n46626 69810\n90368 100000\n971 1480\n86361 100000\n39771 59525\n9350 14030\n91758 100000\n85802 100000\n58368 87550\n65904 98856\n18712 27992\n8832 13235\n12692 19026\n82912 100000\n40171 60122\n94834 100000\n72691 100000\n22852 34164\n19025 28444\n49483 74133\n77579 100000\n46453 69552\n17426 26073\n78440 100000\n14384 21543\n40750 60986\n90362 100000\n35027 52363\n65447 98168\n22485 33608\n7825 11712\n37878 56648\n60614 90924\n29180 43597\n26477 39579\n86199 100000\n23995 35888\n23815 35615\n86852 100000\n27704 41386\n36897 55165\n64877 97304\n7908 11839\n3066 4621\n24056 35981\n22042 32945\n35443 52985\n78606 100000\n72201 100000\n2194 3309\n90643 100000\n89778 100000\n88656 100000\n18037 26997\n23431 35038\n13127 19671\n84809 100000\n1696 2563\n40675 60875\n3472 5230\n90315 100000\n7509 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        "output": "27\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 109,
        "task_id": 541,
        "test_case_id": 42,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n63169 94766\n37030 55574\n8244 12290\n6558 9767\n87180 100000\n41257 61967\n9000 13418\n43002 64594\n54118 81241\n98127 100000\n57276 85995\n66711 100000\n28262 42342\n57991 87058\n77584 100000\n37651 56504\n95083 100000\n97210 100000\n41652 62560\n73522 100000\n65523 98283\n55531 83367\n15053 22471\n61784 92709\n41010 61587\n27099 40589\n75605 100000\n63769 95662\n60328 90537\n49259 73985\n40168 60304\n24748 37045\n58512 87840\n52778 79224\n21334 31934\n46852 70360\n56648 85052\n30994 46479\n53534 80347\n17589 26287\n4101 6118\n40420 60689\n94597 100000\n46209 69382\n80065 100000\n62318 93521\n38015 57053\n64059 96097\n24433 36561\n64793 97199\n16400 24501\n17468 26112\n36237 54398\n30362 45523\n14444 21570\n31944 47897\n65593 98386\n77844 100000\n15615 23333\n41590 62468\n68756 100000\n26488 39663\n55386 83145\n54745 82174\n61342 92051\n13227 19771\n43639 65544\n78379 100000\n10249 15279\n78389 100000\n71753 100000\n72907 100000\n22580 33801\n23984 35895\n24759 37061\n73079 100000\n10395 15491\n79670 100000\n54 78\n66649 99954\n85456 100000\n18188 27187\n42766 64236\n8071 12032\n18195 27195\n48611 73004\n90218 100000\n28063 42038\n7412 11063\n8486 12645\n84002 100000\n76832 100000\n72572 100000\n70161 100000\n31876 47791\n35748 53654\n5731 8543\n58513 87842\n82392 100000\n73016 100000\n41704 62637\n11231 16759\n90083 100000\n29851 44734\n49398 74199\n78328 100000\n84629 100000\n65202 97805\n37363 56069\n41880 62900\n31570 47347\n55261 82950\n52924 79445\n13260 19820\n97419 100000\n90699 100000\n41792 62768\n6457 9618\n55338 83071\n75293 100000\n12237 18285\n91938 100000\n22302 33397\n82333 100000\n24755 37055\n93950 100000\n67788 100000\n40769 61222\n41550 62412\n12766 19091\n37054 55610\n24620 36846\n48621 73019\n18385 27478\n99490 100000\n52269 78475\n95154 100000\n46609 69992\n67333 100000\n44645 67039\n15140 22603\n18208 27216\n51919 77960\n83711 100000\n2252 3354\n79336 100000\n83365 100000\n43597 65480\n67938 100000\n43014 64613\n52674 79073\n82699 100000\n49670 74607\n65389 98085\n88470 100000\n4386 6550\n68460 100000\n33419 50145\n77722 100000\n16165 24146\n92247 100000\n92615 100000\n83352 100000\n52196 78369\n39287 58998\n641 942\n46954 70510\n10572 15751\n2419 3597\n26440 39586\n50277 75503\n49558 74432\n79157 100000\n14496 21643\n70391 100000\n99571 100000\n61373 92091\n46064 69160\n22208 33258\n51758 77719\n17544 26222\n12718 19017\n1429 2128\n6410 9540\n33946 50930\n36111 54212\n54720 82137\n99867 100000\n35777 53698\n13681 20444\n14037 20972\n79245 100000\n55930 83978\n5703 8504\n49543 74411\n70633 100000\n88442 100000\n25599 38327\n17198 25700\n62514 93805\n22395 33536\n17865 26687\n69659 100000\n36505 54784\n80312 100000\n34732 52127\n81739 100000\n54656 82041\n81970 100000\n97466 100000\n47905 71961\n84737 100000\n38982 58544\n74855 100000\n86602 100000\n49880 74924\n45808 68782\n69822 100000\n29179 43732\n17507 26171\n93930 100000\n74193 100000\n45910 68931\n63528 95300\n71015 100000\n25931 38813\n66109 99144\n58320 87554\n68550 100000\n39314 59039\n90316 100000\n4090 6098\n10504 15650\n11251 16788\n69761 100000\n38104 57185\n54455 81736\n98257 100000\n94811 100000\n47652 71587\n22317 33421\n59683 89586\n13949 20837\n36216 54367\n6182 9203\n90858 100000\n58032 87119\n4467 6668\n61482 92259\n64704 97071\n61567 92388\n46775 70243\n81587 100000\n94963 100000\n52556 78891\n89147 100000\n91436 100000\n58443 87732\n71610 100000\n9281 13846\n2590 3858\n56545 84896\n36372 54593\n82662 100000\n20472 30651\n24586 36794\n40965 61518\n90639 100000\n22908 34277\n59027 88613\n714 1054\n73748 100000\n37793 56714\n23201 34716\n52228 78414\n69742 100000\n45405 68175\n12951 19353\n66504 99737\n36342 54551\n80770 100000\n79122 100000\n14042 20979\n35776 53696\n21178 31708\n813 1201\n34813 52245\n3538 5268\n17431 26052\n79910 100000\n71574 100000\n24440 36572\n71505 100000\n20253 30319\n98689 100000\n73640 100000\n65312 97971\n85519 100000\n7139 10642\n23731 35516\n30139 45174\n27370 40994\n85796 100000\n60974 91508\n40032 60107\n26203 39226\n29881 44781\n29198 43760\n39510 59342\n29754 44593\n1731 2580\n97508 100000\n8504 12672\n43040 64654\n60394 90638\n51101 76743\n10298 15351\n10770 16066\n90058 100000\n19522 29211\n77093 100000\n94712 100000\n90522 100000\n55215 82873\n3549 5283\n16725 24986\n63628 95448\n27541 41263\n70743 100000\n47463 71291\n16160 24138\n7150 10657\n61142 91761\n6759 10059\n77282 100000\n15748 23530\n34200 51312\n20299 30398\n43601 65487\n22698 33976\n29821 44693\n14424 21544\n1859 2767\n68022 100000\n72029 100000\n19358 28960\n94368 100000\n94840 100000\n18627 27835\n34205 51320\n2624 3911\n36020 54068\n39405 59183\n69277 100000\n95966 100000\n53518 80324\n89990 100000\n53399 80148\n44493 66820\n60728 91139\n81507 100000\n14471 21611\n53442 80215\n97043 100000\n6896 10269\n38080 57150\n37106 55685\n11038 16475\n96623 100000\n59864 89853\n39535 59378\n17949 26820\n40363 60600\n30693 46030\n73551 100000\n51539 77402\n20876 31264\n40101 60205\n24961 37372\n30728 46078\n5102 7626\n20315 30424\n3458 5140\n24325 36404\n85768 100000\n2011 2986\n75248 100000\n71182 100000\n82567 100000\n74146 100000\n57847 86841\n22488 33672\n53763 80694\n36158 54280\n9059 13504\n15686 23440\n31735 47587\n65592 98385\n83363 100000\n52245 78439\n62206 93348\n52076 78189\n16152 24127\n32604 48902\n88202 100000\n48714 73166\n7860 11712\n44316 66551\n19282 28845\n84509 100000\n53319 80029\n72240 100000\n72254 100000\n81046 100000\n33199 49813\n45253 67950\n38771 58217\n17059 25482\n32628 48937\n58107 87233\n9039 13475\n34962 52465\n66757 100000\n55350 83090\n32257 48369\n80526 100000\n78287 100000\n65739 98600\n60330 90540\n47767 71763\n9778 14580\n73571 100000\n31936 47886\n78719 100000\n50935 76493\n49877 74920\n38427 57692\n82866 100000\n20415 30578\n11982 17895\n4096 6110\n38877 58390\n58563 87921\n56102 84231\n65086 97639\n42778 64253\n64126 96200\n42111 63243\n8983 13391\n17018 25422\n35504 53282\n74531 100000\n12802 19139\n73999 100000\n3867 5771\n82855 100000\n73648 100000\n98448 100000\n42001 63078\n53079 79664\n94994 100000\n3073 4570\n72839 100000\n89954 100000\n39636 59530\n71253 100000\n75396 100000\n92195 100000\n58253 87450\n17953 26827\n11453 17099\n46426 69713\n1787 2662\n93886 100000\n52703 79120\n14483 21627\n82314 100000\n59636 89517\n12815 19156\n36138 54251\n50617 76036\n75910 100000\n56273 84484\n30681 46016\n39260 58952\n78842 100000\n50898 76440\n27839 41707\n68444 100000\n78820 100000\n17914 26766\n11208 16723\n33822 50750\n53347 80073\n25807 38633\n79792 100000\n34423 51642\n17067 25495\n172 245\n39369 59125\n59327 89057\n53898 80904\n22232 33291\n90193 100000\n87212 100000\n71696 100000\n5284 7897\n38990 58556\n18939 28317\n48775 73254\n86165 100000\n78092 100000\n79097 100000\n43955 66015\n97977 100000\n16552 24725\n70972 100000\n78755 100000\n49313 74069\n79679 100000\n63887 95843\n56524 84865\n38012 57049\n35983 54012\n27581 41323\n50555 75942\n58243 87434\n67910 100000\n28226 42290\n68834 100000\n27438 41099\n40289 60491\n92737 100000\n65897 98833\n72436 100000\n83292 100000\n51308 77059\n43643 65550\n36579 54892\n85840 100000\n5995 8926\n1485 2217\n14595 21792\n4945 7388\n11156 16649\n58657 88067\n62086 93163\n31202 46788\n62572 93893\n21751 32568\n77664 100000\n3520 5240\n48623 73022\n3437 5110\n55445 83232\n48191 72390\n47640 71568\n20364 30498\n87152 100000\n96450 100000\n18937 28314\n55596 83470\n90227 100000\n44363 66624\n61414 92153\n85529 100000\n81700 100000\n8024 11961\n30747 46110\n44098 66229\n79148 100000\n69422 100000\n68042 100000\n69725 100000\n87392 100000\n71230 100000\n10505 15651\n78709 100000\n77723 100000\n6304 9381\n6604 9832\n60233 90403\n1444 2151\n57066 85678\n53096 79687\n39342 59080\n72929 100000\n14701 21950\n25831 38668\n89746 100000\n27130 40635\n84594 100000\n98457 100000\n29707 44522\n26099 39068\n32495 48740\n76663 100000\n99881 100000\n94216 100000\n17429 26049\n57832 86817\n91149 100000\n72591 100000\n89846 100000\n27695 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        "output": "31\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 110,
        "task_id": 541,
        "test_case_id": 43,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n43331 65130\n12383 18654\n95189 100000\n91847 100000\n56724 85091\n39838 59928\n34530 51938\n11661 17570\n68896 100000\n28295 42626\n28382 42755\n26156 39397\n5361 8052\n71032 100000\n66624 99968\n75130 100000\n6862 10307\n91029 100000\n89904 100000\n2259 3422\n23555 35519\n26003 39163\n17552 26451\n61445 92150\n504 771\n27700 41721\n66619 99961\n81065 100000\n11919 17962\n97145 100000\n19200 28925\n23921 36058\n98736 100000\n99926 100000\n39104 58820\n66763 100000\n27834 41922\n50 80\n35041 52710\n71289 100000\n97156 100000\n46198 69400\n93037 100000\n30977 46658\n76702 100000\n40095 60307\n49932 74942\n14565 21954\n87018 100000\n39940 60079\n78127 100000\n78225 100000\n5227 7846\n40335 60662\n89137 100000\n17285 26064\n99286 100000\n82012 100000\n29486 44408\n91770 100000\n74281 100000\n77528 100000\n24811 37386\n28269 42585\n26797 40358\n86949 100000\n56470 84707\n48148 72305\n49892 74887\n91432 100000\n19916 30035\n5924 8901\n21651 32637\n82013 100000\n93224 100000\n69211 100000\n22315 33644\n4274 6418\n32256 48570\n77672 100000\n83805 100000\n41992 63135\n33730 50748\n73557 100000\n24916 37545\n16096 24258\n24946 37590\n47613 71487\n72482 100000\n18473 27831\n88910 100000\n2023 3078\n91610 100000\n63932 95886\n61580 92349\n27588 41550\n89982 100000\n36268 54545\n32996 49668\n19427 29284\n95029 100000\n81547 100000\n48886 73398\n25353 38198\n14170 21357\n36397 54751\n24462 36887\n36136 54348\n50293 75498\n46932 70477\n71085 100000\n2589 3917\n33361 50203\n11318 17043\n51865 77858\n18861 28407\n28440 42850\n78004 100000\n37762 56817\n99313 100000\n70682 100000\n81165 100000\n340 522\n47985 72058\n93036 100000\n60026 90063\n52665 79019\n99884 100000\n9136 13741\n61283 91921\n71859 100000\n32617 49111\n66141 99233\n78471 100000\n76009 100000\n11478 17294\n48185 72366\n68956 100000\n51956 77992\n36207 54453\n79422 100000\n89442 100000\n66235 99378\n39097 58808\n98772 100000\n89590 100000\n88908 100000\n28204 42486\n20459 30852\n53594 80409\n49650 74530\n40097 60309\n84717 100000\n25273 38082\n41149 61875\n5127 7699\n30902 46549\n35255 53034\n29612 44597\n67819 100000\n17600 26522\n16470 24820\n32317 48664\n95125 100000\n77370 100000\n12205 18384\n62601 93896\n17323 26118\n87070 100000\n64462 96672\n96268 100000\n50040 75106\n67721 100000\n49398 74162\n4499 6767\n13966 21054\n72471 100000\n60865 91306\n20132 30363\n32056 48269\n59622 89453\n33409 50274\n46816 70308\n64192 96284\n12306 18537\n1887 2874\n14519 21888\n17182 25910\n59662 89512\n19633 29594\n99856 100000\n507 775\n60793 91201\n19209 28941\n27384 41245\n31305 47137\n62813 94210\n19121 28801\n39980 60140\n66556 99859\n19258 29013\n80225 100000\n56589 84889\n79758 100000\n76265 100000\n6114 9190\n6042 9086\n35384 53225\n89532 100000\n29491 44414\n91825 100000\n39930 60068\n33579 50519\n89501 100000\n2475 3742\n12214 18395\n7950 11951\n59178 88787\n33426 50301\n35480 53366\n67465 100000\n96696 100000\n28952 43626\n17014 25649\n71916 100000\n39612 59585\n12844 19338\n96793 100000\n37544 56487\n26627 40091\n66426 99669\n89130 100000\n12782 19251\n72138 100000\n63791 95683\n46423 69729\n61760 92627\n91957 100000\n39125 58853\n41038 61711\n62890 94324\n87517 100000\n6775 10183\n15643 23574\n99002 100000\n49209 73881\n68728 100000\n82236 100000\n7616 11447\n58242 87373\n56876 85311\n53309 79976\n1194 1824\n45244 67965\n53305 79971\n73872 100000\n39942 60083\n47328 71067\n82291 100000\n67797 100000\n24511 36960\n82252 100000\n97953 100000\n56219 84323\n62267 93405\n52444 78698\n6331 9516\n54210 81347\n73725 100000\n17628 26560\n30544 46008\n51839 77822\n57517 86278\n43032 64674\n26861 40454\n15338 23106\n53878 80846\n85164 100000\n43700 65683\n11846 17851\n97039 100000\n75627 100000\n89051 100000\n40427 60801\n1525 2327\n20128 30356\n65052 97573\n44519 66873\n30074 45304\n3234 4887\n79115 100000\n97089 100000\n67631 100000\n21661 32652\n51335 77060\n93552 100000\n96458 100000\n90762 100000\n19383 29214\n41164 61894\n61697 92529\n62396 93598\n45736 68714\n95224 100000\n52473 78741\n98787 100000\n5020 7538\n99798 100000\n47176 70840\n76936 100000\n77847 100000\n46310 69559\n26158 39400\n54494 81760\n19120 28800\n52727 79106\n85265 100000\n83139 100000\n2707 4096\n27854 41953\n7645 11489\n9360 14082\n75921 100000\n40 64\n27094 40799\n95242 100000\n97891 100000\n88020 100000\n54937 82416\n63172 94750\n60519 90789\n48697 73111\n51131 76762\n319 488\n11640 17538\n99088 100000\n87771 100000\n82711 100000\n27689 41705\n51050 76637\n24810 37385\n56215 84317\n13378 20146\n59346 89052\n5236 7858\n54297 81475\n58249 87381\n75110 100000\n55782 83682\n94073 100000\n57193 85774\n65339 98004\n24879 37490\n31577 47559\n38487 57903\n67843 100000\n59198 88820\n46366 69644\n71798 100000\n43466 65331\n18716 28193\n54764 82168\n70160 100000\n57673 86519\n46998 70575\n27376 41232\n27931 42071\n76162 100000\n8501 12785\n259 398\n14284 21535\n50155 75285\n31248 47059\n4469 6722\n96185 100000\n71431 100000\n54055 81117\n39566 59513\n60867 91310\n92231 100000\n46233 69445\n74019 100000\n2102 3191\n24985 37651\n33269 50072\n42672 64132\n14027 21142\n71781 100000\n81116 100000\n16861 25418\n73138 100000\n66610 99945\n85084 100000\n73773 100000\n96429 100000\n37706 56731\n8062 12124\n80960 100000\n64261 96386\n58652 87995\n45425 68234\n77451 100000\n4173 6264\n64076 96117\n25241 38033\n16821 25357\n35602 53553\n77905 100000\n82957 100000\n41428 62279\n53008 79532\n95556 100000\n49939 74953\n50658 76041\n76264 100000\n6448 9690\n23203 34974\n62653 93972\n93922 100000\n52101 78195\n69382 100000\n93684 100000\n28841 43467\n44620 67029\n95554 100000\n69049 100000\n15579 23475\n50960 76503\n39669 59674\n45260 67988\n10599 15944\n11932 17982\n21627 32602\n57226 85829\n39695 59711\n40486 60886\n86212 100000\n65523 98287\n16655 25100\n75781 100000\n47337 71081\n15603 23512\n49107 73719\n81756 100000\n38420 57805\n78105 100000\n14686 22140\n29908 45050\n76199 100000\n99558 100000\n45277 68014\n27302 41115\n12448 18754\n53028 79560\n62682 94018\n97125 100000\n44941 67519\n9943 14971\n13442 20243\n22570 34026\n46775 70241\n619 952\n21452 32328\n10114 15228\n64851 97275\n49763 74700\n81556 100000\n25145 37893\n80784 100000\n34767 52291\n29740 44795\n76445 100000\n62498 93745\n62633 93945\n17735 26724\n5556 8341\n1168 1787\n498 761\n13007 19585\n43581 65499\n18827 28359\n61578 92345\n15203 22907\n88324 100000\n51423 77193\n50510 75824\n13936 21005\n29728 44775\n35375 53210\n81161 100000\n568 868\n2291 3469\n84523 100000\n18775 28281\n72068 100000\n28201 42481\n13239 19941\n13137 19783\n75820 100000\n46953 70511\n53135 79725\n83806 100000\n73869 100000\n80412 100000\n33489 50387\n72208 100000\n63436 95145\n30316 45665\n92486 100000\n27018 40686\n84443 100000\n78275 100000\n88937 100000\n88064 100000\n32843 49443\n28558 43031\n10054 15141\n18393 27701\n96551 100000\n66016 99038\n56093 84141\n58774 88185\n42260 63526\n14405 21715\n73294 100000\n77288 100000\n57943 86923\n54420 81652\n3036 4588\n89699 100000\n41893 62985\n94164 100000\n69441 100000\n76297 100000\n98957 100000\n20923 31546\n56299 84443\n27518 41444\n33274 50079\n26984 40635\n32838 49434\n3850 5790\n7842 11787\n87519 100000\n79201 100000\n73149 100000\n95417 100000\n70475 100000\n93163 100000\n72483 100000\n39986 60149\n77806 100000\n19631 29591\n29942 45102\n75366 100000\n86241 100000\n47004 70584\n47928 71972\n14891 22445\n66289 99462\n60051 90097\n36720 55251\n38131 57368\n34307 51605\n37979 57149\n18110 27287\n7127 10700\n39268 59062\n42819 64352\n69252 100000\n33407 50272\n47927 71970\n54611 81937\n422 650\n43477 65348\n90197 100000\n96280 100000\n46656 70074\n71888 100000\n8387 12613\n87345 100000\n69322 100000\n10438 15710\n56419 84629\n59852 89801\n96326 100000\n57337 86006\n51140 76779\n83482 100000\n63385 95071\n69294 100000\n7479 11240\n75213 100000\n35182 52930\n74155 100000\n46374 69656\n62184 93274\n79352 100000\n10017 15083\n33024 49710\n43815 65853\n56825 85233\n17303 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        "output": "26\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 111,
        "task_id": 541,
        "test_case_id": 44,
        "question": "There are N islands lining up from west to east, connected by N-1 bridges.\nThe i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.\nOne day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:\nRequest i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.\nYou decided to remove some bridges to meet all these M requests.\nFind the minimum number of bridges that must be removed.\n\n-----Constraints-----\n - All values in input are integers.\n - 2 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^5\n - 1 \\leq a_i < b_i \\leq N\n - All pairs (a_i, b_i) are distinct.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 b_1\na_2 b_2\n:\na_M b_M\n\n-----Output-----\nPrint the minimum number of bridges that must be removed.\n\n-----Sample Input-----\n5 2\n1 4\n2 5\n\n-----Sample Output-----\n1\n\nThe requests can be met by removing the bridge connecting the second and third islands from the west.",
        "solutions": "[\"n, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab = sorted(ab, key=lambda x: x[1])\\ns = ab[0][1]\\nans = 1\\nfor i in ab:\\n    if s <= i[0]:\\n        ans += 1\\n        s = i[1]\\nprint(ans)\", \"N,M = map(int,input().split())\\nW = sorted([list(map(int,input().split())) for m in range(M)],key=lambda x:x[1])\\nc = 0\\nx = 0\\n\\nfor a,b in W:\\n   if x<a:\\n      x=b-1\\n      c+=1\\n\\nprint(c)\", \"n, m = map(int, input().split())\\nc = [[0] * 2 for _ in range(m)]\\nfor i in range(m):\\n    c[i][1] , c[i][0] = map(int, input().split())\\nc.sort()  #\\u6a4b\\u3092\\u53d6\\u308a\\u9664\\u304f\\u6642\\u306f\\u3067\\u304d\\u308b\\u3060\\u3051b\\u306e\\u5cf6\\u306b\\u8fd1\\u3044\\u3068\\u3053\\u308d\\u3067\\u53d6\\u308a\\u9664\\u304f\\u3068\\u826f\\u3044\\u3002\\nx = -1  #\\u76f4\\u524d\\u306b\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\u306eindex\\nans = 0\\nfor i in range(m):\\n    if c[i][1] > x:\\n        x = c[i][0] - 1\\n        ans += 1\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\ncondition = [list(map(int, input().split())) for _ in range(m)]\\n\\ncondition.sort(key=lambda a: (a[1], a[0]))\\n\\nright_end = 0\\nans = 0\\nfor c in condition:\\n    if c[0] >= right_end:\\n        ans += 1\\n        right_end = c[1]\\nprint(ans)\\n\", \"from operator import itemgetter\\nN,M=map(int,input().split())\\nislands=[list(map(int,input().split())) for _ in range(M)]\\nislands.sort(key=itemgetter(1))\\n\\ni=0\\ncnt=0\\nwhile i<M:\\n    j=0\\n    while i+j<M and islands[i+j][0]<islands[i][1]:\\n        j+=1\\n    i+=j\\n    cnt+=1\\nprint(cnt)\", \"from operator import itemgetter\\nN, M = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=itemgetter(1))\\nans = [0]\\nfor a, b in ab:\\n    if ans[-1] < a:\\n        ans.append(b-1)\\nprint(len(ans) - 1)\", \"N, M = list(map(int, input().split()))\\nB = [tuple(map(int, input().split())) for _ in range(M)]\\nB.sort()\\nr = 0\\nres = 0\\nfor a, b in B:\\n    if a >= r:\\n        res += 1\\n        r = b\\n    else:\\n        r = min(r, b)\\nprint(res)\\n\", \"import sys\\n\\nn, m = map(int, sys.stdin.readline().split())\\n\\nhostility = [[] for _ in range(m)]\\nfor i in range(m):\\n    a, b = map(int, sys.stdin.readline().split())\\n    hostility[i].append(a - 1)\\n    hostility[i].append(b - 1)\\n\\nhostility = sorted(hostility, key = lambda x: x[1])\\n\\ncnt = 0\\nbridge = -1\\nfor i in range(m):\\n    if hostility[i][0] <= bridge < hostility[i][1]:\\n        continue\\n    bridge = hostility[i][1] - 1\\n    cnt += 1\\nprint(cnt)\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\n\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\ndef main():\\n    N, M = NMI()\\n    ab = [NLI() for _ in range(M)]\\n    \\n    ENDsorted_sections= sorted(ab, key=lambda x: x[1])\\n    \\n    ans = 1\\n    dropped_bridge = ENDsorted_sections[0][1]\\n\\n    for m in range(M):\\n        if ENDsorted_sections[m][0] >= dropped_bridge:#\\u65b0\\u3057\\u304f\\u6a4b\\u3092\\u843d\\u3068\\u3055\\u306a\\u3044\\u3068\\u3044\\u3051\\u306a\\u3044\\n            ans += 1\\n            dropped_bridge = ENDsorted_sections[m][1]\\n    print(ans)    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\na_b_l = []\\nfor _ in range(M):\\n    a_b_l.append(list(map(int, input().split())))\\n\\na_b_l = sorted(a_b_l, key=lambda x: x[1])\\nans = 0\\nprev_removed_bridge = 0\\nfor a, b in a_b_l:\\n    if a <= prev_removed_bridge:\\n        continue\\n    prev_removed_bridge = b - 1\\n    ans += 1\\nprint(ans)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N,M =  map(int, input().split())\\nli = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    li.append([b,a])\\nli.sort()\\nan = 1\\nnow_end = li[0][0]\\nfor i in range(1,M):\\n    if now_end <= li[i][1]:\\n        an += 1\\n        now_end = li[i][0]\\nprint(an)\", \"n, m = list(map(int, input().split()))\\nba = []\\nfor i in range(m):\\n    a, b = [int(x) - 1 for x in input().split()]\\n    ba.append((b,a))\\nba.sort()\\ncount = 0\\nprev_b = -1\\nfor b, a in ba:\\n    if a < prev_b:\\n        continue\\n    prev_b = b\\n    count += 1\\nprint(count)\\n\", \"_,*l = [list(map(int,i.split())) for i in open(0)]\\nl.sort(key=lambda x:x[1])\\nA=S=0\\nfor s,t in l:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"def resolve():\\n    import sys\\n    from operator import itemgetter\\n    \\n    readline = sys.stdin.readline    # 1\\u884c\\u3060\\u3051\\u6587\\u5b57\\u5217\\u306b\\u3059\\u308b\\n\\n    N, M = list(map(int, readline().split()))\\n    AB = [list(map(int, readline().split())) for _ in [0] * M]\\n    AB.sort(key=itemgetter(1))\\n    islands = -float('inf')\\n    ans = 0\\n    for left, right in AB:\\n        if islands <= left:\\n            ans += 1\\n            islands = right\\n    print(ans)\\n    \\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [0] * m\\nb = [0] * m\\n\\nfor i in range(m):\\n    a[i], b[i] = map(int, input().split())\\n\\nab = sorted([(a[i], b[i]) for i in range(m)], key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"from operator import itemgetter\\n\\nN, M = map(int, input().split())\\nab = [tuple(map(int, input().split())) for _ in range(M)]\\nab = sorted(ab, key=itemgetter(1))\\n\\n# \\u524d\\u56de\\u53d6\\u308a\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u3044\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\nAB = []\\n\\nfor _ in range(M):\\n  a, b = map(int, input().split())\\n  AB.append((a, b))\\n\\nRsort = sorted(AB, key=lambda x: x[1])\\ncnt = 0\\nR = 0\\n\\nfor a, b in Rsort:\\n  if a <= R:\\n    continue\\n  else:\\n    cnt += 1\\n    R = b-1\\n\\nprint(cnt)\", \"N, M = map(int, input().split())\\nq = [list(map(int, input().split())) for _ in range(M)]\\nq = sorted(sorted(q, key=lambda x: x[0]), key=lambda x: x[1])\\n\\nlast = 0\\ncnt = 0\\nfor a, b in q:\\n    if last < a:\\n        last = b-1\\n        cnt += 1\\n\\nprint(cnt)\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridges = [requests[0][1] - 1]\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if (bridges[-1] < a_i) or (b_i <= bridges[-1]):\\n        bridges.append(b_i - 1)\\nans = len(bridges)\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = []\\n\\nfor a, b in Q:\\n    flag = True\\n    for x in border:\\n        # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u308b\\u304b\\n        if a < x and x <= b:\\n            flag = False\\n            break\\n    if flag:\\n        border.append(b)\\n\\nans = len(border)\\nprint(ans)\", \"n,m=map(int,input().split())\\nR=[]\\nfor i in range (m) :\\n    a,b=map(int,input().split())\\n    R.append ([b, a])\\nR.sort()\\n\\ndef solve() :\\n    ans,t=0,0\\n    for i in range (m) :\\n        if t<=R[i][1]:\\n            ans+=1\\n            t=R[i][0]\\n    return ans\\nprint (solve ())\", \"# atcoder -take a rest-(easy)\\n#typical greedy\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    conflict = [tuple(map(int, input().split())) for i in range(M)]\\n    newest_destroyed = -1\\n    conflict.sort(key=lambda x: x[1])\\n    res = 0\\n    for l, r in conflict:\\n        if not (l <= newest_destroyed < r):\\n            res += 1\\n            newest_destroyed = r-1\\n    print(res)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n\\n__starting_point()\", \"N,M = list(map(int,input().split()))\\n\\narr = []\\nfor _ in range(M):\\n  a,b = list(map(int,input().split()))\\n  arr.append((a,b))\\n\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if a < pb <= b:\\n    pass\\n  else:\\n    ans += 1\\n    pb = b\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nconflicts = [list(map(int, input().split())) for i in range(M)]\\n\\nintervals = []\\nfor conflict in conflicts:\\n    intervals.append([conflict[0], conflict[1]-1])\\n\\nintervals = sorted(intervals, key=lambda x: x[1])#interval[1]\\u306e\\u5927\\u304d\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\n\\ncount = 0\\nend = -float(\\\"inf\\\")\\nfor interval in intervals:\\n    if interval[0] > end:\\n        count += 1\\n        end = interval[1]\\n\\nprint(count)\", \"x=c=0\\nfor a,b in sorted([list(map(int,o.split()))for o in open(0)][1:],key=lambda p:p[1]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    AB = [None] * M\\n    for i in range(M):\\n        AB[i] = tuple(map(int, input().split()))\\n\\n    AB.sort(key=lambda x: x[1])\\n\\n    ans = 0\\n    prev_x = -1\\n    for a, b in AB:\\n        if a <= prev_x < b:\\n            pass\\n        else:\\n            ans += 1\\n            prev_x = b - 1\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = list(map(int, input().split()))\\ndata = [list(map(int, input().split())) for _ in range(M)]\\ndata = sorted(data, key=lambda x: x[1])\\n\\ncount = 1\\nleft = data[0][1]\\nfor i in range(1, M):\\n    if data[i][0] < left:\\n        left = max(data[i][0], left)\\n    else:\\n        count += 1\\n        left = data[i][1]\\nprint(count)\\n\", \"n, m = map(int, input().split())\\n\\nbridge = [None]*m\\nfor i in range(m):\\n  a, b = map(int, input().split())\\n  bridge[i] = [b, a]\\n\\nans = 0\\nbridge.sort()\\n\\nsub = -1\\nans = 0\\nfor v in bridge:\\n  b, a = v[0], v[1]\\n  if a >= sub:\\n    sub = b\\n    ans += 1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\n\\nls = []\\nfor i in range(m):\\n    x,l = map(int,input().split())\\n    ls.append([x,l])\\n    \\nls = sorted(ls, key=lambda x: x[1])\\nans =m\\nfor i in range(1,m):\\n    if ls[i][0] < ls[i-1][1]:\\n      ls[i][1] = ls[i-1][1]\\n      ans -=1\\n        \\nprint(ans)\", \"n, m = map(int, input().split())\\nl = [list(map(int, input().split())) for i in range(m)]\\n \\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = m\\n \\nfor i in range(1, m):\\n    if l[i-1][1] > l[i][0]:\\n        l[i][1] = l[i-1][1]\\n        cnt -= 1\\n \\nprint(cnt)\", \"N, M = map(int, input().split())\\n\\nab = []\\nfor _ in range(M):\\n    a, b = map(int, input().split())\\n    ab.append((a, b))\\nab.sort(key=lambda ab: ab[::-1])\\n\\nans = 0\\nlast = -1\\nfor a, b in ab:\\n    if not a <= last < b:\\n        last = b - 1\\n        ans += 1\\nprint(ans)\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(m)]\\n\\nb = sorted(a, key=itemgetter(1))\\n#print(b)\\nremoved = -1\\nans = 0\\n\\nfor i in range(m):\\n  if b[i][0] > removed:\\n    removed = b[i][1] - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys,math,collections,itertools\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\\n\", \"N, M = map(int, input().split())\\nneeds = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    needs.append((x, y))\\nneeds.sort(key=lambda x: x[1])\\npb = needs[0][1]\\nres = 1\\nfor i in needs:\\n    if i[0] >= pb:\\n        res += 1\\n        pb = i[1]\\n\\nprint(res)\", \"x=c=0\\nfor b,a in sorted([[*map(int,t.split())][::-1]for t in open(0)][1:]):\\n if a>x:x=b-1;c+=1\\nprint(c)\", \"n,m=map(int,input().split())\\nA=[]\\nfor i in range(m):\\n    a,b=map(int,input().split())\\n    a-=1 ;b-=1\\n    A.append([a,b])\\n\\nA=sorted(A, key=lambda x:x[1])\\nans=0\\nlast=-5000\\nfor l in A:\\n    #print(a,b)\\n    if last<l[0]:\\n        ans+=1\\n        last=l[1]-1\\nprint(ans)\", \"N,M=list(map(int,input().split()))\\nans=0\\nl=[]\\nfor i in range(M):\\n   a,b=(map(int,input().split()))\\n   l.append((a,b))\\nl.sort(key=lambda x:x[1])\\ncut=-1\\nfor i,j in l:\\n   if cut>=i:\\n      continue\\n   else:\\n      ans+=1\\n      cut=j-1\\nprint(ans)\", \"n,m=list(map(int,input().split()))\\na=[]\\nfor _ in range(m):\\n  b=list(map(int,input().split()))\\n  a.append(b)\\n  \\na.sort()\\n\\nleft=a[0][0]\\nright=a[0][1]\\n\\nans=1\\n\\nfor i in range(1,m):\\n  x=a[i][0]\\n  y=a[i][1]\\n  \\n  if left<=x<right:\\n    left=x\\n    right=min(right,y)\\n    \\n  else:\\n    ans+=1\\n    left=x\\n    right=y\\n    \\nprint(ans)\\n    \\n\", \"def main():\\n    n,m = list(map(int,input().split()))\\n    brg = []\\n    for i in range(m):\\n        a,b = list(map(int,input().split()))\\n        brg.append([a-1,b-1])\\n    brg.sort()\\n    ans = 1\\n    s,e = brg[0]\\n    for i in range(1,m):\\n        s_,e_ = brg[i]\\n        if e_<=e:\\n            e = e_\\n        if s_>=s:\\n            s = s_\\n        if e <= s_:\\n            ans += 1\\n            s = s_\\n            e = e_\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M, *A = list(map(int, open(0).read().split()))\\n*A, = list(zip(*[iter(A)]*2))\\nA.sort()\\ncnt = 0\\nR = 0\\nfor a, b in A:\\n    if R <= a:\\n        cnt += 1\\n        R = b\\n    elif b < R:\\n        R = b\\nprint(cnt)\\n\", \"n,m=list(map(int, input().split()))\\nab=[list(map(int,input().split()))  for i in  range(m)]\\n\\nab=sorted(ab, key=lambda x:(x[0],x[1]), reverse=True)\\n#print(ab)\\nnow=10**5+1\\n\\npreb=-1\\nans=0\\nfor i in range(m):\\n  if ab[i][1]==preb:\\n    continue\\n  if ab[i][1]<=now:\\n    now=ab[i][0]\\n    preb=ab[i][1]\\n    ans+=1\\n    #print(\\\"now\\\",now)\\nprint(ans)\\n\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort(key=lambda x: x[1])\\n\\nans = m\\nfor i in range(1, m):\\n    if ab[i][0] < ab[i-1][1]:\\n        ab[i][1] = ab[i-1][1]\\n        ans -= 1\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\n\\ninstructions = []\\nfor _ in range(M):\\n    a = list(map(int, input().split()))\\n    instructions.append(a)\\ninstructions.sort(key=lambda x:x[1])\\n\\nans = 0\\ncurrent = 0\\nfor a, b in instructions:\\n    if current < a: #\\u904e\\u53bb\\u306e\\u6761\\u4ef6\\u3067\\u306f\\u307e\\u3060\\u6e80\\u305f\\u3057\\u3066\\u306a\\u3044\\n        current = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nlst=[list(map(int,input().split())) for i in range(m)]\\nlst.sort(key=lambda x:x[1])\\nans=1\\npin=lst[0][1]-1\\n\\nfor i in range(1,m):\\n  if lst[i][0]>pin:\\n    ans+=1\\n    pin=lst[i][1]-1\\n\\nprint(ans)\", \"n,m = map(int,input().split())\\nc = [list(map(int,input().split())) for _ in range(m)]\\nc.sort(key= lambda val : val[1])\\n\\nleft = 0\\nans = 0\\nfor i,[a,b] in enumerate(c):\\n    if left <= a:\\n        ans += 1\\n        left = b\\nprint(ans)\", \"n,m = map(int, input().split())\\nt = [[n] for i in range(n)]\\nfor i in range(m):\\n  a,b = map(int, input().split())\\n  t[a-1].append(b-1)\\ng = []\\nfor i in t:\\n  g.append(min(i))\\nk = 0\\nans=0\\nwhile k <=n-1:\\n  e = min(g[k:])\\n  if e==n:\\n    break\\n  ans+=1\\n  k = e\\nprint(ans)\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=10**9+7\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\ndef main():\\n  n,m=LI()\\n  l=[LI() for _ in range(m)]\\n  l=sorted(l,key=lambda x:x[1])\\n\\n  ans=1\\n  kiru=l[0][1]-0.1\\n  for x,y in l[1:]:\\n    if x<kiru<y:\\n      continue\\n    ans+=1\\n    kiru=y-0.1\\n\\n  return ans\\n\\n# main()\\nprint((main()))\\n\", \"N,M=list(map(int,input().split()))\\nab = [list(map(int,input().split())) for i in range(M)]\\n\\nans = 0\\nab.sort(key=lambda x:x[1])\\n\\nrecent_cut = -1#\\u76f4\\u8fd1\\u3067\\u5207\\u308a\\u843d\\u3068\\u3057\\u305f\\u6a4b\\u306e\\u5de6\\u306e\\u8857\\nfor i in range(M):\\n    if recent_cut < ab[i][0]:\\n        recent_cut = ab[i][1]-1\\n        ans+=1\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\nab = [list(map(int,input().split())) for _ in range(M)]\\nab.sort(key=lambda x: x[1])\\nans = 0\\npos = 0\\nfor i in range(M):\\n  if pos<ab[i][0]:\\n    ans+=1\\n    pos=ab[i][1]-1\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nN, M = list(map(int, input().split(' ')))\\n\\na_b_pairs = [list(map(int, input().split(' '))) for _ in range(M)]\\na_b_pairs.sort(key=lambda x: x[1])\\nright = a_b_pairs[0][1] - 1\\n\\nans = 1\\nfor a, b in a_b_pairs[1:]:\\n    if a > right:\\n        right = b - 1\\n        ans += 1\\n\\nprint(ans)\\n\\n\\n\\n\", \"# Segment tree (+)\\nfrom operator import add\\nfrom sys import stdin\\n\\n\\nclass SegmentTree:\\n    def __init__(self, size, op, e):\\n        self._op = op\\n        self._e = e\\n        self._size = size\\n        t = 1\\n        while t < size:\\n            t *= 2\\n        self._offset = t - 1\\n        self._data = [e] * (t * 2 - 1)\\n\\n    def __getitem__(self, key):\\n        return self._data[self._offset + key]\\n\\n    def __setitem__(self, key, value):\\n        op = self._op\\n        data = self._data\\n        i = self._offset + key\\n        data[i] = value\\n        while i >= 1:\\n            i = (i - 1) // 2\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def build(self, iterable):\\n        op = self._op\\n        data = self._data\\n        data[self._offset:self._offset + self._size] = iterable\\n        for i in range(self._offset - 1, -1, -1):\\n            data[i] = op(data[i * 2 + 1], data[i * 2 + 2])\\n\\n    def query(self, start, stop):\\n        def iter_segments(data, l, r):\\n            while l < r:\\n                if l & 1 == 0:\\n                    yield data[l]\\n                if r & 1 == 0:\\n                    yield data[r - 1]\\n                l = l // 2\\n                r = (r - 1) // 2\\n        op = self._op\\n        it = iter_segments(self._data, start + self._offset,\\n                           stop + self._offset)\\n        result = self._e\\n        for v in it:\\n            result = op(result, v)\\n        return result\\n\\nreadline = stdin.readline\\n\\nN, M = list(map(int, readline().split()))\\nab = [list(map(int, readline().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])\\nst = SegmentTree(N - 1, add, 0)\\n\\nresult = 0\\nfor a, b in ab:\\n    a, b = a - 1, b - 1\\n    if st.query(a, b) != 0:\\n        continue\\n    result += 1\\n    st[b - 1] = 1\\nprint(result)\\n\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN, M = map(int, input().split())\\n\\nAB = [list(map(int, input().split())) for _ in range(M)]\\nAB.sort()\\n\\nq = []\\nfor ab in AB:\\n    heapq.heappush(q, ab)\\n\\nans = 0\\ncnt = M\\nvisited = -1\\nwhile cnt > 0:\\n    ab = heapq.heappop(q)\\n    cnt -= 1\\n\\n    # print(ab, visited, cnt)\\n\\n    if ab[1] > ab[0]:\\n        heapq.heappush(q, [ab[1], ab[0]])\\n        cnt += 1\\n    else:\\n        if visited <= ab[1]:\\n            visited = ab[0]\\n            ans += 1\\n        else:\\n            pass\\n\\nprint(ans)\", \"N, M = map(int, input().split())\\na = []\\nfor i in range(M):\\n    x, y = map(int, input().split())\\n    a.append([x, y])\\na.sort(key=lambda x: x[1])\\nans = 0\\nfor i in range(M-1):\\n    if a[i+1][0] < a[i][1]:\\n        a[i+1][1] = a[i][1]\\n    else:\\n        ans += 1\\nans += 1\\nprint(ans)\", \"INF = 10**9\\n\\nN, M = map(int, input().split())\\n\\nrequests =[]\\nfor _ in range(M):\\n    requests.append(tuple(map(int, input().split())))\\nrequests.sort(key=lambda x:x[1])\\n\\nend = 1\\nans = 0\\nfor i in range(M):\\n    if end <= requests[i][0]:\\n        ans += 1\\n        end = requests[i][1]\\n\\nprint(ans)\", \"N,M = list(map(int,input().split()))\\nl = [list(map(int,input().split())) for _ in range(M)]\\nl.sort(key=lambda x: x[1])\\nbroken_bridge = 0\\nposition = 0\\nfor i in range(M):\\n    if position<l[i][0]:\\n        broken_bridge+=1\\n        position = l[i][1]-1\\nprint(broken_bridge)\\n\", \"n, m  = map(int, input().split())\\na = [list(map(int, input().split())) for i in range(m)]\\na = sorted(a, key=lambda x :x[1])\\nbridge = a[0][1] - 1\\nans = 1\\n\\nfor i in range(1, m):\\n    if a[i][0] > bridge:\\n        bridge = a[i][1] - 1\\n        ans += 1\\n        \\nprint(ans)\", \"n,m=list(map(int,input().split()))\\np=[]\\nfor _ in range(m):\\n  a,b=list(map(int,input().split()))\\n  p.append([a,b])\\n#print(p)\\np.sort(key=lambda x:x[1])\\n#print(p)\\nans=0\\ncur=0\\nfor i in range(m):\\n  if cur<=p[i][0]:\\n    #print(\\\"i:%d\\u6b8b\\u3059,cur:%d,p[i][1]:%d,p[i][0]:%d\\\" % (i,cur,p[i][1],p[i][0]))\\n    ans+=1\\n    cur=p[i][1]\\nprint(ans)\\n\", \"N,M = map(int,input().split())\\narr = []\\nfor _ in range(M):\\n  a,b = map(int,input().split())\\n  arr.append((a,b))\\narr.sort(key=lambda x: x[1])\\nans = 1\\n_, pb = arr[0]\\nfor a,b in arr[1:]:\\n  if pb <= a:\\n    ans += 1\\n    pb = b\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nB = [0] * M\\nfor i in range(M):\\n  B[i] = list(map(int, input().split()))\\n  \\nB = sorted(B, key = lambda x:x[1])\\nremove = []\\n#print(B)\\nfor i in range(M):\\n  a, b = B[i][0], B[i][1]\\n  if remove == []:\\n    remove.append(b - 1)\\n  elif max(remove) >= a:\\n    continue\\n  else:\\n    remove.append(b - 1)\\n  #print(remove)  \\nprint((len(remove)))    \\n\\n\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\ncd = sorted(ab, key=itemgetter(1))\\n#print(cd)\\nremoved = -1\\nans = 0\\n\\nfor a, b in cd:\\n  if a > removed:\\n    removed = b - 1\\n    ans += 1\\n    \\nprint(ans)\", \"import sys\\ninput = sys.stdin.readline\\n\\nN, M = map(int,input().split())\\nbridges = []\\nfor _ in range(M):\\n    a, b = map(int,input().split())\\n    bridges.append([a, b])\\n\\nbridges.sort(key = lambda x: x[1])\\n\\np = 0\\nt = 0\\n\\nwhile len(bridges) > 0:\\n    t = bridges[0][1]\\n    p += 1\\n    bridges = [i for i in bridges if i[0] >= t]\\n\\nprint(p)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> tuple:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        tuple: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N, M = list(map(int, input().split()))\\n    requests = []\\n    for i in range(M):\\n        a_i, b_i = list(map(int, input().split()))\\n        requests.append((a_i, b_i))\\n\\n    return N, M, requests\\n\\n\\ndef main(N: int, M: int, requests: list) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u5cf6\\u306e\\u6570(2 <= N <= 10^5)\\n        M (int): \\u8981\\u671b\\u306e\\u6570(1 <= M <= 10^5)\\n        requests (list): \\u8981\\u671b(1 <= a_i < b_i <= N)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    requests = sorted(requests, key=lambda x: x[1])\\n    bridge = 0\\n    ans = 0\\n    for i in range(M):\\n        a_i, b_i = requests[i]\\n        if a_i > bridge:\\n            bridge = b_i - 1\\n            ans += 1\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N, M, requests = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N, M, requests)\\n\\n__starting_point()\", \"n, m = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for i in range(m)]\\nab.sort()\\nans = 0\\nnow = 1\\nfor i in range(m):\\n\\tif now <= ab[i][0]:\\n\\t\\tans += 1\\n\\t\\tnow = ab[i][1]\\n\\tnow = min(now, ab[i][1])\\nprint(ans)\", \"N, M = list(map(int, input().split()))\\nAB = sorted([list(map(int, input().split())) for _ in range(M)])\\n\\nAB = sorted(AB, reverse=False, key=lambda x: x[1])\\n\\nlast_b = AB[0][1] - 1  # \\u6700\\u521d\\u306b\\u6f70\\u3059\\u6a4b\\ncnt = 1  # \\u4e0a\\u3067\\u4e00\\u3064\\u58ca\\u3057\\u3066\\u308b\\u306e\\u3067+1\\nfor a, b in AB:\\n    if a <= last_b:\\n        continue\\n    else:\\n        last_b = b - 1\\n        cnt += 1\\nprint(cnt)\\n\", \"\\nn, m = list(map(int, input().split()))\\nl = [list(map(int, input().split())) for i in range(m)]\\n\\nl = sorted(l, key = lambda x:(x[1], x[0]))\\ncnt = 0\\ncon_l = 0\\n\\nfor i in range(m):\\n    if con_l <= l[i][0]:\\n        cnt += 1\\n        con_l = l[i][1]\\n\\nprint(cnt)\\n\", \"n, m = list(map(int, input().strip().split()))\\nab_list = [list(map(int, input().strip().split())) for _ in range(m)]\\nab_list.sort(key=lambda x: x[1])\\n\\nres = 0\\nmin_r = 0\\nfor ab in ab_list:\\n    if min_r <= ab[0]:\\n        res += 1\\n        min_r = ab[1]\\nprint(res)\\n\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"(n, m), *l = [list(map(int, o.split())) for o in open(0)]\\nx = c = 0\\nfor a, b in sorted(l, key = lambda p:p[1]):\\n  if a > x:\\n    x = b - 1\\n    c += 1\\nprint(c)\", \"N,M,*A=map(int,open(0).read().split());c=0\\nfor a,b in sorted(zip(*[iter(A)]*2))[::-1]:\\n\\tif b<=N:c+=1;N=a\\nprint(c)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = []\\n\\n    for a, b in d:\\n        idx = bisect.bisect_left(down, a)\\n        if idx == len(down):\\n            down.append(b - 1)\\n    print((len(down)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nQ = [tuple(map(int, input().split())) for _ in range(M)]\\n\\n# \\u53f3\\u5074\\u304c\\u5c0f\\u3055\\u3044\\u9806\\u306b\\u30bd\\u30fc\\u30c8\\u3001\\u5236\\u7d04a<b\\u306a\\u306e\\u3067\\u305d\\u306e\\u307e\\u307e\\u4f7f\\u3063\\u3066\\u3088\\u3044\\nQ = sorted(Q, key=lambda x: x[1])\\n# \\u5883\\u754c\\u3001\\u53f3\\u5074\\u306e\\u533a\\u9593\\u306e\\u59cb\\u307e\\u308a\\nborder = -1\\nans = 0\\n\\nfor a, b in Q:\\n    # \\u65e2\\u5b58\\u306e\\u5883\\u754c\\u3067\\u5206\\u3051\\u3089\\u308c\\u306a\\u3044\\u3068\\u304d\\u306f\\u53f3\\u306b\\u305a\\u3089\\u3059\\n    if border <= a:\\n        ans += 1\\n        border = b\\n\\nprint(ans)\", \"n, m = list(map(int, input().split()))\\nab = sorted([tuple(map(int, input().split())) for _ in range(m)], key = lambda x:x[1])\\nremoved = -1\\nans = 0\\nfor a, b in ab:\\n    if a > removed:\\n        removed = b-1\\n        ans += 1\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\ndata=[]\\nfor i in range(m):\\n  a,b=map(int,input().split())\\n  data.append([b,a])\\ndata.sort()\\nr,l=data[0]\\ncnt=1\\nfor i in range(1,m):\\n  if data[i][1]>=r:\\n    cnt+=1\\n    r,l=data[i]\\n  else:\\n    r=min(r,data[i][0])\\n    l=max(l,data[i][1])\\nprint(cnt)\", \"def IslandsWar():\\n    n, m = list(map(int, input().split()))\\n    a = [list(map(int,input().split())) for _ in range(m)]\\n    a.sort(key=lambda x: x[1])\\n    removes = [a[0][1]]\\n\\n    for i, j in a[1:]:\\n        check = False\\n        for k in removes:\\n            if i < k:\\n                check = True\\n                break\\n        if not check:\\n            removes.append(j)\\n    print((len(removes)))\\n            \\ndef __starting_point():\\n    IslandsWar()\\n\\n__starting_point()\", \"_,*li = [list(map(int,i.split())) for i in open(0)]\\nli.sort(key=lambda x:x[1])\\nA = 0\\nS = 0\\nfor s,t in li:\\n    if S<=s:\\n        A+=1\\n        S=t\\nprint(A)\", \"N,M = map(int,input().split())\\ntable = []\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -= 1\\n    table.append((a,b))\\ntable = sorted(table,key=lambda x:x[1])\\ncur_r = table[0][1]\\nans = 1\\nfor i in range(1,M):\\n    l,r = table[i]\\n    if cur_r <= l:\\n        ans += 1\\n        cur_r = r\\n\\nprint(ans)\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    n, m = ns()\\n    d = []\\n    for _ in range(m):\\n        a, b = ns()\\n        d.append([a - 1, b - 1])\\n\\n    d.sort(key=lambda x: x[1])\\n\\n    down = -1\\n    ans = 0\\n    for a, b in d:\\n        if down < a:\\n            down = b-1\\n            ans += 1\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import bisect\\nN, M, *AB = [int(_) for _ in open(0).read().split()]\\nAB = sorted(zip(AB[::2], AB[1::2]))\\nl, r = AB[0]\\nans = 1\\nfor a, b in AB[1:]:\\n    if r <= a:\\n        l, r = a, b\\n        ans += 1\\n    else:\\n        r = min(r, b)\\nprint(ans)\\n\", \"n,m=map(int,input().split())\\nans=0\\nhead=1\\nfrom operator import itemgetter as it\\nfor x,y in sorted([list(map(int,input().split()))for i in range(m)],reverse=0,key=lambda x:(it(1)(x)*(n+1)*10-it(0)(x))):\\n    if not(x<head <=y):\\n        head=y\\n        ans+=1\\nprint(ans)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N, M = LI()\\n    ab = [LI_() for _ in range(M)]\\n    ab.sort(key=lambda x: x[1])\\n\\n    # \\u533a\\u9593\\u30b9\\u30b1\\u30b8\\u30e5\\u30fc\\u30ea\\u30f3\\u30b0\\n    ans = 0\\n    # print(ab)\\n    right = -1\\n    for a, b in ab:\\n        if right <= a:\\n            right = b\\n            ans += 1\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"N,M = map(int,input().split())\\nls = [tuple(map(int,input().split())) for _ in range(M)]\\nls.sort(key=lambda x:x[1],reverse=True)\\nls.sort(key=lambda x:x[0],reverse=True)\\nr = N\\ncnt = 0\\nfor i in range(M):\\n    a,b = ls[i]\\n    if b <= r:\\n        cnt += 1\\n        r = a\\nprint(cnt)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 10**9 + 7\\n\\ndef main():\\n    N, M = list(map(int, input().split()))\\n    ab = []\\n    for _ in range(M):\\n        a, b = [int(x)-1 for x in input().split()]\\n        ab.append((b,a))\\n    ab.sort()\\n    # print(ab)\\n    ans = 0\\n    x = -1\\n    for i in range(M):\\n        if ab[i][1] > x:\\n            ans += 1\\n            x = ab[i][0]-1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from operator import itemgetter\\n\\nn, m = map(int, input().split())\\n\\n# \\u533a\\u9593\\u306e\\u7d42\\u7aef\\u3067\\u30bd\\u30fc\\u30c8\\nab = sorted([tuple(map(int, input().split())) for i in range(m)], key=itemgetter(1))\\n# \\u524d\\u56de\\u9664\\u3044\\u305f\\u6a4b\\nremoved = -1\\nans = 0\\n\\nfor a, b in ab:\\n    # a \\u304c removed \\u3088\\u308a\\u5927\\u304d\\u3044 = \\u307e\\u3060\\u53d6\\u308a\\u9664\\u3044\\u3066\\u306a\\u3044\\n    if a > removed:\\n        removed = b - 1\\n        ans += 1\\n\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\nn, m = list(map(int, input().split()))\\n\\n# for i in range():\\n\\nab = [list(map(int, input().split())) for _ in range(m)]\\n\\nab.sort()\\n# print(ab)\\nans = 0\\ndiv = -1, -1\\nfor i in range(len(ab)):\\n    a, b = ab[i]\\n    # print(a, b)\\n\\n    if a == div[0]:\\n        continue\\n    elif a >= div[1]:\\n        div = a, b\\n        ans += 1\\n    else:\\n        div = a, min(b, div[1])\\n    # print(div, ans)\\n\\nprint(ans)\\n\", \"N, M = list(map(int, input().split()))\\nab = [list(map(int, input().split())) for _ in range(M)]\\n\\nab.sort(key=lambda x: x[1])  # Sort the list of (a, b) by b\\n\\nans = 0\\ncur = -1\\nfor i in range(M):\\n    a, b = ab[i]\\n    if a < cur:\\n        continue\\n    ans += 1\\n    cur = b\\n\\nprint(ans)\\n\", \"N, M = map(int, input().split())\\nreq = []\\nfor i in range(M):\\n    a, b = map(int, input().split())\\n    req.append([a, b])\\n\\nreq = sorted(req, key=lambda x: x[1])\\n\\nans = 1\\ncurrent = req[0][1]\\nfor i in range(1, len(req)):\\n    if req[i][0] < current:\\n        continue\\n    current = req[i][1]\\n    ans += 1\\nprint(ans)\", \"N,M = map(int,input().split())\\nwarzones = [[] for i in range(M)]\\nfor i in range(M):\\n    a,b = map(int,input().split())\\n    a -= 1\\n    b -=1\\n    warzones[i] = [a,b]\\nwarzones = sorted(warzones,key=lambda x:x[0])\\n#print(warzones)\\nshaku = warzones[0]\\ncnt = 1\\nfor i in range(1,M):\\n    #print(shaku)\\n    #\\u5c3a\\u7d99\\u7d9a\\u6761\\u4ef6\\n    if(warzones[i][0] < shaku[1]):\\n        shaku[0] = max(warzones[i][0],shaku[0])\\n        shaku[1] = min(warzones[i][1],shaku[1])\\n    else:\\n        cnt += 1\\n        shaku = warzones[i]\\n\\nprint(cnt)\\n\\n'''\\u5c3a\\u53d6\\u6cd5\\u306e\\u521d\\u671f\\u5316\\n\\u6700\\u521d\\u306b\\u914d\\u5217\\u306elists[0]\\u3067\\u521d\\u671f\\u5316\\nfor i in range(1,M):\\u3067\\u307e\\u308f\\u3057\\u3066\\nok\\u306e\\u5834\\u5408lists[i]\\u3092\\u4ee3\\u5165\\nng\\u306e\\u3068\\u304d\\u306f\\u30ab\\u30a6\\u30f3\\u30c8\\u3092\\u5897\\u3084\\u3057\\u3066ng\\u3067\\u518d\\u521d\\u671f\\u5316\\n'''\", \"# \\u521d\\u671f\\u5165\\u529b\\nimport sys\\ninput = sys.stdin.readline  #\\u6587\\u5b57\\u5217\\u3067\\u306f\\u4f7f\\u308f\\u306a\\u3044\\n\\nN,M = map(int, input().split())\\nans =1\\nab =[0]*M\\nfor i in range(M):\\n    a,b = map(int, input().split()) #\\u4e89\\u3044\\u306e\\u3042\\u308b\\u90e8\\u5206\\n    ab[i] =(a,b)\\n\\n#ab\\u3092b\\u3067\\u30bd\\u30fc\\u30c8\\nab.sort(key=lambda x: x[1],reverse=True)\\nmax_a =ab[0][0]\\nfor a,b in ab:\\n    if max_a < b:\\n        max_a =max(max_a,a)\\n        continue\\n    else:\\n        max_a =a\\n        ans +=1\\nprint(ans)\", \"from operator import itemgetter\\nn,m = map(int,input().split())\\nlis = []\\nfor _ in range(m):\\n    lis.append(list(map(int,input().split())))\\nlis.sort(key = itemgetter(1))\\nans = 0\\nlast = 0\\nfor i in range(m):\\n    if last <= lis[i][0]:\\n        ans += 1\\n        last = lis[i][1]\\nprint(ans)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, M, *AB = list(map(int, read().split()))\\n\\n    Q = [[] for _ in range(N - 1)]\\n    for i, (a, b) in enumerate(zip(*[iter(AB)] * 2)):\\n        Q[a - 1].append(b - 2)\\n\\n    min_y = INF\\n    ans = 0\\n    for i, ys in enumerate(Q):\\n        if ys:\\n            min_y = min(min_y, min(ys))\\n        if i == min_y:\\n            ans += 1\\n            min_y = INF\\n\\n    print(ans)\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"n,m = list(map(int,input().split()))\\nl = sorted(list( list(map(int,input().split())) for _ in range(m)), key=lambda x: x[1])\\nbr = -1\\nans = 0\\nfor i in l:\\n    head, tail = i[0], i[1]\\n    if head < br:\\n        continue\\n    else:\\n        br = tail\\n        ans += 1\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nN,M=list(map(int,input().split()))\\n#- 1\\u8981\\u671b a\\u2192c,b\\u2192c\\u5206\\u65ad\\u8981\\u671b\\u306b\\u5bfe\\u3057\\u3066\\u3001a<b\\u306a\\u3089b\\u2192c\\u3060\\u3051\\u8003\\u616e\\u3059\\u308c\\u3070\\u3044\\u3044 -#\\nwant_list = [0]*(N+1)\\nfor _ in range(M):\\n    a,b = list(map(int,input().split()))\\n    want_list[b]=max(want_list[b],a)\\n\\n\\n#-\\u5206\\u65ad\\u3057\\u305f\\u6642\\u306e\\u6a4b\\u3068index\\u3068\\u8981\\u671b\\u3092\\u898b\\u6bd4\\u3079\\u3066\\u3001\\u8981\\u671b\\u3092\\u6e80\\u305f\\u3057\\u3066\\u3044\\u306a\\u3044\\u306a\\u3089\\u30ab\\u30a6\\u30f3\\u30c8\\u3059\\u308b-#\\ncnt = 0\\ncutNo = 0\\nfor idx,val in enumerate(want_list):\\n    if val >cutNo:\\n        cutNo = idx-1\\n        cnt += 1\\nprint(cnt)\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN, M = list(map(int, input().split()))\\nrequests = []\\nfor i in range(M):\\n    a_i, b_i = list(map(int, input().split()))\\n    requests.append((a_i, b_i))\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nrequests = sorted(requests, key=lambda x: x[1])\\nbridge = 0\\nans = 0\\nfor i in range(M):\\n    a_i, b_i = requests[i]\\n    if a_i > bridge:\\n        bridge = b_i - 1\\n        ans += 1\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\"]",
        "difficulty": "interview",
        "input": "100000 99999\n89369 100000\n46044 69130\n47367 71107\n617 941\n59484 89303\n9082 13675\n4113 6174\n65267 97907\n4790 7187\n95816 100000\n69383 100000\n60961 91518\n41549 62412\n90040 100000\n63790 95723\n55447 83221\n70804 100000\n80347 100000\n15776 23706\n56040 84118\n28191 42353\n48556 72936\n40947 61507\n79888 100000\n44654 67029\n15663 23542\n34029 51179\n72963 100000\n47258 70942\n35409 53225\n38326 57626\n33783 50802\n47080 70677\n51227 76892\n26417 39699\n30133 45276\n45630 68507\n37626 56575\n56054 84140\n79860 100000\n71771 100000\n87859 100000\n95162 100000\n70265 100000\n33421 50265\n17485 26296\n68327 100000\n97899 100000\n5436 8166\n99538 100000\n27718 41659\n31460 47310\n55237 82902\n25560 38419\n6802 10235\n89635 100000\n42340 63593\n67092 100000\n76443 100000\n63144 94778\n20224 30421\n2591 3911\n46036 69121\n14016 21103\n68204 100000\n69634 100000\n71392 100000\n51790 77736\n19973 30044\n32446 48804\n57741 86663\n23716 35679\n94654 100000\n8933 13455\n90845 100000\n65516 98278\n27412 41201\n82583 100000\n93629 100000\n39764 59747\n73254 100000\n46442 69733\n53911 80919\n84590 100000\n71585 100000\n34916 52498\n43980 66047\n18918 28465\n66535 99816\n33365 50177\n47164 70800\n47739 71671\n16406 24665\n35921 53997\n12022 18128\n16513 24825\n52629 79004\n5628 8448\n36787 55314\n26888 40407\n62891 94402\n49612 74506\n4515 6773\n38752 58265\n92920 100000\n56124 84238\n50245 75441\n59940 89981\n1318 1986\n95074 100000\n34382 51698\n5686 8531\n40982 61557\n55909 83916\n40434 60735\n94037 100000\n50105 75225\n94121 100000\n69798 100000\n11276 16980\n36339 54651\n38768 58289\n22475 33807\n31338 47123\n7586 11437\n12162 18331\n36814 55352\n89881 100000\n48603 73002\n86145 100000\n87199 100000\n26577 39928\n19244 28947\n85955 100000\n56774 85201\n79385 100000\n65713 98566\n36380 54714\n65179 97777\n25811 38794\n97990 100000\n78431 100000\n26249 39446\n34165 51379\n66361 99557\n7521 11335\n54124 81239\n73973 100000\n30016 45100\n19815 29801\n53267 79943\n58850 88344\n73459 100000\n42278 63497\n19526 29365\n49125 73772\n40639 61048\n99805 100000\n93421 100000\n77376 100000\n36358 54678\n21782 32764\n53737 80646\n3755 5634\n54128 81244\n41071 61685\n61927 92950\n89455 100000\n71402 100000\n81194 100000\n80215 100000\n15724 23625\n98618 100000\n71210 100000\n17368 26125\n90036 100000\n99510 100000\n8611 12977\n38886 58462\n86538 100000\n10943 16481\n67042 100000\n71695 100000\n86247 100000\n71762 100000\n53972 81007\n49482 74305\n71412 100000\n9454 14247\n99119 100000\n62923 94450\n30304 45533\n65339 98009\n18772 28247\n6101 9158\n10973 16522\n93324 100000\n25139 37799\n10627 16004\n92250 100000\n54004 81054\n614 937\n93611 100000\n64043 96093\n83921 100000\n48576 72962\n42197 63371\n14696 22127\n487 733\n62572 93920\n43993 66066\n86686 100000\n85036 100000\n7008 10556\n14641 22045\n98472 100000\n44302 66517\n81591 100000\n12011 18110\n27157 40809\n96245 100000\n99171 100000\n80071 100000\n72567 100000\n89908 100000\n96217 100000\n52592 78952\n20802 31304\n96546 100000\n36857 55422\n60577 90924\n76348 100000\n61811 92777\n83162 100000\n57888 86881\n5282 7939\n41864 62885\n77258 100000\n32380 48704\n50250 75449\n99946 100000\n73776 100000\n47841 71821\n87876 100000\n66449 99691\n32813 49363\n24651 37075\n77502 100000\n83521 100000\n87332 100000\n65740 98607\n86352 100000\n48614 73018\n70247 100000\n53000 79554\n6083 9128\n80333 100000\n12610 18990\n9102 13706\n71383 100000\n87229 100000\n60467 90761\n24896 37436\n92464 100000\n61900 92912\n43617 65507\n29446 44253\n14322 21571\n45370 68121\n60238 90416\n61955 92993\n98610 100000\n29206 43894\n15522 23333\n40890 61423\n56316 84526\n30268 45483\n90536 100000\n72278 100000\n20762 31242\n45918 68939\n41301 62030\n94310 100000\n58352 87591\n83902 100000\n99284 100000\n18504 27844\n78772 100000\n93732 100000\n12399 18684\n94871 100000\n88436 100000\n67133 100000\n76926 100000\n29722 44673\n96264 100000\n39197 58914\n32817 49371\n55242 82910\n3736 5604\n81167 100000\n66425 99656\n44127 66266\n89832 100000\n36542 54953\n83523 100000\n63423 95187\n3073 4637\n42577 63951\n77446 100000\n2365 3575\n10951 16493\n18256 27472\n55536 83356\n61097 91718\n53236 79897\n30731 46195\n95324 100000\n59007 88579\n68925 100000\n60098 90212\n26632 40009\n81804 100000\n77202 100000\n39471 59324\n41265 61978\n95551 100000\n87920 100000\n64528 96812\n87545 100000\n60445 90731\n83267 100000\n40053 60169\n70516 100000\n10479 15788\n37697 56682\n27700 41631\n13803 20779\n3014 4548\n90519 100000\n93685 100000\n90720 100000\n92445 100000\n9897 14898\n92848 100000\n42540 63893\n24322 36575\n33147 49866\n77474 100000\n99497 100000\n17354 26105\n85480 100000\n38465 57838\n14088 21200\n55633 83499\n42433 63729\n7143 10764\n80582 100000\n95486 100000\n16565 24905\n5430 8158\n18032 27136\n96470 100000\n18010 27100\n45369 68119\n48954 73513\n2965 4474\n30922 46480\n13275 19990\n91611 100000\n81560 100000\n88539 100000\n85432 100000\n67652 100000\n50702 76111\n65209 97821\n88385 100000\n86215 100000\n97875 100000\n77507 100000\n8540 12873\n78360 100000\n66503 99768\n8852 13330\n284 426\n17872 26894\n10579 15930\n57947 86970\n56103 84208\n19334 29080\n22857 34375\n13224 19911\n14202 21382\n28199 42364\n10757 16201\n74551 100000\n75216 100000\n13206 19887\n59098 88715\n38671 58140\n39413 59237\n65419 98124\n92289 100000\n89329 100000\n95299 100000\n70235 100000\n19226 28918\n40661 61081\n79587 100000\n27394 41171\n42031 63128\n98993 100000\n72426 100000\n57680 86569\n96915 100000\n81872 100000\n47999 72074\n53843 80815\n27303 41032\n23743 35721\n90166 100000\n94284 100000\n69051 100000\n95718 100000\n4696 7047\n77085 100000\n23385 35170\n676 1028\n40963 61530\n70502 100000\n99125 100000\n16299 24507\n64487 96750\n50874 76362\n13753 20701\n62654 94042\n69400 100000\n45962 69006\n42901 64433\n81066 100000\n83444 100000\n70702 100000\n32287 48569\n33464 50322\n6862 10323\n94574 100000\n95933 100000\n52467 78765\n51046 76621\n4386 6581\n83502 100000\n24624 37032\n24654 37080\n83960 100000\n32989 49629\n94839 100000\n49155 73816\n77026 100000\n62216 93383\n13168 19831\n51470 77261\n79993 100000\n19524 29363\n86655 100000\n6779 10198\n51533 77352\n24581 36966\n73647 100000\n44283 66487\n41274 61989\n11851 17870\n71198 100000\n12098 18244\n37400 56239\n23682 35626\n92270 100000\n89785 100000\n54396 81645\n26873 40384\n67312 100000\n95868 100000\n88716 100000\n56362 84588\n89266 100000\n25043 37658\n31705 47683\n4269 6404\n23402 35195\n6454 9709\n42568 63936\n24161 36343\n14207 21390\n16960 25503\n57536 86351\n94623 100000\n27199 40872\n93998 100000\n17012 25578\n98982 100000\n38943 58551\n11203 16869\n31965 48066\n17864 26879\n21330 32089\n33682 50648\n17948 27006\n61191 91857\n2811 4245\n46195 69359\n44585 66926\n83406 100000\n47637 71514\n75399 100000\n4468 6703\n89296 100000\n76998 100000\n86195 100000\n8805 13263\n9052 13633\n89838 100000\n3280 4941\n34510 51880\n4967 7449\n90092 100000\n606 923\n11613 17505\n36454 54824\n68003 100000\n5376 8078\n32013 48138\n41487 62321\n10439 15736\n89540 100000\n21881 32918\n90126 100000\n95949 100000\n90629 100000\n21925 32982\n35329 53111\n91651 100000\n59444 89245\n11806 17806\n51645 77519\n84976 100000\n65299 97952\n7207 10860\n18523 27871\n69551 100000\n70888 100000\n52949 79479\n72606 100000\n13422 20210\n42696 64133\n48583 72973\n93857 100000\n82640 100000\n24314 36565\n80102 100000\n52636 79016\n82495 100000\n60627 91004\n37447 56311\n21312 32065\n53898 80899\n22172 33353\n46645 70028\n30770 46250\n22443 33755\n85186 100000\n66078 99127\n79048 100000\n55965 84004\n24473 36802\n51336 77065\n6733 10126\n89232 100000\n72031 100000\n70865 100000\n10129 15255\n50749 76180\n67984 100000\n36591 55024\n20140 30299\n7255 10931\n98118 100000\n27534 41381\n31074 46715\n59417 89208\n12575 18941\n59137 88773\n32564 48984\n19583 29453\n51870 77859\n36851 55411\n59180 88838\n88570 100000\n61368 92115\n95948 100000\n2720 4111\n7722 11641\n8515 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        "output": "30\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc103/tasks/abc103_d"
    },
    {
        "id": 112,
        "task_id": 559,
        "test_case_id": 1,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "2\n1 0\n",
        "output": "1 1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 113,
        "task_id": 559,
        "test_case_id": 2,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "3\n0 0 0\n",
        "output": "0 0 0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 114,
        "task_id": 559,
        "test_case_id": 3,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "5\n0 1 0 1 0\n",
        "output": "0 2 0 1 3\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 115,
        "task_id": 559,
        "test_case_id": 4,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "2\n0 0\n",
        "output": "0 0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 116,
        "task_id": 559,
        "test_case_id": 5,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "2\n0 1\n",
        "output": "0 1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 117,
        "task_id": 559,
        "test_case_id": 6,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "2\n1 1\n",
        "output": "1 0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 118,
        "task_id": 559,
        "test_case_id": 7,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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0 0 0 0 0 0 0 0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 119,
        "task_id": 559,
        "test_case_id": 8,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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0 0 0 0 0 0 0 0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 120,
        "task_id": 559,
        "test_case_id": 9,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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0 0 0 0 0 0 0 1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 121,
        "task_id": 559,
        "test_case_id": 10,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1 2998 1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 122,
        "task_id": 559,
        "test_case_id": 11,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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0 0 0 0 0 0 0 2998\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 123,
        "task_id": 559,
        "test_case_id": 12,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 124,
        "task_id": 559,
        "test_case_id": 13,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "2999\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 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        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 125,
        "task_id": 559,
        "test_case_id": 14,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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988 0 928 0 83 0 1815 0 378 0 708 0 2177 0 1595 0 2169 0 974 0 642 0 1446 0 1057 0 2320 0 518 0 1764 0 347 0 101 0 413 0 173 0 1639 0 89 0 2986 0 524 0 569 0 377 0 2908 0 2174 0 62 0 854 0 1776 0 1224 0 1470 0 2745 0 186 0 2818 0 430 0 2569 0 1899 0 2571 0 2379 0 165 0 586 0 68 0 327 0 1957 0 2889 0 349 0 562 0 876 0 437 0 2806 0 2212 0 2313 0 2055 0 1221 0 1215 0 490 0 898 0 1513 0 2788 0 2130 0 667 0 1054 0 1291 0 327 0 721 0 1884 0 601 0 832 0 2489 0 1967 0 87 0 117 0 881 0 2489 0 1821 0 919 0 2024 0 1854 0 2873 0 638 0 1318 0 925 0 989 0 554 0 1826 0 370 0 839 0 2986 0 1465 0 2925 0 2301 0 1818 0 1206 0 2427 0 700 0 1680 0 2081 0 2122 0 895 0 2362 0 1188 0 99 0 907 0 332 0 2112 0 2566 0 536 0 2680 0 1965 0 527 0 249 0 2325 0 1071 0 2249 0 1880 0 1936 0 1929 0 1772 0 525 0 1532 0 1907 0 831 0 2502 0 2007 0 1998 0 521 0 552 0 2089 0 1597 0 2115 0 1788 0 2257 0 1311 0 750 0 2624 0 750 1499\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 126,
        "task_id": 559,
        "test_case_id": 15,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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1844 418 1041 247 121 2711 670 817 974 492 2325 2675 2403 1833 1773 1528 2464 740 353 1748 1669 555 757 2067 1839 1305 2161 2447 2114 1770 2723 1937 1559 2705 751 2362 1871 2984 743 67 1426 2368 1033 504 2215 2693 1334 2812 1828 167 1165 1900 1576 1740 807 2040 1819 2011 2370 649 1289 2750 1580 2584 927 981 977 2065 572 2268 857 186 1819 2065 778 2223 2450 2859 670 1705 1766 2652 657 1406 1259 2488 1378 2663 2521 2732 484 2108 638 2971 1950 2117 2272 2310 2491 1943 1741 1272 2657 1675 715 956 1871 2522 2568 15 2544 2043 2138 1512 583 582 2841 1373 2194 276 2473 395 606 819 1940 2090 1307 995 2756 844 227 2621 2765 438 1300 723 2198 1471 2816 1784 512 994 1430 1282 2487 687 608 788 2044 2729 1267 2090 111 1864 2980 2516 2969 1498 369 841 667 370 742 2413 2444 1648 769 300 705 2162 2780 2574 13 1969 2549 1050 1932 1779 2169 1578 2026 1592 927 1376 2119 2159 931 317 179 2475 1615 1508 765 83 2893 1932 2587 765 1547 2305 2244 601 491 1804 2348 268 2396 2781 2789 1209 258 2187 1017 2216 2339 893 407 237 2145 733 227 2440 616 744 1560 1424 1920 2988 2166 966 1921 179 1092 2550 729 257 1814 2956 2395 2304 2640 2840 2910 598 944 2434 381 2035 2304 2955 805 1994 2922 1661 1325 1889 2816 966 2189 921 1134 866 1423 1214 1645 672 2716 1402 2976 1782 1007 2942 2204 2398 1885 840 18 1137 2803 2291 2021 1537 982 2311 508 2632 2850 2737 1394 2903 2107 482 2247 1827 2829 1611 2460 466 546 550 447 2450 2200 400 1000 981 1636 1688 376 1772 1764 1956 69 1536 954 259 686 554 1675 2465 1914 733 934 2212 2093 2875 1742 1068 2510 474 2768 2704 730 49 2618 1588 263 1136 350 2571 2405 2020 2890 696 2163 1709 363 377 2448 38 1261 2721 986 2275 1005 541 1403 2394 2331 1108 1149 2348 2898 453 1525 2219 1497 828 132 2989 2467 2682 59 874 2072 1040 800 2053 685 2555 2343 2873 932 892 2712 1451 2945 1965 318 2344 1251 1830 2593 812 459 2718 1432 1163 2918 973 1264 1236 758 2400 2350 1955 2129 2728 1995 198 1021 1252 439 92 1377 1885 1946 2398 1802 83 233 332 1693 2626 937 747 2552 1558 939 2576 1317 1348 1737 2349 189 918 5 1227 1817 1918 1511 1466 1046 1483 621 1095 1526 125 2022 1883 1892 1526 515 2630 1351 1475 1748 8 1594 2393 2050 936 1411 955 2740 2701 1474 415 858 2882 2037 1657 139 348 1727 880 752 2810 1209 2395 1915 2507 461 421 369 1679 2352 1048 2577 2004 1109 750 2970 2917 2174 2880 1013 2145 1182 1404 1926 1036 2678 1729 2637 2224 953 2766 2150 1993 1769 1084 2900 2963 1709 1519 2113 855 546 403 81 646 177 2456 2163 1771 2674 2620 537 1977 1493 1481 1392 1385 1327 909 192 1856 280 2611 2890 1648 2853 481 2947 256 612 278 85 2705 1806 1137 1201 2555 2946 495 2587 2554 2183 886 955 2109 981 596 1124 259 308 512 2212 430 741 223 2261 1731 201 43 2161 2370 553 2887 2594 793 1237 1567 1177 2016 953 1863 317 2636 1577 2871 1151 28 2172 1123 1824 1626 1267 1578 2861 594 1125 2662 131 1632 1404 1127 201 2827 2874 80 43 2087 1647 2175 1263 2771 2011 2634 2071 2459 1166 464 1014 1044 202 2105 1510 2798 2264 156 174 2401 2109 455 722 1242 1578 2724 2746 1022 2568 889 2117 2638 2969 101 418 2136 650 503 357 870 920 208 2604 1424 1066 2924 962 2646 2020 150 266 1913 2641 596 2317 2501 2488 2549 1700 797 399 1663 1811 1689 1017 1794 2382 763 2568 1855 2779 1186 1913 607 2780 1156 956 1137 624 2764 2461 1834 2880 1852 811 2792 2469 2776 426 123 1607 1378 1422 122 1574 975 806 2707 2271 1409 2083 2821 2898 1546 571 1110 2460 2873 72 1857 648 79 2851 1461 1909 2441 2707 862 1833 979 2492 994 2446 1968 1809 848 2173 86 1175 67 1908 2121 1495 2941 1435 1947 950 2471 635 1757 2590 2956 2981 1743 1800 840 1370 2324 1272 2894 2687 1534 0 2117 2599 374 1130 692 2179 426 1828 2555 2374 968 1047 1917 2453 2742 941 1279 913 382 1626 2377 2553 641 599 2659 827 938 2667 2164 2674 2962 401 2404 820 1837 554 2463 1619 1758 511 1508 1432 349 1644 2215 2578 2806 640 2400 2351 2555 2391 2970 2715 1073 311 1903 209 1346 709 1322 443 240 2505 1265 1186 751 1880 1641 2267 2078 531 1467 891 169 1994 975 725 678 583 741 1227 543 2693 605 1520 2048 2646 347 614 1143 1815 97 2846 1269 1565 2574 2468 2718 779 27 1513 2788 465 1492 579 2443 1901 439 1253 1963 1204 2382 509 2695 1745 451 1298 41 2522 2873 1288 807 747 1975 2295 2185 1408 934 2178 812 1135 639 2375 2774 1285 1453 1503 1002 1847 444 1334 645 1902 1832 1931 682 1469 313 447 2679 1901 228 1301 2612 1053 988 2626 180 1787 830 2969 2471 101 2576 1412 1795 716 1443 430 2838 1720 899 339 1532 467 989 1153 587 601 2028 2453 2884 1240 26 1517 1464 2042 1241 932 252 628 2049 1151 862 2628 1523 1910 1601 1111 732 38 355 749 2941 534 53 1385 2586 1789 283 1944 2056 636 1970 877 1322 942 309 2292 2944 1759 1735 1622 2761 2606 1895 2104 1839 2788 2313 2402 2383 385 1007 519 2244 2543 960 2011 361 893 2826 1446 685 25 1614 995 2537 2687 52 38 1450 1024 699 1742 2157 1062 539 953 379 1542 2297 2677 688 1917 1817 1890 1069 2945 842 400 1730 311 1278 1872 1434 418 1555 2299 482 595 2629 2660 1937 2106 2725 975 2216 2595 68 1200 2560 1749 2795 1974 2867 2442 1950 1522 1576 1687 27 70 898 252 361 2133 1728 1003 1906 2678 2990 20 2442 1629 1920 1070 1245 667 2265 2069 1194 2734 2515 1883 912 378 1808 412 118 1883 784 1719 2483 402 2719 1749 345 1332 444 2324 465 2404 2946 286 2711 76 2551 1440 2150 1848 174 1988 721 791 2799 1260 2451 1970 377 2183 773 1525 1707 1186 461 1058 859 239 1989 1893 152 2047 1445 606 580 1907 1072 1248 1231 714 2875 2742 2249 2212 1208 461 2432 2693 538 2850 2605 453 2725 81 2263 36 568 2053 1078 1459 1005 1840 2032 845 1704 1394 1559 1035 1839 1704 2717 675 1135 191 959 480 654 2612 1969 2547 776 860 2198 878 268 986 437 964 1614 2416 1160 2549 1039 1698 2253 2832 2600 386 1742 1693 2410 9 1221 1221 593 2292 2221 1950 1129 2805 1808 1453 1954 1681 225 1915 2809 2689 1136 302 2777 2765 2417 1491 1549 221 2655 1659 571 1640 2289 2693 2675 862 1106 117 916 1998 2915 571 2106 854 2967 2467 2455 1488 980 1066 2306 1720 1200 766 2356 737 2002 179 2038 336 149 836 2308 456 135 941 1625 2068 56 2770 2409 2518 1451 2817 629 2447 2196 1384 2122 1789 1402 698 968 1507 1547 282 324 2940 1318 2826 2175 1984 416 228 511 661 287 790 1819 169 754 231 985 2243 822 2773 332 2820 1532 2308 2745 432 441 1110 780 1520 1267 2127 293 186 444 1909 1982 341 1482 1745 1445 2104 2803 1114 406 500 1706 2861 1909 2806 73 2264 2800 1668 2133 1894 2070 1745 2169 991 843 1218 2115 1627 1830 2529 2986 1529 886 1016 954 401 1501 1252 2926 465 278 294 1030 2374 1076 839 1657 1932 1793 2114 2379 1429 2587 189 1351 2745 2420 437 621 2310 1942 1578 2783 1302 1672 1021 1894 742 534 1950 2860 1359 816 1514 422 2422 251 1341 1996 1137 847 269 1653 162 2668 1038 675 2944 2560 2849 1733 2432 2301 536 2531 566 2979 2527 1009 858 880 2178 1493 2651 2541 1147 602 1096 527 258 2882 2567 699 2494 1758 2342 720 1544 407 2380 966 1981 2375 2736 1031 2464 1490 437 2179 685 2221 19 2012 2627 2005 1793 969 2280 2246 1371 896 2049 12 1183 663 539 2358 868 324 1376 2023 1895 1512 2577 1268 1602 269 2515 2260 1310 1450 2030 2031 2512 1152 278 32 2356 220 1908 808 845 1581 577 214 168 1858 985 2801 415 1926 400 401 2309 2816 11 1229 1871 2507 224 1851 1211 1273 1980 716 1193 1162 2817 338 388 754 2856 2200 1350 1653 2063 1762 513 988 2922 2539 2381 2736 21 2778 2692 1437 2521 591 1978 1424 1400 1478 528 1612 1543 34 123 1860 2260 1237 178 665 647 874 474 1723 989 1699 2307 2252 1184 1445 2847 1624 870 262 2244 1256 1979 1237 2199 2451 224 2720 2759 1614 991 1413 1010 452 1702 2380 259 1041 1668 1466 1982 1665 1151 217 1780 2867 2729 1390 2681 2385 1614 1014 2113 767 2931 2881 132 615 1726 2591 2809 245 981 2590 1875 1019 1059 2266 2030 46 837 2064 2383 369 1073 557 1232 2510 1225 1055 2555 2837 1397 1458 1792 1835 1843 2883 2534 813 1554 2514 1582 104 1246 2635 316 2987 919 132 235 1109 981 350 537 2594 1099 1058 2698 277 1234 216 1446 2120 1002 501 1424 896 1422 2267 1199 110 13 1286 1757 2694 2269 1034 1250 2099 1684 1101 535 1847 320 10 19 450 2373 2773 2520 415 1266 2096 815 2603 816 1624 2211 2137 1442 865 343 1137 1375 730 2788 2624 1542 153 2413 1210 2448 890 2557 758 1453 2753 2616 672 1617 1463 2812 2279 2934 1406 486 2005 1621 577 2482 772 2187 177 2266 660 2578 751 54 2329 247 1943 2172 131 391 1834 548 832 2147 522 2910 2132 60 2053 2035 94 177 1831 1764 1524 1632 531 1323 100 1627 250 2974 608 1295 1208 533 1157 2560 2160 214 2911 2698 1572 2124 846 2191 1379 1199 1447 753 291 2292 1397 1476 2092 1774 2291 536 1557 1669 1158 1604 1616 892 1011 2191 2399 82 2659 1828 2391 2466 2646 1669 2345 1121 2753 799 2696 28 1162 1352 2592 570 2064 1785 1778 1061 2574 2988 957 2104 1142 1097 1096 1504 358 343 1012 2336 2648 1801 2376 784 1522 532 1467 2448 682 41 2315 447 1635 660 2860 77 2307 2421 649 1580 1997 1535 2537 70 1441 2914 677 1801 449 2252 2838 2714 2230 1088 2357 111 943 1601 567 2526 1278 2430 1827 2671 2884 127 1765 2646 525 2694 2164 1183 2525 1927 39 568 1527 2257 1806 1407 533 2826 2144 980 2719 452 291 1031 2533 2859 336 1503 890 252 1172 86 2000 2526 688 276 2868 497 2161 166 2255 690 1290 1714 844 1204 1021 1589 1355 979 139 1448 446 16 2618 148 501 2212 1807 1497 1908 867 1211 1057 331 1899 636 66 2624 1727 2092 65 523 1633 2690 747 164 684 2907 1770 2121 1117 1284 1321 2074 2213 1717 826 466 2275 1882 373 2253 321 422 634 2636 326 1643 2659 1171 1953 699 336 2945 2885 2540 668 1865 918 1903 241 2895 519 2551 2243 1756 472 2175 2697 545 1378 717 338 454 412 1966 1012 663 1015 1556 819 2559 2786 2167 281 2378 2648 820 622 852 330 1408 1319 2875 946 2944 2651 386 2989 570 1623 1858 1336 2618 1511 2046 2254 752 2852 2677 1538 875 201 2379 1549 2323 1565 2922 603 1722 99 2963 196 2436 2951 289 2755 2081 1880 2056 601 1526 1450 2295 2372 2531 168 2076 1485 1085 2964 225 2435 2054 1610 2909 2631 252 2448 667 2795 495 669 1066 2581 177 461 1756 2111 2104 602 608 1359 2459 1268 2274 51 421 1231 1634 2732 623 1057 652 1714 2976 848 1046 2384 2309 1686 1559 683 504 927 1705 554 384 1174 2506 2617 1426 1419 721 2494 1307 1018 1611 369 712 1987 1529 1562 1700 2774 2364 312 175 948 2860 2196 2342 2133 263 2964 601 2871 1470 441 942 2924 2926 926 242 964 2432 2581 147 2204 2961 837 1263 2744 581 2680 1423 2105 1884 2673 250 1377 2818 961 2260 218 508 790 299 1622 1309 1872 585 2198 432 1818 876 1254 292 2107 1877 2604 2452 442 781 87 2837 2855 2467 195 2121 596 663 1988 1321 2166 724 1532 2721 2541 2300 585 1534 578 514 1575 429 1222 2203 2522 1700 898 851 2501 2137 2394 2570 174 2830 486 256 2025 1500 2548 2946 1885 2170 1591 772 2531 345 368 2172 632 1607 2304 1128 541 499 2187 746 890 1220 2014 1378 2603 1410 1862 193 2352 1308 2432 117 164 70 1965 1254 169 2759 1096 1351 384 2452 1297 403 2589 2838 2689 339 2717 2894 2545 2080 2684 1396 2814 2919 2050 1805 1953 844 1919 6 1874 2469 1084 2727 2663 538 577 1199 2398 2457 2216 730 2508 381 262 1584 2210 2062 684 199 2263 2334 328 1904 2666 548 864 1568 648 1867 718 2038 1604 2985 1835 720 854 2124 2609 1150 982 1818 2774 880 2273 2593 18 1288 1038 2097 1373 950 2335 2739 2664 1588 554 2761 873 1686 1282 322 2301 1645 2275 2398 2766 1242 1157 2342 1669 1163 1436 1959 597 1188 333 1434 1610 609 1195 1808 2786 2385 960 468 2047 2662 2974 2893 1506 1337 1954 1547 576 1970 1492 2388 389 47 982 994 226 2291 2889 2181 2681 1145 2839 2183 831 2826 1021 971 1819 752 1942 2053 168 2180 2381 965 812 204 896 2923 1395 2126 2852 577 1210 2185 1230 1501 230 499 956 2364 1477 2515 357 1318 2449 2428 39 1514 1961 2708 1866 2088 2872 361 1386 1467 1940 2532 2966 1197 225 780 2103 1762 1259 2980 1633 1990 1934 2976 2516 2065 2412 2768 1330 1452 2144 2416 756 2957 474 451 1057 1434 596 2592 496 2484 1262 2806 377 2849 1816 2846 1552 842 1385 317 2686 1478 760 433 2352 2467 120 2298 1836 1630 2240 2924 2410 1149 1657 1568 2666 1058 2219 1377 2492 260 810 1101 1028 552 2603 61 1678 392 342 2377 1623 2391 526 1304 206 925 2573 1092 1901 239 602 2826 1655 818 1300 1754 458 2069 2101 2726 335 747 2811 635 1756 1746 2749 354 562 1666 1919 1770 1814 1300 1256 1450 1041 1163 1446 2272 1119 2978 2570\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 127,
        "task_id": 559,
        "test_case_id": 16,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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1644 2020 2860 1551 2553 2983 381 2851 2498 787 1192 1502 1091 2132 1788 1942 2668 1100 2363 2933 375 1272 907 2934 2476 1366 309 2252 2835 2315 92 1229 878 1882 1715 1678 925 786 1282 2173 2533 724 1117 2626 746 2678 2577 2365 363 2673 1356 340 1828 1046 2300 2663 54 114 459 2331 1134 2081 1096 2758 104 2480 448 756 1243 2527 824 302 2454 1621 2282 2661 2545 2587 1033 1987 2336 1984 1443 2180 440 213 832 2718 621 351 2179 2377 2147 2669 1591 1680 124 2053 55 348 2613 10 2429 1376 1141 1663 381 1488 953 745 2247 147 322 1461 2124 2798 620 1450 676 1434 77 2396 1277 2900 36 2803 563 48 2710 244 918 1119 943 2398 1473 1549 704 627 468 2831 923 1514 1914 35 2774 564 945 1389 90 368 2747 551 2332 204 2504 2330 1933 418 2822 2538 1243 888 895 2397 2391 1640 540 1731 725 2948 2578 1768 1365 267 2376 1942 2347 1285 23 2151 1953 615 690 1313 1440 2316 2495 2072 1294 2445 2615 1825 493 382 1573 1580 2278 505 1692 1981 1388 2630 2287 1012 1470 1437 1299 225 635 2687 2824 2051 139 803 657 866 2736 35 2398 128 1529 2558 2057 75 73 2073 2757 2035 567 418 2852 795 38 2162 1736 255 2418 319 1576 894 1115 326 2749 1622 181 2038 739 2781 2491 2209 2700 1377 1690 1127 2414 801 2567 1181 2123 1745 2707 892 1122 395 547 2557 2218 2912 162 144 532 2804 878 2403 2336 1011 1678 833 2275 1467 278 458 699 2414 1465 2421 2485 1424 2570 1777 796 477 1299 2101 2148 498 862 605 429 2825 169 2513 2743 974 1499 451 53 1114 829 1408 2227 468 2654 2631 827 2367 1392 695 1871 2458 2500 812 2253 2109 1779 985 1621 396 1589 1137 2806 647 1691 567 2882 2835 2929 1034 1745 2830 240 1903 1648 2615 547 1702 2596 410 161 310 2660 282 105 454 919 315 1603 185 80 949 1194 1046 2155 1080 2993 1125 530 1915 272 336 2461 2422 1800 601 542 783 2269 491 2618 2737 1415 789 937 2315 2800 736 665 2671 1095 333 2451 2135 1431 2351 1132 2281 961 1395 14 1164 2279 2145 875 390 1849 2017 1181 225 2119 726 406 2981 1711 1961 902 1626 2049 664 260 335 1411 2445 238 2126 1313 1717 2677 698 1354 724 601 233 1757 1842 657 1330 1836 1563 1040 2402 1811 2666 1565 1389 2390 1804 1191 213 614 2039 2531 952 337 25 106 1493 1662 1045 1452 2423 1029 1507 611 2610 2952 2017 2005 2773 708 110 818 318 1854 160 816 2168 173 1978 2028 1180 2247 1057 946 2831 819 618 2034 2187 2795 2103 76 1604 873 147 2422 1789 814 1769 1498 2769 2500 2043 635 1522 484 2642 1681 550 571 2960 1485 1038 291 1133 911 127 2638 1613 1532 1059 467 33 1802 2774 2219 896 1237 1740 19 1366 1009 1065 23 483 934 587 231 1669 1547 855 583 2243 42 2525 2548 1942 1565 2403 407 2503 515 1737 193 2622 150 1183 153 1447 2157 1614 2682 313 1521 2239 2566 647 532 2879 701 1163 1369 759 75 589 1850 1342 1431 333 1941 780 1622 507 2739 2189 1898 1971 2447 396 2938 1321 2607 2657 622 1376 608 2473 1695 2793 2074 426 1907 1098 2760 2397 173 1344 2181 1699 1245 2541 930 898 273 2664 2252 188 2364 1243 1253 250 2645 2437 1333 1080 1229 1185 1699 1743 1549 1958 1836 1553 727 1880 21 429\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 128,
        "task_id": 559,
        "test_case_id": 17,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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1527 0 1920 0 752 0 1808 0 2169 0 2852 0 2419 0 1435 0 2271 0 1601 0 2555 0 567 0 1249 0 1265 0 171 0 2173 0 2562 0 763 0 1745 0 975 0 1308 0 2223 0 1993 0 1745 0 2023 0 397 0 1965 0 548 0 1162 0 1107 0 2611 0 1039 0 2722 0 1405 0 1879 0 2645 0 1392 0 377 0 2093 0 940 0 656 0 1597 0 2426 0 27 0 2891 0 499 0 2925 0 356 0 8 0 150 0 1216 0 633 0 1589 0 2536 0 96 0 2569 0 2111 0 200 0 1980 0 2088 0 2231 0 293 0 2487 0 320 0 1195 0 1538 0 894 0 423 0 2605 0 1503 0 1969 0 576 0 1090 0 1616 0 1513 0 256 0 210 0 1619 0 2061 0 944 0 1562 0 242 0 2408 0 2584 0 1127 0 2488 0 1506 0 2939 0 644 0 2473 0 57 0 461 0 945 0 2899 0 2238 0 2208 0 2519 0 1364 0 576 0 253 0 2563 0 1367 0 1634 0 2047 0 2257 0 1022 0 1599 0 2692 0 1447 0 128 0 2042 0 1917 0 1633 0 940 0 2887 0 1545 0 910 0 1147 0 446 0 2994 0 2198 0 1318 0 458 0 766 0 2045 0 1192 0 2065 0 396 0 2840 0 2176 0 2637 0 2158 0 2717 0 2804 0 1886 0 2110 0 2559 0 617 0 16 0 2666 0 432 0 924 0 2835 0 328 0 375 1499\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 129,
        "task_id": 559,
        "test_case_id": 18,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 130,
        "task_id": 559,
        "test_case_id": 19,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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1437 1488 2050 1673 2373 1041 888 802 197 1737 793 2782 173 2657 1087 2198 1572 2586 2685 873 1053 2096 489 2626 2618 586 1496 1456 2022 1022 2796 1779 1406 1314 2849 2921 1730 1893 315 2760 2213 313 2107 1672 2681 295 809 2881 2529 1994 2257 262 566 1527 1740 1923 666 640 2419 2982 2067 2472 2104 2234 1792 434 101 936 2692 1211 1052 1312 188 2114 2709 1857 788 1367 407 1202 2409 2593 867 2567 413 657 2024 2015 1036 2005 2742 1792 1281 1747 94 753 2078 2577 716 1086 2216 2396 1089 1706 1551 1877 2412 880 1767 546 199 2046 1294 700 2658 83 173 503 1446 2882 1488 198 2487 1133 1584 543 1951 1624 1220 2492 330 1184 2997 179 562 2440 1776 2407 2647 147 1368 1396 1283 581 1835 1234 1469 2346 2857 2323 2331 2773 2869 2191 343 2829 849 422 806 696 121 1099 729 1429 2034 2387 2810 1108 2680 251 1217 407 1737 613 1632 1404 1872 630 2802 1983 2984 1874 670 1392 2948 1542 1493 1283 1528 551 1080 170 498 1667 1761 1842 1034 715 2841 573 2624 2695 2635 2169 2920 2436 974 1394 220 1863 1271 2199 654 925 2394 2485 2074 613 1342 759 390 2990 1776 11 1980 1692 2571 664 2340 2241 2743 1421 1320 568 1018 1669 859 611 2914 1572 309 1650 2449 570 621 1008 472 1125 264 1809 137 2973 1470 2237 515 2802 349 2864 864 151 1549 2251 492 2265 2938 2866 316 2662 205 782 1501 1852 774 1534 1423 2569 628 597 1586 2531 1378 2992 1513 1670 451 25 1343 1348 404 928 1373 728 816 1976 2339 25 739 370 1768 1613 2988 2876 729 2374 927 1062 2005 2884 38 860 1368 2917 2303 1329 453 1320 1603 2236 1331 585 1949 1327 1384 2997 1282 1923 2393 242 688 1753 2580 241 1839 2747 2342 749 1441 1908 968 1927 877 2004 2106 1138 2972 116 336 1211 2683 2342 895 2925 738 690 1256 1748 108 1518 347 2031 641 1697 1325 2132 1302 2486 2247 50 2379 554 2958 250 1673 2379 986 2553 324 1751 1230 1943 1718 908 2755 340 22 569 2337 1420 2900 2403 2743 1641 2764 913 1412 1667 565 2186 2482 1600 426 433 2327 2932 790 269 2105 1072 2739 2762 819 2190 2849 2472 776 1707 817 1039 297 245 1857 2833 1312 2154 480 1700 2587 387 2468 2473 294 601 450 1522 931 96 1344 2085 2653 1358 304 2136 1299 733 525 1187 2947 751 526 2506 2256 1043 494 2654 2283 1125 2599 1853 1740 1247 2935 2826 1788 331 416 186 1790 1749 1310 314 643 1806 1583 2467 2125 905 1296 2890 1201 1363 1909 1373 458 995 1609 432 2363 2246 1063 1899 2181 2565 365 2397 2151 234 1345 2544 1636 2451 391 652 140 1920 2708 1889 1181 2694 757 564 1554 2773 2418 1151 2672 122 2399 2330 1192 911 1687 1653 2256 386 1724 1853 1188 1242 838 859 432 752 2249 1298 200 1679 653 2893 2868 25 2006 2441 783 704 2544 1485 2111 227 1120 2659 2634 1286 1209 1855 1532 2671 1417 2776 1042 1265 1832 2468 2888 2679 1000 2507 1365 444 1778 256 167 716 889 1302 566 1778 2551 1599 2350 311 470 574 2583 2191 218 2910 2305 2672 2753 2405 1260 2905 160 952 956 1974 2250 662 2105 2912 911 1954 1748 397 1873 2928 2371 2594 694 915 1493 674 1202 1841 1335 705 2715 2438 2504 2229 2419 384 1617 498 2134 2586 692 2289 2138 10 2344 2854 1561 1527 1534\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 131,
        "task_id": 559,
        "test_case_id": 20,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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        "output": "1 2982 719 1371 954 2617 2397 2503 271 2931 1001 119 2099 1640 2495 346 2040 1849 1354 2253 2594 2346 638 1877 810 947 2165 2281 350 2747 1815 1107 2106 304 2704 2640 2010 2780 144 1088 726 1702 2157 1049 2168 1667 2000 1920 944 958 1235 2561 1177 802 2124 23 2923 2322 2284 510 727 1959 635 998 1378 1236 1649 202 2704 1857 492 2828 1212 1348 1371 2068 1927 1365 2020 320 283 950 920 2688 1569 764 428 1978 2461 1593 2002 2002 1218 2417 181 1851 1605 1255 2827 1905 115 1668 1315 1932 1862 2246 1313 1248 2927 1940 2748 1016 1433 188 372 611 660 2872 72 2266 460 2868 2170 265 917 2101 1018 1733 1013 1866 768 1502 2544 2867 343 321 2334 2515 2742 2686 2877 669 2418 2669 990 1201 2646 2014 2858 1661 2225 2467 445 1946 570 584 382 2885 2893 1304 1123 464 2479 2094 1564 121 2314 1777 660 1941 257 1108 220 1505 2038 2043 886 303 1864 385 1855 1692 1199 1799 1277 2253 1598 114 1964 106 2308 1189 2959 2074 635 22 2341 1 1236 1368 2560 1857 1699 1869 106 434 2745 889 1837 2135 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1844 2850 764 2976 2599 725 2854 2698 1887 598 748 465 2916 2957 945 1926 2586 1472 2570 2696 746 1724 2937 613 2648 491 533 1634 847 2915 1459 1609 2683 1597 1072 1541 2517 516 1478 2485 1638 744 1156 2060 1644 1425 1308 2993 461 286 896 2519 1281 2665 2469 2110 2480 1833 1656 439 440 1180 1255 6 1943 38 930 1129 1931 1235 2995 543 1411 1219 1122 1642 612 2190 2856 202 385 2518 63 1015 2432 540 1318 2597 2590 1817 84 2424 2318 1931 2494 2038 1172 630 465 2721 970 2215 127 2980 2248 607 279 41 2767 1269 2558 343 2456 2613 196 1127 2599 2368 428 1241 2301 2979 2769 1706 1872 1062 2199 1085 2957 1076 855 375 1183 2232 537 672 866 614 1210 2334 2567 952 2354 999 2327 2129 2693 1459 1166 1050 943 2770 2718 1951 1302 1862 1890 2785 1291 758 998 1958 1755 2307 1222 1953 494 519 1052 743 771 1422 1776 1723 242 2831 1520 642 747 1615 974 1686 1643 2758 2467 2145 1229 577 2856 1385 966 882 2512 2744 379 2073 426 1952 2379 2865 1417 243 2567 1923 2923 2671 54 264 2430 1724 2881 812 2447 750 2263 1829 2477 81 996 1078 1536 341 387 2247 974 2131 791 2940 933 1772 546 1013 1785 2917 2710 2392 1480 2429 2228 1198 2573 1141 1758 2951 1762 2840 1698 917 1119 2316 422 304 2128 270 416 171 2217 2499 2991 1199 964 2220 2620 1578 2020 347 268 2135 501 1456 1265 1654 1565 98 1774 224 1089 1150 2084 1983 337 1474 1741 1500 708 461 2502 401 1481 981 732 282 2656 645 1961 1386 313 1276 1767 1945 1216 1428 2400 1563 178 1826 531 793 2718 2759 244 907 1753 771 1361 2174 1069 1543 304 2655 720 1403 731 2901 1926 174 2089 1871 2399 2863 1224 2336 2000 1569 1840 18 788 1600 913 1796 1848 1984 1225 2667 556 1458 77 1707 1566 363 235 824 49 2924 144 2418 2058 2907 1554 2818 1748 484 2203 1973 1941 2731 1684 2700 1453 1659 262 1378 245 1543 746 465 773 2578 1249 2825 2899 2313 1988 641 616 1305 2020 1564 1422 1458 452 1866 1342 1663 1028 355 1032 1625 661 1525 2775 1543 1344 1085 191 2172 88 644 1220 416 1775 1274 2347 1028 2206 701 823 687 1287 94 487 1674 2949 2853 900 1460 2179 899 672 344 1515 2202 426 2810 1298 2942 1209 750 1674 338 591 342 2023 756 263 1419 1925 2753 2942 2010 1740 1065 1440 1871 2960 628 1684 2197 222 1564 481 1227 1014 2350 922 2225 1656 2122 911 1793 140 1565 1385 1620 1362 1871 1687 2971 253 2600 2239 1559 977 1739 2664 1066 1606 551 2989 802 170 502 542 464 2933 646 553 769 2495 2407 1452 507 1626 1482 2948 2593 2229 297 2753 2330 1826 2055 2993 2863 452 2889 2535 2509 2889 1722 2532 1554 1924 174 409 2478 612 929 874 1601 1392 2898 1914 2262 1463 1404 1529 1804 1955 1898 2367 20 417 2774 2539 2530 2315 857 1648 739 1588 1497 2728 651 1113 614 228 2506 2031 737 721 2802 149 2281 720 873 2306 569 228 2234 2498 2427 1878 826 2170 2207 2628 660 2664 2869 1350 536 2333 1392 1514 369 339 2706 1179 2483 47 1504 1771 1854 1093 1389 2855 700 1456 870 2051 2333 1689 1901 2789 618 208 442 2748 213 2154 3 970 241 1235 812 4 1423 969 176 638 153 1471 387 1267 2128 1897 1910 541 720 796 1396 1618 512 110 2035 1896 437 2834 1475 1238 1766 596 135 953 504 2670 2560 1272 39 2965 199 1912 1870 568 1636 2618 1630 1639 302 1321 1123 563 93 1538 1689 1539 993 2782 1670 634 1771 81 2167 1337 445 2777 95 2642 2917 279 1535 1022 1092 2696 2663 1328 1034 1137 1067 2186 1369 2080 2941 80 530 1605 2976 1533 1669 2865 2261 293 1060 186 1359 64 636 2771 1115 2779 2594 867 2222 2743 518 1323 2370 2669 1846 2516 1016 699 1030 2785 2819 2711 352 686 2848 534 798 2445 514 2603 2212 1464 468 2874 1423 2863 1965 465 1553 2264 1557 2607 1224 590 1473 2159 487 800 2648 2986 165 940 1719 1703 293 2769 1893 547 314 2115 321 1746 1425 2754 979 1140 140 2482 1940 1765 1465 1990 2556 1660 1769 734 117 2074 1600 572 1157 923 929 2361 2044 1163 1875 833 1748 1647 2455 1822 248 888 2897 1287 2024 2423 25 2551 1160 102 2122 1315 1824 2457 126 1591 2460 2203 111 1321 1697 1708 154 1135 386 1428 1220 683 2172 2885 2797 856 346 738 495 715 1463 1353 981 2755 2686 467 1706 1301 266 2802 96 1995 1638 1875 2285 596 2178 2819 1736 2348 756 460 1660 1313 2176 703 2167 1132 1918 2559 2548 1368 1382 1636 917 1886 2989 676 1861 729 2450 2476 1852 1349 1371 830 1578 1755 408 2018 2827 2194 2626 263 2852 2689 2750 589 689 103 1101 1365 851 608 2833 1459 2289 1778 1674 634 769 2368 2244 1688 660 2484 1083 1615 1610 326 1622 2726 2796 2181 2341 1358 53 353 907 945 448 2552 302 2378 832 1034 1635 966 2308 2402 833 2195 2061 345 106 478 2980 502 723 1853 2781 2961 833 1030 2882 368 2136 1995 338 2235 876 1091 163 827 145 1321 2765 2788 2432 2595 123 1725 843 2634 2185 2145 139 2287 2368 1892 619 2708 2178 98 1853 2146 1393 2989 1460 1746 1854 2661 2156 1588 2207 1446 1233 566 2761 2454 293 2878 62 2286 695 786 2354 1689 2834 75 2541 332 1053 2511 1656 1644 2088 315 2689 799 1284 2053 2565 247 1173 2151 455 177 330 634 528 1611 256 450 19 3 1936 1736 1935 1321 646 2777 1270 2787 2821 2897 2904 1980 1658 1734 382 31 2016 701 1634 2973 1708 2790 1224 238 2084 162 1426 2105 1881 2272 1734 2362 131 2651 2543 2801 1283 2699 2327 1881 17 810 2998 2281 954 2619 2897 1786 1715 256 1336 242 2331 2810 174 2924 2484 2829 500 2437 147 2303 632 754 1940 495 859 525 2251 2463 2012 1497 1722 2649 2419 297 2720 2574 818 885 2367 753 2432 2236 395 731 2768 1491 2842 1505 904 1280 1621 1993 453 2200 1379 1919 2960 616 200 2114 2241 1185 2397 1807 2252 1341 887 703 1147 2602 527 1872 80 608 101 2406 1772 2682 2130 510 213 1136 1334 1001 938 1819 2611 1921 2751 1654 1049 2524 211 2510 2192 2344 825 610 1072 1105 839 851 2422 163 1717 2933 417 1817 2763 2441 2259 2175 2183 168 291 2425 632 1601 2481 1141 2194 1085 2455 2790 1337 2461 2016 1316 1260 2434 894 615 1020 2702 2606 2091 1308 1846 515 2577 2380 1317 240 2626 1751 2307 2498 1776 1377 1666 2458 1899 2238 2336 1946 55 1750 2858 1939 518 2188 569 463 2248 1477 1837 1688 2555 2033 1879 1801 1112 1960 1848 1168 2368 2764 1606 709 359 65 387 1797 241 2013 1225 1489 2668 791 570 2100 902 2450 100 404 2710 100 739 1068 2116 1204 735 899 713 2400 1030 1443 445 2114 191 2712 1865 114 2428 1764 656 610 2950 1539 2635 863 1349 1526 391 127 2591 1650 195 1110 384 2341 2284 824 321 90 1367 162 752 2783 263 1015 74 1910 1078 2500 1760 108 189 440 1791 2746 1448 364 514 1374 1281 688 2901 816 192 1211 1357 1685 2071 1790 401 2520 1016 2161 2828 1586 1956 889 1423 2471 1603 2994 1106 1575 272 2911 183 946 2553 2130 2520 1008 2017 764 329 573 1650 2466 2668 222 1289 1053 1490 2398 644 1078 1076 48 2860 27 719 2480 2730 1957 1047 1906 1199 715 2472 1448 2703 593 1031 236 507 1244 127 2125 2097 2419 1381 772 1004 249 548 599 2693 2227 2439 82 286 1038 2620 2349 2966 2719 70 1615 1792 919 769 1896 2418 306 2358 2291 7 2297 2006 2296 322 863 374 524 849 1375 901 1317 893 158 630 1435 294 941 1002 1633 1647 1082 1659 904 2629 1265 1595 1785 632 1713 1080 942 1727 2892 1360 427 392 469 41 1114 1770 1021 2292 932 743 1125 463 2106 2216 2083 1730 2855 2244 615 2562 1835 870 2164 2955 1829 1299 1926 2295 1417 321 1757 1141 1627 1808 2559 819 2700 1972 915 1120 2092 1077 334 751 506 1538 1592 1882 1742 1774 2204 1275 428 718 2413 1692 1730 1491 1820 1694 1155 1971 584 1629 241 1396 1798 1799 41 2724 1471 1481 2440 2925 1728 2568 329 2568 2996 221 265 942 715 2795 2155 1845 1949 666 1469 101 767 2455 2832 66 2201 1425 1305 2347 1189 254 1682 535 2757 766 2144 1089 2589 2362 1899 1857 2091 2801 737 1244 269 2867 1147 2402 35 803 2163 2891 989 2848 1585 1572 718 1636 1202 2920 1730 2450 1013 2421 1401 554 617 2496 2985 2000 2017 22 2933 1737 2878 276 1029 750 1810 1324 2407 2735 2032 2140 1711 886 2601 1630 2954 871 354 2562 412 2602 2519 2710 25 81 1194 748 2428 437 2565 602 44 1261 635 2712 1759 1667 1567 2662 1037 2502 2455 852 2677 2479 2892 255 2378 2264 1541 577 2695 2828 171 1764 70 957 1842 1716 579 1301 1130 1720 871 11 1494 1308 2406 2039 2571 895 1654 2399 2335 2253 1892 2418 195 2344 2681 1974 2118 1129 2002 687 887 1371 2758 483 1554 1644 2928 343 2734 1248 2661 1652 2237 1142 2324 2688 1193 1589 1764 2767 260 864 1409 927 2241 1073 1723 347 1117 2133 2720 91 2404 291 2214 2214 1140 2985 1627 2508 2961 2526 1005 1685 973 213 1487 1970 1505 71 2557 2388 2589 2759 2170 224 2773 1892 1926 704 2072 1550 2755 2938 445 1153 2582 1829 1267 547 334 149 2418 1936 1087 74 991 65 1669 15 432 1438 1850 2231 921 2276 1920 2308 929 1392 1019 1045 1240 874 1291 1507 845 443 1746 1365 1834 653 207 343 992 1093 1938 2205 1898 29 75 921 1018 860 2387 1122 2900 1955 129 661 65 2835 403 377 190 970 810 102 1136 947 2652 10 2625 250 2540 541 38 835 828 1935 1186 2032 2205 1860 2691 995 208 112 2202 443 906 2438 1822 2349 6 475 2822 1907 1096 231 869 1018 536 1689 1139 2445 896 1531 411 2629 1028 2964 1424 122 2761 294 923 585 1239 499 609 476 1745 80 2817 2702 285 868 573 300 1608 1326 2103 460 1030 2229 944 792 1601 1030 2150 1733 1226 2774 717 1750 359 2898 1176 627 2688 1735 1325 1783 685 178 99 1327 908 1148 1648 1527 2890 1647 2850 30 1534 137 2775 2159 2895 1462 1501 1596 2503 1368 1930 1919 2900 1718 702 1216 2554 2368 1039 778 2737 352 467 218 2453 1025 2426 184 1481 710 1713 2962 2068 255 1713 2843 2823 999 422 2369 2474 1761 2466 1750 492 2953 2317 686 2031 1715 1374 1324 1119 1565 2668 693 2973 1752 409 929 1978 551 1375 618 2911 1412 2766 2935 2318 2211 2187 1292 996 235 214 1240 1002 823 1970 1972 572 153 2208 2522 2437 102 2038 2513 2788 407 1920 2210 1282 2673 1332 1719 2656 2306 2130 2 1357 2091 935 2219 2051 1667 2668 1808 2988 354 1885 504 458 1285 1127 1029 1056 1645 769 461 2289 1054 363 517 2225 2406 2490 2879 1483 2244 366 324 2767 1156 2216 2570 1415 896 2968 266 2213 2129 756 532 292 2430 875 136 2673 1132 2967 1253 445 1756 1938 1905 2731 2589 1695 1085 446 1754 269 2926 644 1532 617 2031 2867 2594 1577 588 2159 2671 2366 218 2586 1456 1875 2227 255 623 95 2385 2647 124 2994 2893 1850 2862 2049 2595 0 106 1835 2671 810 282 1930 469 2579 2369 1103 978 1692 984 83 350 1399 1745 1463 1948 726 1098 740 205 465 580 855 107 133 2809 1959 2579 2112 228 601 1775 1286 395 2389 1503 2115 1881 722 310 2059 1182 1665 611 119 2377 1235 2481 188 356 882 943 2143 2162 2449 1623 1596 2509 672 366 2110 1363 524 1624 2910 1563 2850 686 932 2437 1334 583 2780 2522 2556 1665 1609 1670 2908 2051 2362 164 2503 2539 2370 255 2946 244 1804 685 1482 275 1166 2734 1219 951 641 1960 2618 607 1089 2540 1286 1090 1035 1288 437 2433 329 337 823 176 2122 1007 478 1628 2590 1104 1274 691 1981 1056 1248 1475 2199 2831 104 1934 365 237 1876 2553 2560 1278 1999 783 1724 1451 2933 2614 27 2700 2407 1761 2292 814 292 1811 2647 2376 1825 1377 2582 1568 924 2894 46 464 677 2815 31 1076 1531 423 67 622 878 2067 1673 1198 292 1096 355 2107 2713 1855 735 920 1649 2062 2127 2329 608 565 1459 2071 2580 1368 270 2506 1432 953 1986 574 2121 2675 2249 589 2991 1957 2546 2228 2261 1792 49 548 1577 1502 1998 868 499 2012 2178 1469 2511 1345 66 1560 994 1498 2256 1506 2758 1570 2566 2432 2554 2468 1290 2303 33 1688 244 1811 2889 1039 1393 2026 461 2691 876 2343 1427 302 1762 1005 1246 114 1090 2483 2671 1789 929 1718 1261 1694 511 142 1433 2760 2098 2258 27 449 1719 1635 598 2284 1072 307 2375 1242 2512 2789 12 2965 494 1340 170 1960 1547 988 2439 1635 901 2430 1965 492 1371 39 367 1971 2616 647 1059 2178 175 2745 2433 1324 2773 1237 988 962 969 833 2975 468 2477 2637 2902 2011 2458 1407 1313 2689 888 634 1644 2728 2375 1516 1132 1436 533 423 872 2930 978 2396 417 971 1669 2888 1275 557 1373 633 1699 2659 673 427 713 226 1036 315 2394 2397 2218 2726 437 2185 1663 2142 1157 936 1418 364 1215 1606 272 1527 2583 2155 2615 989 423 970 521 2596 1386 1006 2191 2323 2737 1504 994 493 2411 2091 1908 2370 2801 1005 2910 1630 2563 1535 2002 1770 1289 1010 1759 2751 815 1539 2254 1010 673 2752 2874 2581 1874 91 2185 1001 2272 347 175 1595 2488 1730 2695 2198 1587 2991 954 582 2511 1187 1845 349 1787 2970 210 41 2142 640 1817 2209 2396 2777 1383 940 1101 489 1183 2762 2831 1217 1671 375 1648 749 230 1739 2288 277 838 415 1775 620 370 1358 1796 351 81 2009 248 2270 2661 448 290 929\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 132,
        "task_id": 559,
        "test_case_id": 21,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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963 2371 292 2457 2968 408 2141 242 2633 1255 1164 737 421 2422 205 262 43 80 2396 1926 752 1471 1033 1650 2005 2596 2324 459 1109 1449 2835 1248 739 1888 601 2520 2087 2823 1185 1435 2351 1097 302 1293 1837 1001 749 946 713 2950 1441 1948 1093 492 2220 1081 1696 59 338 1633 1739 703 642 2981 1685 842 2323 782 2842 2878 1913 1343 1944 2344 849 905 1259 1565 178 167 1969 1600 2385 657 406 971 1271 1851 2074 123 636 1470 2684 2993 1514 1621 642 1811 1498 355 1852 25 1144 1782 913 1961 2658 2558 1465 418 1883 2713 2218 1284 1846 979 698 1336 539 2590 66 2326 2020 563 1455 1366 2171 1601 2321 1359 1577 2158 2233 872 1632 653 1379 124 622 2371 1705 1896 2573 1192 1561 320 949 2527 726 2048 901 2094 613 1605 511 761 879 2471 1869 1224 2746 1905 1755 337 1753 1410 1917 610 1122 1841 128 2598 2948 1233 2366 1265 2781 34 744 1961 2195 2117 1767 2370 950 147 1166 463 1351 1777 1917 2312 542 493 700 293 2407 2194 988 2170 2314 600 780 2145 2740 1797 1228 349 833 512 2677 2639 744 973 387 1417 2254 2324 2965 229 82 28 2 2956 1300 108 1374 1398 1484 1772 1284 2065 1986 1098 2514 2686 1972 1722 293 861 849 1449 2797 525 2595 2045 2650 1407 1404 5 357 61 10 2605 1831 1404 2844 1804 1470 2585 2893 498 333 88 1210 1575 2803 1970 268 526 2814 1531 2699 2475 650 1680 1473 1913 100 768 2001 2851 2460 1956 1194 2284 1265 2708 1348 763 8 1009 559 1441 1683 1097 2227 1747 1505 1248 1473 540 1455 124 2412 2568 111 1202 2169 2881 820 397 1478 2099 2893 674 393 270 342 2411 515 257 2559 1035 2902 102 1934 2061 598 2746 2409 780 1118 1696 1043 321 2875 1338 185 201 294 466 1087 550 1847 848 98 2524 1147 370 2953 1114 148 2968 2656 674 2084 1272 2620 645 2929 484 1901 77 1176 1291 798 1053 1354 2326 1125 2306 1267 2815 1039 2268 132 2870 111 2240 910 2952 2641 739 130 1476 1774 1048 1069 2687 920 502 2777 651 2910 2899 1836 2448 214 2704 896 2480 1152 2888 1756 2406 1660 1478 2397 395 2294 1103 262 976 983 1780 1856 1172 2121 238 2127 519 1086 311 2961 1305 451 1400 1789 499 2137 1725 2329 1107 862 228 2943 2711 2996 991 848 1852 2515 208 2632 2751 1270 1310 2047 2971 2647 1437 1999 1117 1049 681 1118 2373 977 1107 434 1927 2031 634 1114 870 886 2889 2596 2355 1018 943 1188 2938 36 138 976 2196 1742 2097 2097 61 138 411 231 1646 373 1310 2099 2614 1110 666 2537 1548 90 1656 2095 1125 2380 2214 2623 2874 1979 1680 1041 1940 119 1204 2968 2331 2227 2678 410 75 535 285 1050 389 2489 1170 864 2329 635 1749 695 570 1376 219 361 2248 1849 350 2218 1350 1177 1369 1418 64 1000 2117 998 2489 2777 2885 627 2627 743 2727 586 2496 1998 1111 2947 1055 2639 684 766 1221 489 638 828 971 1083 1704 1253 2243 1760 2110 2818 927 1647 85 219 1806 2968 1658 835 963 2104 2928 517 2074 2768 1840 971 136 1528 184 1244 659 2820 2905 366 2380 722 1108 1428 150 1762 1697 928 0 2413 2739 909 2481 2472 1956 2152 2328 336 1887 1758 1524 2974 377 2515 848 1441 2252 0 1328 984 303\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 133,
        "task_id": 559,
        "test_case_id": 22,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "2999\n1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 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        "output": "1 660 579 572 2400 1738 2744 302 2322 414 2940 2062 260 2836 537 880 616 803 2480 1102 2936 2989 736 546 1412 287 2272 2451 2557 970 1653 1970 2742 1771 1982 450 2906 241 1840 1083 604 717 1455 39 605 1472 960 1352 1124 154 2071 2821 1757 1806 817 2629 1552 172 1690 2975 196 1688 1493 2435 29 1736 983 2552 2822 2639 609 2957 2103 676 1307 1009 2961 717 1638 1784 179 1253 969 890 2501 31 1557 1200 414 1974 2085 2588 1073 990 2445 29 1808 2588 2705 763 1151 1078 289 2123 1217 120 2719 1273 2713 2841 1433 392 82 2824 2900 1714 189 251 374 2501 1429 2800 2295 2066 1644 513 1289 494 764 2088 58 2581 387 2853 2151 1020 2877 2467 2395 1336 2648 630 904 2255 1207 2599 606 1578 1896 977 2175 1942 808 179 2887 1823 2456 1476 1406 1951 499 1120 1394 1405 966 1685 484 1748 523 272 1917 2217 815 1246 1947 994 1150 2411 2831 2549 2791 768 2728 263 780 2342 1342 408 1882 687 1365 473 2407 2952 1223 1812 2332 1162 2434 528 318 76 1058 2711 181 194 2594 298 1152 1819 2306 892 1337 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2905 1963 1137 2950 488 2694 1858 493 2000 16 749 2450 1114 2509 1876 1938 297 1677 2636 12 495 628 122 2585 695 2032 1158 321 635 2631 726 215 721 1583 118 2801 778 2797 587 76 2746 2624 959 2862 2274 65 2977 141 1176 755 1794 1991 867 1932 2386 1419 1707 1174 1502 2022 723 316 142 875 648 836 2967 1412 1535 2802 999 2716 1516 1883 288 422 351 2827 376 112 498 646 2659 1343 1516 994 816 2792 2054 2314 937 254 2521 1963 1632 1137 1718 1849 78 1044 2674 1058 136 1622 2224 1581 2169 714 443 735 154 2572 2785 1970 699 1038 890 2534 1091 2840 2624 2317 1229 2933 1990 2687 445 2619 1706 1493 2948 2259 56 1933 2426 565 1811 627 196 2883 2677 1835 503 509 1483 1975 452 805 2179 2198 1334 1322 2434 2996 488 1740 2860 468 2067 2081 766 1508 213 2410 904 1495 1279 2969 27 2210 2741 409 1981 2389 944 241 164 1306 1991 2220 1885 908 401 304 601 338 2526 677 2905 2939 775 2436 1782 490 827 1183 2682 1612 283 2624 940 635 186 543 1842 544 2338 755 2904 1835 741 1857 2347 52 377 2924 2818 2272 1521 353 178 2768 2402 1179 1057 2077 570 1668 1216 1644 1319 2094 973 77 2388 2359 852 1947 883 2147 1919 1835 2530 232 2764 679 858 1581 376 2567 1624 2319 962 2575 639 2205 2274 1966 2633 2297 324 484 1772 1961 1187 2448 553 1563 477 1105 792 313 1502 643 947 1207 784 1066 330 219 2669 211 939 1761 1864 480 2543 9 131 671 430 870 843 366 892 1412 1262 1938 2989 1914 992 169 2676 2026 882 2088 1706 2251 2543 1205 624 443 718 1053 139 1968 1426 1152 918 2348 1277 1205 2941 2795 19 1628 1348 1064 1339 2803 2991 315 1935 1539 538 2359 340 1143 998 1376 2612 2448 687 437 2358 1126 474 1634 283 2516 673 1953 36 1163 2129 263 2822 2564 947 2829 1164 831 1068 666 2702 2958 2146 2762 141 856 452 2000 92 560 2484 2700 1087 1279 2718 1319 2541 176 2396 1626 1420 1127 2157 647 2086 127 419 2247 2837 2323 2365 639 2237 2177 1451 750 1733 355 2252 9 2980 733 1132 2154 436 1158 1810 1659 2271 665 2246 2112 993 454 784 2159 800 737 495 1421 1545 1286 2152 2139 1851 2922 2711 726 2412 544 1274 137 1978 1829 1550 2776 101 189 2223 1193 848 266 1916 1596 1949 1541 2796 1954 2059 2459 1175 2427 601 924 39 897 1509 2702 2375 1415 1193 586 1842 1219 2584 192 898 1123 2614 421 1034 1027 344 771 1936 573 93 1464 2489 942 2596 2124 1835 225 2646 627 1301 1941 816 2573 2340 2514 2281 645 1595 1452 1762 914 515 1093 864 2219 290 2204 1381 126 1221 916 1749 1316 2111 1821 2183 742 878 2664 464 264 1674 2495 1651 1008 1081 2485 2195 2033 281 1241 603 2147 538 2329 1218 1922 986 40 208 2677 2082 548 2100 1959 81 2770 2373 2013 2989 401 778 1462 282 1325 1169 796 1690 1581 2978 1315 584 62 810 2428 1143 912 2309 1787 621 2476 443 2042 2759 2638 97 954 1739 29 886 1200 822 1263 54 2945 454 2914 2534 1583 284 1617 631 2943 2356 1767 1673 920 1464 867 2996 2903 2085 2668 763 1381 2631 1486 1717 2879 429 130 1210 2886 1148 476 354 399 1581 1061 2814 1951 2095 2496 136 1152 2806 2360 1424 2985 2728 2701 2625 613 854 470 961 2539 502 1964 2454 2649 2974 1392 893 652 1795 1271 2350 2731 554 2113 572 1813 630 1326 491 675 372 2432 715 1240 2126 2313 1859 2718 1740 968 329 1674 2486 81 1739 1028 1168 2718 2745 509 1973 1755 514 2447 895 2294 416 1415 2167 639 2317 2663 1272 1402 2609 1350 1103 1042 469 2264 1180 329 1152 2169 443 1409 1861 2295 2650 2846 2558 1590 1478 2723 1479 932 2765 1433 2749 691 364 2321 964 2713 2757 1754 1781 2001 1891 53 1127 1935 530 1272 1768 651 2079 1448 897 89 692 3 2311 2265 2494 2496 1193 1211 507 2785 358 288 2657 2026 847 2824 1895 336 2579 1601 1889 1648 1666 1261 2497 1496 2541 683 2967 613 2704 2915 1697 47 1629 2021 1878 2529 22 2799 1307 772 2706 2882 128 1317 1573 615 2996 296 1712 1615 1364 1220 1394 1485 2255 1044 2701 2186 2625 2195 125 2209 2730 1026 863 2922 2786 1975 2841 1145 2634 137 410 2708 1016 2014 2229 1991 567 1074 1182 1719 1297 969 16 1660 2499 2384 2176 1385 875 2796 337 409 1926 2972 1194 1808 2656 1091 671 1491 1455 2972 2413 1714 219 1638 89 624 687 1470 1362 2244 1630 1450 2795 2923 1997 1277 1785 2971 1314 675 1800 1977 2195 1779 1458 2676 1978 2351 841 2278 1025 1861 1811 427 161 375 1377 1302 2185 278 351 2400 1597 2053 2363 103 687 834 1479 2325 614 625 2955 265 2540 2294 2381 413 1320 2967 2259 2432 2705 1029 2184 410 792 1104 1455 1976 2835 2669 2947 1768 1346 1510 1124 573 477 501 930 244 2933 2225 2084 2616 1263 1628 597 2846 2737 1664 1984 2840 1047 1731 1578 6 235 2696 2324 1102 1166 1528 2529 1042 1142 121 54 256 169 2837 239 2048 225 1557 990 303 976 1931 2987 1669 1207 1040 1918 2037 2227 1299 906 2991 1081 1414 2855 1639 2733 2368 1792 341 1242 1751 1716 2025 2981 1988 371 516 1975 165 753 1123 2181 1301 2954 514 1 518 1704 2399 1079 2835 2909 2824 1585 1 1353 512 357 966 1496 2386 952 1351 1813 842 416 1306 2030 1914 2062 2989 1796 1089 334 314 2850 2054 458 128 330 2454 1040 1226 2612 432 1746 1982 1027 1733 1002 964 1150 1155 2914 906 2218 1900 2407 2413 1911 603 1108 1988 2843 1712 2147 659 2252 2778 1435 373 64 820 2892 2120 1302 1733 1640 1588 2985 1223 2124 1149 253 800 2583 2650 1196 1876 2790 2289 468 481 2755 163 2527 1160 1955 686 2676 2877 2358 2841 2154 58 868 2213 2414 466 1857 237 2688 2829 510 1603 625 1916 967 781 630 1305 1173 696 2383 1251 100 2873 555 2564 2938 115 286 2347 2299 2356 277 391 1477 766 142 695 2844 1601 1214 2357 1002 652 60 595 1777 2555 1721 1157 1391 915 700 801 641 1628 1833 320 1858 149 2751 1613 1826 200 2431 373 375 731 1662 2218 2895 1239 2328 2782 2329 2746 2221 1952 2781 2712 1932 480 449 1463 2809 2479 1898 998 2509 2503 544 1329 417 534 781 2847 440 463 2433 2133 2900 23 1804 2738 1713 711 1036 2981 1654 1418 950 1653 1686 1476 2898 817 2110 2768 2425 89 471 1330 2322 461 645 610 2625 2894 1154 323 2026 1904 1225 935 1676 2066 1330 1203 379 1949 155 1667 2379 114 892 1020 1999 1403 2803 2504 284 1404 2832 1217 2178 1491 876 2439 819 1221 652 973 1422 1878 421 355 1815 658 2843 2977 412 2924 727 2754 2546 718 271 709 1686 1630 326 2145 318 60 2935 530 533 2327 982 2967 963 845 53 1547 929 569 1312 808 554 895 2226 1651 1967 1904 241 1141 2192 761 1237 1890 1191 2590 741 2807 1617 2538 2205 496 1995 2470 1168 1166 758 848 882 1140 2865 1393 590 690 1060 36 1294 1332 1026 1446 2413 497 780 701 1258 485 1575 780 2592 383 737 2378 563 1909 992 346 273 611 571 1000 2973 365 103 362 2879 629 51 678 2498 388 1632 1970 718 1383 1727 2188 1750 887 1029 1916 159 2203 1908 1038 2988 1058 1694 1977 216 1862 283 1227 1770 0 1542 1083 1688 302 2152 2290 1780 2850 1957 2601 1998 966 425 2523 2510 521 1617 1232 2416 2942 560 344 720 9 846 1965 2796 291 1204 2077 1458 920 2947 2036 2375 1880 1347 595 1000 2923 1544 1015 2837 766 1813 226 929 2081 1141 2158 167 2875 609 117 2595 2302 55 779 2158 2792 1887 144 1916 1454 2115 1090 2463 1945 209 203 2330 2837 118 209 1900 2343 2754 1565 1090 237 2364 1019 2974 959 2441 319 2158 1790 1957 2649 1537 1302 421 925 2752 1830 1379 2385 2749 2516 695 1189 304 200 1028 1265 2871 2426 1668 2449 118 1816 652 1841 1251 2247 2887 2692 394 1006 802 2941 2062 2546 2945 2091 543 161 323 1438 1002 2793 2964 1982 969 2007 461 2155 2126 1247 1095 1933 2399 1869 763 535 620 2781 2600 2693 365 1082 1756 179 1011 1401 2273 2653 718 1026 1533 1220 2880 2697 2238 938 2202 2525 1126 2984 2302 2884 411 993 1403 201 1180 663 1659 1080 1662 880 1234 1699 1104 29 44 2312 335 2348 381 354 922 1410 333 584 49 1542 2737 216 2480 1930 1852 2328 2881 1915 2983 1521 1857 1294 331 2553 243 1332 135 1667 1900 1215 685 2320 1540 2222 2986 2205 242 90 2563 1510 133 1906 280 2841 762 2377 1972 2474 481 765 1535 2707 1014 2161 777 1681 1643 906 309 2033 2211 2443 2817 1410 1426 2536 2202 470 1725 1561 2883 1983 416 1676 2394 1557 526 342 2915 254 698 729 988 484 738 1399 2414 1083 120 2397 1773 1540 2364 1320 654 2127 2005 2413 2648 2757 300 2239 1355 605 592 2820 2226 1976 2379 1338 1918 1043 2528 262 1096 2685 2399 456 2727 1033 1907 1688 126 2681 2011 1010 473 2299 2622 764 678 328 2054 2304 2508 588 1255 2252 1964 2960 312 957 27 64 444 830 2271 1678 1209 2179 117 1436 1989 1942 863 1442 2854 1262 1959 2128 936 2261 2403 1804 2968 2005 2010 2111 2778 2439 256 1387 1820 996 1614 2188 67 1529 1234 1482 435 2538 1098 1669 727 268 2307 1298 862 557 1061 593 1866 596 2967 1810 385 966 1269 1485 2161 1555 34 1432 799 2061 2760 1747 2573 414 1651 337 1386 1886 509 646 1259 1948 2980 2831 1431 1810 203 2237 1132 1762 456 620 974 2218 2337 988 2697 2581 1692 1330 492 1363 909 1342 2329 997 1132 350 2491 514 403 965 1265 2898 848 1417 1997 209 909 2336 2389 966 929 1773 2643 2903 903 1198 2952 330 1231 464 2107 2094 2235 2442 2720 2536 1395 1692 784 269 2974 28 2984 2622 1797 838 1813 37 1438 2778 124 1985 2539 888 859 1079 2634 1526 1947 1260 1889 1173 2859 1640 2109 1702 1809 478 1593 720 33 1864 13 1868 726 864 1900 932 444 1925 1606 2465 1558 668 1456 937 172 1233 190 1279 280 2074 2544 349 240 379 1134 1051 831 184 207 766 1063 1704 1186 1242 205 1162 1688 629 1461 1722 489 935 1753 1487 1176 541 1043 163 465 2930 2324 2876 1826 1576 1916 2 1528 1753 101 724 860 380 1335 368 2741 2945 1981 1189 1713 1304 819 941 1808 2663 1997 2990 1480 2192 1497 1286 2291 993 224 182 1023 2794 619 1515 2354 575 620 2191 215 1848 1370 1048 2013 156 2217 1556 555 1677 1494 790 200 441 244 1582 816 2629 845 2916 1444 2392 838 2444 1979 153 2118 641 2865 422 2598 1147 270 2478 2130 2904 2500 402 2279 2258 2384 905 1901 2114 276 576 566 678 1224 2585 2345 952 2693 1956 2108 515 1535 2109 1770 589 857 1021 1558 2197 346 1103 587 974 520 1658 1281 1713 644 2836 2004 1274 1714 2145 2106 2777 2684 1173 804 270 736 1556 1751 1865 955 2270 276 2169 2505 2288 887 2447 64 26 597 1531 556 2376 909 2577 2092 2935 1047 456 1544 2607 1615 2932 1412 41 2836 1918 1445 1966 954 1736 2888 2805 2095 2429 1936 1466 2687 2535 1436 2246 872 2277 206 2495 1242 385 434 1837 671 2054 898 407 2090 47 169 451 164 1912 2911 920 1451 1086 1409 1610 2733 2886 2830 776 1292 2430 2062 1983 2162 2099 453 5 541 2236 1924 1604 1333 2775 695 362 2015 1022 2323 2041 1738 1728 203 398 1697 696 1250 1693 376 498 709 439 305 782 2407 915 2463 1992 1390 1128 1274 2628 1927 914 1436 1922 2434 23 906 1538 2858 262 1170 2312 251 2447 384 2685 969 2507 1901 1278 576 1554 916 1782 1895 1979 2133 2841 2299 1038 1753 1189 1699 156 2284 1327 184 2757 2749 155 1850 987 649 1463 1033 2672 1347 887 2182 2454 1542 1015 88 2916 464 1136 2278 1693 2141 1395 1371 116 1930 547 2335 868 194 206 518 1908 2648 1616 639 479 320 1791 1870 2759 1760 1396 1268 2245 2344 658 140 2222 42 156 758 138 1717 2393 1086 2645 1332 2217 2844 2012 1032 1626 849 2316 1115 2265 40 748 682 1465 2125 1185 2896 210 132 642 324 1784 966 2575 243 831 281 1290 2004 1251 2446 361 1942 1006 194 1829 986 1869 1708 1833 751 852 2675 607 2620 1637 1840 1215 2396 2320 1837 2754 465 1365 1562 1209 2275 382 1642 1271 749 2494 1545 1164 2766 688 2931 2120 611 868 723 841 2007 298 876 1027 140 1673 175 389 1426 302 355 2314 2964 772 989 1519 1175 2703 2715 97 2813 1342 719 2213 2706 1034 1217 2352 2002 1098 1182 1420 2787 1035 288 2670 1334 2086 2064 935 2376 1155 664 2001 2567 2284 1396 1812 2381 2493 1878 1085 1727 2752 2575 524 1053 121 2670 1193 777 736 2304 2712 2744 828 1099 1273 968 317 2127 2623 1466 2779 1333 1340 1462 609 1363 896 2735 2600 818 249 1604 1214 1770 2784 1899 632 2274 1392 1567 892 967 1404 2518 1162 2636 2330 2868 879 2079 2154 123 954 451 1818 2346 877 1912 1834 1973 2586 738 123 1674 174 2863 1447 2970 1080 98 1266 2452 976 2764 1067 2991 101 89 1326 2609 2630 2324 1945 1824 1766 1265 2637 1921 2775 572 353 2791 958 2185 2466 2681 4 1237 2695 2254 1852 919 2674 524 995 1317 1497 2009 1096 454 1813 799 2309 2817 741 1966 2836 1717 2947 909 692 785 608 881 2173 2519 99 739 95 1257 520 880 1480 88 2255 171 741 85 2345 2584 1934 2817 2452 58 2969 662 916 1309 1271 1560 2643 20 1787 2643 1603 2692 990 1125 2376 1701 880 1312 419 2135 1220 1520 1834 585 512 1103 2717 1797 2629 2388 2974 676 160\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 134,
        "task_id": 559,
        "test_case_id": 23,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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44 2888 1876 1270 793 643 50 1744 803 2435 1 2797 707 2744 2894 1775 715 1478 444 1776 828 2453 610 1612 1786 2935 2827 2839 2365 2625 2768 1730 1717 776 2765 2829 1324 1926 2854 1422 1523 2101 1975 2933 371 1602 2800 2323 90 668 10 495 1844 625 1264 1176 2551 1600 2188 1236 1723 2610 204 1892 2059 360 1140 738 611 1916 2732 1513 1274 279 585 2063 1285 435 1027 2949 2654 1275 810 2003 1175 1430 2252 2347 1625 268 2023 1665 80 1609 2545 1934 2910 2861 1182 497 333 1041 968 604 2247 1929 82 774 2619 1959 1607 568 364 1919 2479 1171 1711 2613 2904 2467 2140 2376 1289 2708 1983 1837 715 300 1204 1093 979 2289 1911 2747 1222 651 842 1706 2178 1822 501 508 1649 82 1309 1579 1408 1954 1510 1228 2845 2120 2601 2153 2485 172 2599 1221 2889 1527 2186 67 2708 595 1174 2593 1216 1525 2498 947 1852 426 1430 2211 2455 2736 2607 2663 994 992 571 766 752 802 1069 2501 1586 2134 1262 2078 2234 287 716 2428 868 713 1725 1487 2344 1954 514 1428 1097 755 188 1100 399 1837 2844 2373 1373 584 140 1063 2268 2373 930 2666 520 513 107 120 2729 171 1777 1269 1532 2317 1720 623 2606 2760 1892 2956 2458 2692 603 920 1842 2102 2222 2239 1369 2161 2091 627 1849 145 236 398 2138 351 20 1704 1000 1589 2112 2631 2315 1428 2742 2114 18 2195 2563 2457 971 2448 770 2913 2689 1800 63 1405 894 2781 857 1808 1758 509 1941 1749 1213 1064 2527 1849 413 1367 1892 695 754 2423 1202 471 2971 2730 878 1400 1314 444 362 246 207 352 1861 2409 1350 2470 2989 1496 1041 766 2792 550 1000 2619 2988 2474 478 711 2291 2125 314 1003 1616 594 2246 489 1628 2609 1488 246 2252 2206 2423 2466 2341 426 1706 2152 1538 1734 255 203 2923 1379 608 577 2631 577 1412 1085 2298 133 531 2936 1114 1828 2277 1451 918 140 1942 1785 2155 2469 2100 2831 1084 690 2256 2226 2647 700 1549 2526 896 2993 698 1147 1930 1673 799 2346 2870 1183 2460 744 2685 142 1825 2863 434 642 2414 1904 2245 1264 2031 2656 2488 918 675 2578 666 1564 477 1249 454 830 1863 2826 1334 1588 1308 2810 1489 2381 1588 1837 1733 1752 132 1337 63 574 2785 806 69 2138 1035 666 576 238 2601 265 725 1448 1053 797 446 2419 554 408 2403 2268 2465 692 378 1827 1904 2466 1208 285 1871 1306 1409 196 421 1174 2235 2996 894 2581 954 2615 1531 2123 1966 129 2765 2884 337 2548 1855 1594 2047 49 859 1502 2599 2541 1161 324 1490 1684 1278 2528 2150 482 487 628 233 1863 1361 1177 2011 59 982 1463 2510 383 499 1531 604 552 855 1254 2121 1134 105 2929 1557 797 2364 2495 2065 2218 1064 2087 2672 2039 2777 2909 518 1928 2419 2206 2108 2936 1960 1090 2746 1102 272 2761 1771 1211 431 2232 1948 1861 888 2645 507 497 2035 1928 1131 72 1258 2795 2347 2339 1187 1825 2564 750 855 487 1017 2619 2972 481 583 814 2152 224 267 224 1218 2393 116 160 1555 478 144 2286 2908 1725 1620 66 402 934 1146 54 367 795 2067 2930 2572 1811 1696 346 301 1920 562 1481 2499 942 230 1365 1911 478 626 553 2210 259 502 1259 1028 22\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 135,
        "task_id": 559,
        "test_case_id": 24,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "2999\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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1 1 1 1 1 1 1 1 1 1 1\n",
        "output": "1 1567 1557 2761 2224 1136 2950 878 13 1966 2898 874 599 1834 906 231 2030 351 593 2992 1654 217 2317 43 1187 2798 1781 2836 2127 2686 1636 1811 1736 1171 1225 1081 227 1627 1118 122 142 1751 1460 2331 874 1753 2221 2829 1407 387 2623 2707 242 1899 941 2935 41 2324 1308 2476 2377 407 1444 197 1280 1402 633 641 125 20 2160 1786 2874 735 1620 178 622 1794 301 2263 215 1320 2162 2680 1574 2033 1276 1689 1144 2671 1268 183 2572 861 1432 2955 1023 1305 2733 304 2796 1518 2758 1331 1220 1533 2329 512 1662 1553 2274 515 2105 1467 2918 2430 778 1507 1868 2073 685 1604 1002 875 2297 192 2903 218 673 1715 1674 706 9 1101 2750 2355 134 302 2287 2346 902 152 462 2573 2274 2845 2643 2954 1037 742 1940 548 106 2837 952 47 248 20 1769 375 2836 2599 76 722 2236 2694 2949 289 563 858 1098 1395 1567 2753 2819 583 2660 2014 155 1493 937 1893 2653 2588 2839 2848 2801 188 578 2298 144 1232 2585 2827 1677 2502 2881 1416 296 84 2725 921 2162 833 14 1672 1481 425 698 2829 2980 2409 2 1796 584 494 17 2026 1048 81 25 1885 497 1740 46 1937 2585 2444 2837 1574 2940 530 1901 1000 1724 2678 1695 2349 1934 2263 2540 261 901 82 966 469 1797 2529 2416 597 2496 336 1175 661 1294 639 2282 1320 2917 98 2693 2851 777 2979 2719 1487 792 1301 1582 960 1871 1509 1067 411 1836 1739 2377 2771 1468 1043 2497 778 2556 1147 1539 1471 1439 1903 1596 2207 960 1902 1481 1961 2963 1987 2446 2215 1025 2252 477 1419 660 2473 1961 261 1737 2074 756 471 346 1718 2963 2577 2705 2287 1304 425 1593 323 693 2307 2979 1973 940 1436 2863 2593 2061 2142 1972 244 2153 1402 2957 2765 1890 78 261 2387 490 2860 2733 594 2238 894 615 1230 230 1131 632 212 1005 1745 2430 183 817 637 1818 2536 2729 1332 691 2712 1051 2060 1024 1025 1471 10 2486 2774 1481 2488 1335 836 1259 2085 1061 989 2673 2059 2874 695 2202 13 1986 624 330 1408 777 475 2304 1183 871 1743 274 1310 356 1458 1882 605 335 1432 2926 338 724 1037 685 786 548 2166 18 340 2100 2485 2843 1388 1954 680 1409 1447 2894 2924 339 2675 2461 1660 2969 2625 2247 1710 323 1637 2776 2355 618 243 1779 1058 1068 2829 346 1112 373 681 1812 202 2819 2744 206 1555 2029 1310 875 895 1989 2349 503 711 1344 2419 580 2130 2517 320 2033 278 2925 1284 1762 1960 1058 372 1155 2707 1685 618 2200 433 745 2076 2168 988 2251 751 2581 1948 393 1676 2573 549 84 1649 2095 1887 2765 145 1671 2520 797 2094 2042 766 903 1031 2058 2747 2569 2091 899 537 2923 1936 2848 2913 821 2244 2905 982 1251 2542 1243 1204 450 2037 495 802 1009 620 505 1520 2605 2709 2078 2151 1798 2234 427 2987 2543 336 1231 1399 1382 513 1023 2394 829 1063 2666 2478 147 3 199 2106 1252 1669 836 2212 183 769 2003 2785 2697 2841 842 2648 2099 1889 2226 2763 800 2607 2649 1935 788 1950 1023 694 1170 514 2652 2505 164 1013 514 482 1029 13 455 1931 2562 1541 644 1465 143 359 1438 684 438 191 1606 1655 368 1605 1062 2236 507 436 2594 1933 415 2360 1316 2355 576 2611 2028 556 2973 2007 1861 2672 2526 221 995 711 1423 670 1113 1591 2750 2452 209 339 1243 1880 2875 360 380 136 2797 2386 380 110 2867 2881 1536 2031 826 1143 2225 372 1771 362 810 2762 2405 2369 2189 2280 87 1017 2797 654 1576 67 2303 821 45 1157 1959 2984 2879 2362 2975 2017 323 2325 2648 1294 1321 2336 851 2600 2579 1758 563 1121 2350 2064 1970 1233 2385 1483 1392 1889 21 1543 1190 2225 2652 1656 1108 1839 1737 281 537 1076 2822 874 1108 1220 2732 1913 604 723 678 885 476 1056 181 1372 1773 2889 1157 167 774 424 301 1094 1473 26 1661 2733 2048 674 1850 502 34 611 852 2756 425 2489 598 626 1884 2088 718 149 1784 2571 2058 2 1575 1443 433 1480 1548 66 1361 1693 907 1522 1103 749 1344 1713 1829 702 721 620 1121 2154 2164 1318 2927 2732 769 2366 279 2466 2093 1527 2739 445 556 697 2125 462 1411 554 2210 2897 2341 1614 1248 528 1979 1300 156 292 148 2612 877 2160 1586 2892 2270 2811 1137 668 98 1456 867 509 949 2704 950 2948 2420 755 880 1318 1044 2421 1194 1139 381 408 1776 1787 2014 1409 1004 1708 2448 2243 1952 484 2698 1988 1307 1300 626 2874 565 245 976 2820 1485 803 1709 1934 2725 1900 1440 1830 2472 91 598 1873 2632 2313 1747 574 925 2180 98 810 1666 142 2979 2493 1275 1588 1439 2344 915 1269 1654 41 1594 1340 1880 2542 1373 1156 2356 438 2342 2690 1028 2616 317 2551 1633 1464 1436 872 2334 153 1559 1926 1792 247 463 2148 15 2923 1051 1932 2946 2131 226 1675 1860 2988 2826 2142 1132 1289 2979 2453 1850 2804 907 2917 1066 1879 1566 634 520 2164 785 1020 242 2441 2781 1526 2271 2465 365 901 859 838 465 2815 1889 1495 593 2711 1570 1233 617 1132 1729 2853 1166 1421 2364 79 690 207 881 481 826 1548 2889 593 1387 433 5 2973 230 312 428 2771 1263 2267 580 2845 2820 688 1376 1696 878 2627 2553 1550 406 718 1880 2451 2154 2561 1749 1877 2035 1281 742 1574 1262 2716 861 1107 2625 2787 1258 1476 1254 2191 2759 1892 1005 2259 169 2770 1900 1904 2260 1656 2613 2114 2477 1800 1781 198 2162 144 530 1633 287 422 2369 1885 340 203 2528 2940 1154 71 1205 2199 1467 1923 723 1237 2222 2631 1271 1070 1497 53 1297 1004 1424 229 71 2352 1266 1338 1315 2405 1456 287 1549 1595 1528 422 1285 1479 1013 2688 2556 2218 1595 2131 2821 856 607 82 2814 292 2094 1439 1313 95 1962 1589 1351 2315 2826 1208 2388 1903 1225 2922 2237 2575 685 1395 2770 919 953 2311 1555 208 1005 2392 2407 908 852 1462 545 2215 1158 1586 727 1369 2095 2728 2859 886 1345 2823 2876 2195 1153 1938 2034 507 1993 173 1730 170 171 1768 2216 2435 14 566 1031 738 2793 2519 836 925 139 1071 409 789 1406 1213 834 2612 2855 428 2182 2801 2343 1272 2025 2919 1330 2154 2028 2469 1828 959 1222 2928 1564 1488 1987 1149 1762 2700 459 1191 404 2175 554 156 2528 656 2322 2112 1796 2059 2091 693 1671 219 2414 805 2810 2195 2361 291 2797 1171 609 1995 2248 1185 2010 1190 236 2600 1522 2775 301 1485 2993 635 1391 2596 2812 1096 1354 1745 1379 2061 2566 2691 1875 58 2906 2613 1180 2062 2901 1112 1585 2967 2195 883 99 1234 1834 1856 516 841 2870 15 1446 1423 1444 1132 688 1971 2482 2093 2986 2608 2553 2449 2385 1042 1828 2997 347 2762 512 1865 1187 2537 890 2250 514 2161 2330 742 1525 1438 1186 1455 443 1509 2965 1534 1225 600 2288 852 1112 111 1865 801 273 698 692 2317 1939 2820 233 714 1614 1587 674 937 1294 1985 295 1940 1775 1848 1030 1472 1524 2667 2521 2194 2938 921 637 761 692 2556 2346 2879 614 1060 254 150 1509 79 1459 1827 301 2485 1998 55 1265 1797 638 195 2907 82 2547 2629 1028 679 1797 2202 48 565 1872 1706 2449 582 1847 1277 1847 2329 2052 1382 2332 1691 2970 1088 1833 1763 2736 821 1800 1167 907 502 2963 1074 1310 2167 1913 1845 1436 979 1600 198 2898 1469 1445 1965 2923 1738 664 850 1485 1892 2602 1037 1277 234 217 2009 599 1296 869 2868 1283 410 2934 2646 407 883 2081 1270 791 2924 2455 2 2639 277 1306 319 1398 204 403 2669 1896 996 2060 336 161 2474 2949 656 2803 1065 1448 1940 2111 2202 949 625 2164 1827 916 866 1881 1776 2151 861 1904 1542 731 2748 1092 2741 2725 75 845 1946 2786 1863 519 416 1364 1698 1072 2163 106 127 1413 588 847 2154 1941 2788 1202 642 2589 2102 114 151 1571 2008 562 1126 2195 1134 2646 971 472 2264 2 1810 1138 302 1903 1153 2082 124 1268 947 1010 1 1953 489 2255 1761 1885 2981 1855 2768 2136 2384 1312 2249 211 1254 894 1352 232 279 1592 960 1577 317 2960 2352 2662 1359 2263 585 1932 2206 1599 901 735 147 1417 205 2851 1431 1085 313 2555 111 1335 2940 1165 908 898 1037 2201 403 938 1706 1321 1059 1500 2163 1083 2609 1035 315 2449 702 715 1632 1836 1619 901 1427 2673 935 2940 2348 1542 2510 306 2884 1266 1909 2714 834 681 628 839 2964 1572 2829 893 1654 2377 457 696 1660 686 1508 1553 1328 2503 1036 857 596 1547 1024 1200 1235 1352 1107 1490 82 2886 2622 2196 1597 1743 2368 297 1494 2843 2950 488 2020 468 1260 2137 2332 2684 546 1774 2866 765 2277 2452 824 2463 2341 51 927 624 664 678 2382 1370 1896 367 189 74 1965 49 1167 992 535 1776 175 2743 234 389 1903 933 1293 107 1036 1475 1726 520 308 1564 2307 2642 1776 291 2063 975 26 2078 2009 1463 2777 968 1978 2887 157 2727 713 1392 1300 1898 1354 526 2041 1139 141 908 381 59 242 2638 668 2694 1429 1481 1044 2918 198 972 426 142 2013 2407 586 2376 2653 318 2153 2410 2075 1627 2752 236 2641 2167 2345 2490 1125 293 2756 1830 1060 2774 2207 2356 1747 2478 2610 2735 1765 2058 1378 1344 2746 2485 568 2007 1311 628 734 1278 2890 1791 1119 2510 2985 1728 2723 1795 1960 612 2197 1402 582 1361 2554 981 834 2370 952 1937 435 1387 1788 1279 2566 11 154 2971 982 2934 2042 2461 2615 2717 441 2627 1815 57 1596 1261 1406 578 524 950 1193 528 244 652 694 1203 2760 1872 2000 971 225 1946 2259 601 552 907 2723 344 138 2037 2399 2772 2466 2523 345 133 1062 1557 2040 2455 852 2586 2103 1171 1596 1005 718 392 1535 1982 1702 699 1106 42 784 247 2888 2279 1240 2697 2302 2202 2023 1355 861 1966 386 519 2492 2883 2630 2378 1831 2901 756 1299 21 660 926 2207 1642 2375 1091 1354 2596 932 73 310 1681 1706 513 1367 687 2724 1040 2731 1468 2542 689 1191 379 2810 1764 2472 1123 2954 1299 1343 1577 792 1060 205 2599 1046 239 261 1168 418 1881 661 2720 2350 175 306 1015 1335 1627 214 2273 71 387 1756 1011 2463 1617 2687 2353 2875 2914 2230 1889 1491 2527 1962 2030 1971 187 1133 1644 1446 1925 1695 1635 1111 1680 126 2321 2966 2751 1230 2878 2393 537 2413 413 853 1505 199 1498 617 1443 1147 796 113 2292 1324 1571 669 2943 209 2812 2445 2500 155 2032 478 970 1450 1198 202 2544 1441 144 1758 2658 1291 1747 1373 2054 2812 2682 1571 2622 1810 2565 1440 705 635 2705 918 2618 555 207 2726 1623 1327 341 473 1533 1399 2495 296 1296 1355 2063 2909 1797 2941 31 271 782 841 2300 2357 370 1979 267 406 1108 2544 1093 23 827 1282 251 1836 1264 2497 1121 561 1757 2836 748 473 2807 227 956 2454 329 2879 1119 908 329 1942 917 1248 1458 156 826 2481 1951 189 767 690 167 779 2116 795 1396 1864 1346 2322 1059 764 2199 1257 265 978 2140 1305 600 1565 2705 1908 2303 259 1037 1262 853 2901 2041 1599 1488 2207 1848 468 924 955 758 1903 553 2470 1419 450 783 1866 2144 551 2918 2761 1039 1341 2563 69 1349 2859 967 691 1722 1369 2561 370 1626 170 691 2067 2076 35 2825 1942 2385 426 1853 1925 2828 1262 1961 2921 429 2648 2658 546 2374 787 281 1023 372 2662 2061 1643 1521 212 2873 313 1635 1698 187 2307 183 2578 2086 1642 13 1803 2156 713 356 1709 1255 1885 2888 2778 518 2831 1879 356 778 1822 2812 1795 2148 1585 807 1935 1528 968 672 2046 1896 2509 599 2709 1745 2780 1598 2340 1954 474 1794 367 2489 1582 1905 2693 2786 928 257 2406 214 1360 492 572 1341 736 2161 1342 2538 2172 2795 392 903 1886 2390 2687 2749 490 346 34 1250 68 538 509 681 16 1390 1753 2693 2898 2702 2356 2226 2275 719 79 2500 1015 2238 864 1883 2129 2901 646 1095 1271 2406 359 2961 819 2559 656 1711 1774 2468 1301 2734 1713 129 670 144 930 42 2350 1538 2655 1122 951 756 978 625 2978 1295 2692 923 2132 2709 2867 2337 422 1986 2327 2970 888 1881 1760 2082 1810 636 1950 2970 2633 1390 1388 2478 2048 2657 308 2037 1118 560 1351 2573 101 2717 131 1654 1437 142 455 141 1663 344 180 2957 1594 304 1561 2264 1598 1552 776 2131 2218 776 2041 411 1075 2294 747 611 858 2328 1749 253 2979 147 2158 1626 1318 38 2431 2863 206 1639 132 996 737 1922 265 606 400 624 1576 1975 329 300 2140 1983 1966 218 1708 2433 1589 900 1879 2651 213 2431 689 2528 1852 1114 2745 927 1620 224 2624 1178 1138 1606 1233 1133 959 2951 1312 459 2823 2159 1436 391 41 1946 2320 1496 1234 1122 1633 2443 2117 156 191 2746 866 492 498 185 340 403 1059 1516 2858 2690 2162 1636 503 1646 1270 1368 836 932 1588 191 2847 644 2945 2583 1790 2603 1352 528 2326 126 1435 2990 2873 1370 1425 313 2915 1702 2290 1626 2959 2021 2629 1129 439 1335 1695 565 1743 2836 2206 141 2906 1758 2727 2037 2993 54 1346 1260 1801 2746 1937 1792 1160 2810 1482 2332 1503 2167 2489 977 792 47 1505 629 1776 1305 1037 1339 592 1832 1449 1661 2318 2392 145 1699 1625 1915 753 1227 1485 289 508 1741 156 2603 309 1196 826 963 707 187 938 2576 61 70 199 1385 1062 2081 2649 633 1642 27 2172 2398 478 558 1147 1087 2076 1491 1700 2496 797 1450 2742 2462 851 1060 881 2792 1245 2633 2810 755 1387 2760 316 1251 2299 1102 1809 1640 2581 2002 961 2641 805 2369 2988 881 1450 2228 746 1517 1896 1261 1154 2273 208 1038 87 287 972 2056 250 2874 2257 860 2892 1944 2202 101 2380 887 2130 1221 1031 85 796 1652 2064 1250 1820 2598 1796 2148 1889 1216 1848 1467 2609 453 1780 1232 1411 989 1109 1819 1869 311 1254 2337 2770 2465 9 2929 2080 132 1717 2321 86 1643 2598 1897 1244 720 174 2515 815 1168 277 2248 2285 2361 2773 2364 2156 465 744 1894 945 2069 2403 458 778 707 2320 412 1591 2808 1604 539 428 2218 136 2008 1942 2624 1647 1451 1983 2203 2191 2748 1716 2084 1124 728 1754 1825 2185 908 2480 2359 1104 788 0 881 2038 2515 2868 317 1239 1425 1425 1070 863 2696 589 2394 1890 1258 381 1545 591 2005 2610 1737 670 922 2857 132 1741 2212 359 942 2413 2547 2173 1288 772 1691 1863 2383 1078 1778 235 1733 74 2334 2672 1307 309 940 1904 2128 1257 220 1571 870 1528 531 239 1254 1230 1958 2530 1407 383 2239 2075 1556 1717 578 2236 1246 2404 2934 487 557 2440 2323 2483 431 2261 818 2715 2364 2292 776 2907 2461 460 5 2789 187 1546 334 663 2833 640 106 1066 177 1615 392 2360 2591 929 86 2497 840 2396 856 95 1640 2284 482 2590 1469 1478 1612 2698 159 390 1867 663 1848 1076 400 392 720 2541 2188 2372 2131 1107 2227 1730 1640 2257 480 1183 2660 168 2088 1918 1873 2346 1338 2418 617 5 2090 2207 1828 1283 668 714 688 1450 1020 364 1441 817 1322 1354 1055 1074 283 1438 2762 2294 2173 2653 1170 86 2300 1131 108 510 2492 1355 2605 2081 1130 1815 1846 810 1756 82 560 1373 1384 544 2871 296 2490 224 2972 506 853 356 18 2305 2460 121 607 743 2706 2278 173 2967 979 1962 1478 2311 466 2764 2357 2743 2096 1875 2414 1575 1745 2662 1648 2308 257 1592 1547 2609 985 2644 1495 800 889 2216 998 338 429 1224 2967 110 2862 613 1316 776 1814 2115 2010 1996 2161 418 1841 2083 1321 1344 2200 567 1592 1834 1684 219 2045 1587 533 2881 2694 223 2231 1722 786 2091 91 2261 1820 2662 636 1232 820 98 1589 2255 1617 2394 2302 1943 84 1655 1089 272 2884 1226 2630 1565 2325 1984 2450 1485 1551 1866 386 552 1992 1806 728 2963 1809 716 334 2728 2403 2407 857 1337 2310 561 721 24 104 1319 2748 1836 1175 2773 2662 2228 1187 524 92 1046 2911 15\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 136,
        "task_id": 559,
        "test_case_id": 25,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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275 2600 1953 1016 1972 923 1638 2400 880 2322 2051 852 1512 1754 1043 1682 2816 2632 1165 927 40 2014 2138 584 614 625 729 1167 128 2846 2643 1269 1365 2000 1733 1935 2209 710 1260 462 1369 402 1347 194 471 2272 1033 2678 782 2486 2511 21 2107 2472 2106 1372 703 2557 2637 667 1944 113 1341 2591 1050 385 641 335 2622 2161 1892 2893 361 1232 2651 1072 593 1517 1256 2060 1755 2143 86 1631 698 56 1620 594 2617 2659 875 2820 1034 779 2185 1301 577 1911 2800 27 2709 1893 994 1764 47 717 2962 1286 2071 1859 2581 2046 1350 495 1681 1716 1229 2350 2861 1149 1321 1584 2980 93 334 1522 758 78 1828 1470 539 2097 469 72 1226 2049 1651 1705 1125 1912 901 1430 1524 2958 2884 2457 601 1320 484 1577 1278 2268 2631 65 2523 1225 949 248 2890 60 22 208 876 921 2437 2593 251 192 1270 2465 404 548 1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 137,
        "task_id": 559,
        "test_case_id": 26,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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2897 2186 816 2975 1080 1013 2462 1088 2618 2312 2354 718 2511 2978 721 2468 573 478 1493 780 991 2023 1681 1239 481 1491 863 661 1084 305 1879 2172 564 766 2771 64 776 302 2330 242 2519 1226 2545 1486 2659 107 1157 1787 1494 2098 839 2018 2142 378 186 2216 2882 1110 139 410 631 1441 2043 857 1275 2162 1689 2261 2469 1018 2132 1000 2821 2902 1101 2139 106 2933 955 2889 1853 2762 2877 1703 2734 1557 2680 1290 396 2722 2333 1358 2079 1861 2722 1183 1877 628 2806 1926 1102 1220 2084 2337 2477 1883 1730 21 258 2596 1893 1422 493 1685 1637 1633 1003 2754 2249 121 654 236 2646 50 2191 2090 2582 2658 1022 1750 2008 2567 493 422 187 255 99 2079 1391 2223 1883 833 416 404 1570 156 2273 58 1755 2439 2332 873 620 1374 2726 1086 155 624 2650 2540 122 976 996 1451 499 222 2676 2994 1137 2556 1124 119 564 2094 1250 549 742 373 2508 970 1017 2074 971 1424 1068 236 341 2175 280 480 1139 2025 1340 362 668 2700 1835 1647 331 2810 870 1221 910 255 298 2904 2782 1937 2199 2068 1629 1516 2858 2527 577 1235 2291 172 2049 501 1499 1840 1496 2377 1014 87 1480 2501 1622 2625 1646 550 583 2938 2304 802 1913 526 2125 2891 27 109 1361 516 1792 1188 1734 1483 1761 2446 1592 797 1050 2297 2349 2643 1435 1155 930 642 1522 660 2808 257 2394 517 1290 1244 2911 1542 375 953 1073 319 2492 1312 510 1837 301 2932 216 2233 1484 871 2286 117 537 1545 1249 690 1455 1889 927 960 141 276 329 1324 1469 426 1331 352 788 2101 811 1371 2606 2513 2273 2884 1144 2239 2965 1345 1875 2510 439 2382 2078 1403 971 2388 981 332 2944 2965 2452 287 1133 1510 2269 1132 1404 864 2651 1975 767 1085 144 1852 1234 1892 873 879 2895 1862 861 319 825 520 58 452 2897 2390 133 815 427 2633 1534 943 2724 348 2060 2386 1494 742 2896 2273 666 2025 359 1765 2950 1400 747 1582 1381 1653 2019 1537 75 1539 1067 765 2069 1516 980 1982 2979 297 123 991 15 1729 58 851 1245 2932 674 210 732 2071 2480 1942 2590 1791 1889 1040 849 921 1868 1178 2781 2886 1304 1988 2166 2979 1230 2803 482 2748 2421 1391 2063 1103 2982 901 2528 2579 1335 2954 100 1694 1072 1403 778 1940 2213 2797 920 883 749 194 1365 1001 1436 282 890 509 289 1748 1389 984 2955 1384 2010 1248 696 1553 165 234 1915 667 83 2347 1469 884 519 2166 2407 1476 2881 2201 1101 1131 1117 2929 2349 2789 2224 381 78 1540 1086 1629 97 1898 2979 1500 1740 1134 2051 2617 1931 868 1150 2843 888 2712 2737 980 613 695 1330 1352 1651 662 240 1824 2030 2263 2168 2139 11 2408 2379 702 2343 855 2759 1757 930 2923 973 272 1237 1863 1766 2381 1874 2441 1875 2489 2897 2328 259 2022 2899 2994 2703 757 2355 1823 2107 1927 422 2223 408 2785 1344 509 1451 1188 337 2502 362 270 1645 2951 2188 359 174 1150 1599 1855 1839 1516 2276 2376 715 2747 1001 373 2033 1600 1455 118 2665 1647 1113 809 2266 2791 1613 2538 368 435 2586 1794 18 2049 2231 46 376 375 260 791 1619 2857 602 572 849 439 950 382 1416 12 2271 2992 793 1984 2445 1707 236 2684 2199 838 1871 1616 2057 260 1820 1660 953 15 1777 112 597 1336 1416 789 673 2165 750 292 1414 2928 1970 133 2780 501 2061 1045 1135 19 1952 1375 2312 525 1108 264 1818 2376 2020 266 2739 1424 2086 2395 747 504 146 1632 577 2836 2484 1551 2750 322 689 2400 2789 1505 2499 2951 2403 379 2048 1697 2316 690 123 1396 2512 2060 1603 104 2948 278 1742 517 1727 1275 2816 1704 1527 1276 22 1648 1729 2496 1069 2595 114 1350 2841 2790 2096 1417 2036 1016 2177 978 1632 2236 2735 1622 2335 1493 2495 1644 1699 2830 2974 463 2466 1686 163 1708 2247 722 2358 172 2421 2982 2198 38 1393 1962 2328 2873 1436 1591 828 1660 717 953 1237 1161 209 1527 462 1706 2607 1137 1645 161 2678 2610 1834 35 677 2446 605 1323 219 2156 2890 2886 413 313 1149 2424 1629 2684 2437 1576 829 23 2440 633 324 85 2647 1900 1886 2552 929 2316 575 2038 355 1538 1611 895 1942 415 1643 806 2920 2823 2413 266 2784 673 1602 911 1888 688 1068 2835 1608 2708 4 586 1019 429 1424 1867 1186 1818 860 51 1666 1274 1132 1480 2024 2390 2551 707 2135 2580 741 1790 538 2341 1828 1749 2272 2824 2601 1943 173 279 1814 394 1517 612 1931 2283 998 1498 2753 2427 1325 2594 660 2511 2079 1648 1548 1235 418 1915 39 711 2197 2897 876 416 2616 300 2194 1394 793 1799 501 1778 533 376 2982 790 704 2558 1531 1094 2246 1395 897 1766 104 681 2354 2916 742 2576 215 622 2385 447 1530 375 2133 2807 1539 2365 2838 2357 2304 953 1444 1149 1609 2566 1966 1254 2710 1499 1696 2191 581 1752 2606 2014 1760 2114 608 1885 1939 785 727 1501 1698 56 2271 1247 1392 2958 2813 1500 196 164 493 994 2153 1423 87 1296 518 2863 1130 1651 2945 338 610 2443 2095 2729 145 87 382 598 66 2135 923 153 1789 1868 1286 1511 640 186 1206 1617 914 844 1491 1004 828 943 2217 1183 1083 1337 1099 2433 1504 946 2058 2557 340 2963 47 3 1253 824 948 1352 1158 2991 1341 2088 1217 1285 498 2399 510 1007 2800 1489 1143 2567 270 2167 2752 2735 1187 2945 1236 79 1375 639 210 1276 946 1766 932 1152 1390 2389 1143 2661 2777 601 1024 2987 2920 909 2310 2128 884 410 160 856 245 257 1361 1305 2056 760 944 1755 2900 724 2955 1315 926 1603 2611 370 2563 602 591 1093 936 1045 780 27 2374 718 1016 542 1818 871 1961 2551 2458 399 1408 2786 2447 2291 1898 2580 1048 2299 1351 292 2454 1861 1584 1510 1376 3 851 2106 802 2981 632 1478 1030 724 82 19 162 251 317 2805 2273 1049 2831 175 1875 2675 2349 943 104 2745 2155 946 1124 345 1878 1470 911 493 168 864 1907 238 1494 153 2471 1197 590 55 2408 219 2840 1587 590 2111 502 1532 2820 2219 1663 2091 2421 445 2112 2482 1301 1429 471 1477 802 2014 2584 260 2474 719 2713 2592 2403 1900 2958 108 905 491 1077 892 377 861 1199 1698 2416 14 812 1838 574 724 950 2986 2975 1480 2935 2660 2709 2146 2130 472 2408 1949 623 2682 2454 2096 251 1 2924 1946 1761 2585 1253 1553 2757 1242 1964 2661 2870 1533 911 2790 747 1649 1208 1421 531 1171 2536 1706 438 1474 293 2798 850 1445 795 1680 1515 11 2958 2582 1018 2443 485 2103 1157 763 2535 2346 1288 2519 850 267 1185 154 537 2017 593 2471 605 1140 1364 1567 2190 37 926 2386 915 1053 1883 960 2192 1622 2151 2700 756 1901 935 816 1911 1368 2228 166 492 2447 2119 200 1337 350 2685 1762 935 1872 36 2201 1156 760 698 2139 2552 1461 989 104 970 955 1971 886 2758 436 1377 387 531 174 1028 1637 1034 416 2951 140 2652 1004 1719 1588 759 1290 188 2040 722 2010 1270 2081 2218 2094 2542 1076 2037 112 806 2223 1629 1184 2167 268 1095 1177 1338 1807 2434 2312 1590 2562 2835 2875 1352 1259 1803 2810 1285 2188 2345 1999 2571 1715 2041 2461 1340 2064 570 2408 1053 1425 1097 2298 2755 1137 679 980 2295 1260 862 1996 1717 1017 1931 940 123 924 2196 2819 1447 1255 2209 2132 1249 2165 203 814 2128 1078 2841 1367 341 2707 2269 1252 711 2192 545 2068 560 1401 1520 419 404 1246 2588 158 2699 676 189 378 2875 849 837 2781 18 2593 759 442 1479 547 707 2333 2003 712 2027 710 161 907 2063 716 2286 1579 2097 2947 1317 2328 765 775 1882 2428 2358 508 1195 616 1855 1461 2962 1346 1141 2003 1780 1303 12 2914 1193 1450 1938 2631 290 545 396 1370 1412 1569 120 1516 180 1742 1422 1646 1186 1602 1083 2956 2326 508 759 2278 2070 1651 1452\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 138,
        "task_id": 559,
        "test_case_id": 27,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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        "output": "0 1376 2941 2946 2489 1588 2221 2110 908 2422 87 641 2422 1359 2152 2534 1665 2207 1030 2906 2269 1308 180 2296 458 149 1624 863 701 2853 1306 2317 1311 2427 204 719 2389 1548 1021 1179 2149 1967 1231 2688 2610 960 2399 495 487 2832 2081 2920 525 1297 1266 968 297 1254 2955 1081 912 2960 2915 977 1045 1210 460 120 1500 575 274 447 1877 2113 2247 317 2711 2443 1023 2785 1970 1984 43 191 1960 2850 2904 87 2875 1573 2029 923 380 138 1204 1383 814 596 2991 455 134 144 367 1675 2609 1415 2380 1146 2741 219 2560 2873 92 2815 465 1917 1773 1563 529 771 2638 292 1868 55 1139 2480 753 491 2452 2128 881 568 2471 2948 810 36 885 1908 2991 729 514 2467 2654 1884 2587 2727 2548 997 1674 2452 2974 106 749 2459 2414 2819 1296 1620 2324 2913 1249 97 875 808 478 720 475 1411 1307 1231 2671 2189 1435 1231 1615 114 1144 1589 1497 1795 1045 2228 1030 1947 166 700 1508 2947 1566 873 1129 79 2126 200 2919 148 1832 2545 592 2126 2515 409 1899 2019 2949 2232 791 2977 1410 2619 2951 1564 751 636 240 809 2973 2949 897 1559 1026 1212 961 1629 935 2881 2821 1267 1616 66 1178 932 428 1297 2357 1635 1465 832 2866 802 2323 390 2576 477 1046 458 2402 2319 1075 1300 1820 153 323 2406 24 1463 921 1069 2454 1751 611 2675 2922 972 2821 2998 749 183 2458 2365 971 2285 1529 2116 2998 2870 1253 1830 178 1205 1506 1903 638 659 1084 1071 254 2616 1622 2583 243 1659 1593 509 1667 1496 2195 261 1453 720 2602 1908 1235 1152 45 2874 371 220 2389 168 91 2233 56 1658 2292 1130 2509 482 2447 2661 1669 470 2387 39 1161 956 2111 2147 740 398 1528 444 1860 1928 528 2734 993 2422 2827 537 1827 2492 2148 2712 102 1869 80 1087 840 700 2521 1550 1327 659 661 1998 2660 1188 1001 1610 1285 106 2176 709 519 1906 1501 632 2273 2693 2527 2786 2610 2334 436 882 41 1149 1450 218 629 599 1146 2294 747 1252 1664 2092 2059 461 2774 1032 1045 2104 598 2685 2009 995 894 493 1188 1124 1132 2445 542 1643 2183 1381 1315 2406 688 976 1271 2994 395 1533 2968 234 971 1048 2636 633 1642 2738 826 35 2557 1909 588 2830 2545 1990 261 2625 985 1193 980 1345 1239 759 806 2216 1508 363 282 1394 563 920 2966 121 553 1039 1662 215 2277 1923 1665 1501 2200 2203 2462 2173 312 1640 2436 2327 1481 752 452 2277 2407 1363 2767 936 2773 72 49 2967 792 694 1687 124 2268 394 744 1462 2987 1106 2658 2789 2816 934 2049 2392 2694 930 507 294 2829 1324 2647 2845 1275 726 2034 2819 2312 1763 822 969 1365 1108 877 2020 1116 213 842 2592 1694 909 1446 2057 1495 2123 2649 1263 2405 1174 1438 1998 1987 1086 949 2329 530 1469 2356 1856 2938 2113 279 712 1382 2002 2993 2894 1063 477 334 527 1467 5 1868 2362 780 1299 2110 2522 962 1794 350 842 42 2293 2734 460 2679 2234 528 2414 944 2414 1867 1049 1553 1819 2613 342 756 520 2571 1398 1065 2848 1387 542 756 1335 2181 859 2910 122 875 1009 1337 232 1459 1829 2879 2448 1495 1797 2437 2248 2508 660 1465 514 1722 2262 2231 2173 1857 2429 2748 957 379 1353 436 2989 151 1378 2257 2149 1523 1382 1473 2359 2908 4 1553 1926 2146 988 65 1870 1477 531 2127 1746 2861 1338 1019 1557 2603 2548 1591 558 1068 2140 2889 648 2225 300 2987 1441 240 2032 1239 2461 1180 139 252 1264 1461 67 2522 120 2228 2649 1365 185 2556 1799 876 1509 2599 1840 898 258 2910 2712 2259 2539 1537 275 34 35 717 1251 2128 1232 611 2183 2956 1349 581 1423 2557 2020 1767 1494 2143 721 2761 1698 2758 1847 134 2391 790 2710 1685 1348 414 1719 2860 2524 2676 1726 40 2121 852 601 48 1778 1376 926 2067 2375 1303 2946 1423 1647 1860 1699 463 1273 1583 562 1663 1003 1584 2190 635 1583 1075 1872 1157 441 2015 91 998 2595 2401 2322 312 1037 938 552 32 827 2686 197 2379 2213 1264 1314 988 1436 956 2634 2804 61 40 2829 1697 2303 2828 2442 1636 2186 2220 2916 1229 2253 921 643 2865 692 2554 1757 1384 1671 1059 1352 261 2214 2364 2087 228 798 1057 18 634 2700 26 2669 2601 1903 2387 2810 1554 1323 1097 1683 2242 2948 664 101 1924 1078 1479 1227 1431 1338 902 2608 1258 2093 2464 2765 2463 1165 852 609 1731 590 659 182 1856 2900 903 83 2007 2527 1995 2845 807 1821 1033 1199 1927 1468 617 2799 1017 1506 1824 670 1483 1729 163 499 80 2947 896 538 95 2134 2571 1344 1097 1663 816 153 1361 2897 401 1032 2328 1611 938 804 2294 300 1591 2836 2096 219 275 307 712 2706 2668 2716 1975 79 2524 239 2491 1495 499 1867 824 474 943 552 1388 2519 2985 426 1561 1718 2427 1987 1211 2821 1571 2796 1397 488 2870 2015 2391 2987 2301 1206 212 1360 2792 1055 2387 2634 1191 1427 1988 2419 1139 1433 1314 801 1129 1501 1065 2639 2235 645 1087 1469 2249 1503 2012 785 2512 2170 1983 1404 616 2956 1915 1520 1479 2432 780 1129 1327 21 1884 1699 2438 71 1621 2302 1061 1408 1170 1840 765 2868 2797 1637 2284 1154 796 2812 2574 725 2293 2029 2729 2087 1232 59 2510 2610 2280 580 688 1699 2765 205 2380 1328 2282 424 75 542 1343 2544 247 602 184 1778 2398 754 2683 1276 841 2817 999 2133 522 2418 909 486 2701 2216 1233 1759 1111 2939 1503 2804 2879 2599 681 201 2975 2733 2199 825 744 1173 209 2376 1517 2059 681 473 2334 206 2053 1394 935 2936 2706 2309 2077 461 1044 2052 357 1739 95 1696 2706 879 108 2503 701 2488 1230 46 140 2847 2507 2856 2112 1891 773 163 1025 1710 485 2116 80 1155 1480 1314 1910 597 768 1001 901 1163 1828 513 1006 497 2269 1469 1391 189 1896 386 1847 2004 1841 2557 1019 2321 1549 2316 2463 1678 1041 507 2580 2348 886 2219 459 321 2613 961 2070 2429 1006 462 1372 2919 1985 256 1787 811 2970 857 40 1644 1213 1 2083 1543 709 1047 2725 2750 659 2183 2439 272 1336 165 722 859 2994 136 2340 1774 126 560 1672 1815 2718 272 986 823 2903 1818 2430 2337 2615 605 463 1297 2487 638 2781 2726 2707 727 2660 2370 1921 1659 466 1227 1996 1398 963 567 738 2145 2504 2069 2845 2458 948 2070 1734 2229 2366 127 2812 2323 2715 1291 2178 265 2427 956 943 452 1499 1084 88 970 793 1731 1938 2183 2321 2818 1267 350 969 1141 1014 1759 852 1455 2101 2394 2729 2610 2298 468 1165 205 1323 1379 418 1301 122 2716 275 51 2269 2570 90 1955 2596 386 2757 368 2287 1714 574 1721 1321 1171 1599 1133 257 1793 2560 2373 1241 255 95 2957 1203 760 980 2928 1066 511 761 2073 1861 2062 1170 170 2259 2553 2699 1324 2919 2069 2533 1237 1242 2585 87 481 2627 1393 993 2582 68 1827 2277 1139 1058 2350 1953 2156 1925 2517 2440 824 2189 2799 2001 2543 986 349 1265 2912 465 156 612 1874 907 327 2339 2494 150 375 1797 1860 956 74 2921 2442 521 148 684 505 1447 514 2008 2571 343 2195 1598 183 1872 1001 565 2285 1288 2836 727 339 1614 1895 645 908 1516 583 2412 1076 594 1959 1664 2359 2559 2193 2394 1078 2011 586 1915 2014 2194 1707 1554 604 642 919 680 798 2297 369 1928 482 246 2927 354 373 2434 252 1431 1420 1430 963 878 2660 1820 1174 2807 337 1265 1910 561 330 2431 2576 1926 1951 479 1517 2249 356 1007 1018 2472 1709 2311 2128 1794 1606 2172 656 2734 1812 2263 347 2822 1266 1293 2082 1306 426 304 1350 2952 2751 1144 457 1100 1498 1480 2669 2510 2292 249 920 2861 75 584 1145 2881 409 2111 1850 2727 1994 767 2651 962 2429 2892 1430 561 2918 1885 394 2653 1169 366 1910 2448 2355 664 226 303 77 2117 1060 125 1041 1597 555 308 701 542 2904 643 1344 2806 1014 1042 1937 2614 2698 2623 13 1067 1884 1681 305 16 2676 1192 1532 801 1034 694 398 1760 1455 982 2528 2838 2272 253 2816 2047 602 973 908 353 2038 1697 1032 129 691 2967 925 622 1391 1732 1622 1500 2539 751 616 2646 2764 347 2048 428 2502 1881 2233 2470 2792 650 2995 2032 1930 26 614 817 9 1229 2843 92 564 2482 305 2831 2022 2053 2893 1998 2622 1700 2618 2654 398 2944 2850 1634 2758 224 1778 2517 2314 240 2832 643 1043 591 345 1988 1441 62 1199 2692 2650 604 273 2686 1960 671 2356 2750 2481 340 637 2910 1169 1672 619 1750 563 525 20 544 1399 2321 2598 2547 899 1578 2830 103 2697 2764 832 1027 1383 333 1635 485 1666 193 676 484 1463 1131 961 1540 379 1152 2098 1198 1929 1045 2821 1811 1099 2099 1986 2419 1484 707 379 806 1122 1709 2467 1798 1910 697 98 1802 2954 2832 1252 1429 1146 142 2977 403 2337 1959 794 763 1269 2897 669 1912 2745 367 1245 2032 1042 881 2326 2121 1523 621 1019 1527 1436 888 13 876 1644 1852 1849 283 2114 184 2992 1199 2613 2632 1638 511 712 262 2074 2042 305 934 2127 2505 2295 318 609 1601 1761 1171 1562 2419 202 687 454 194 1771 87 2591 1792 2007 921 2050 2748 1776 2135 1043 2578 2617 2492 446 668 1754 2129 1130 1800 2971 1670 153 424 1095 894 2054 1427 1912 591 2245 947 2639 1939 1998 2948 2035 206 309 526 596 2374 317 2937 2129 2598 646 1200 2096 2502 653 356 273 51 2079 1177 2876 693 2830 1599 1512 821 1918 1587 1897 2444 2948 1239 2531 359 1529 1183 1135 1626 476 2898 1524 166 1241 542 1708 2132 851 1420 625 31 1823 676 221 616 1194 2156 2719 1553 48 253 1704 2117 2285 1908 28 575 1796 831 1778 881 1315 1948 1728 1475 1297 715 837 558 850 2067 2896 2594 867 467 11 1343 1905 2130 2230 1274 2858 2144 2896 1390 961 1075 1883 746 2762 2602 2389 2046 195 1923 1831 2253 521 342 1671 2768 8 851 325 380 750 626 2155 2721 326 1296 2083 1722 1664 23 2037 524 1695 2917 2764 2092 1243 1828 982 2577 1522 756 922 1618 562 979 219 1073 129 582 2847 2451 961 2901 1003 385 2404 990 723 1463 2769 2339 298 1757 1560 1098 2702 1766 733 1355 2162 1680 2927 1145 1754 779 1708 1921 506 2630 2161 1759 1610 2904 2745 764 957 1627 1986 2859 1754 548 481 1129 2749 562 1803 641 2381 439 1272 481 405 292 1955 2189 2732 376 525 1263 2832 291 889 1064 1213 2759 1011 1853 2961 528 548 1565 2667 2765 475 1987 2059 2547 2741 959 2604 1115 1839 427 390 889 674 1030 57 13 965 239 554 202 837 1673 1623 2390 1223 856 2507 358 914 1797 1919 2406 1409 761 1172 2316 735 2051 1559 2200 734 1502 1623 723 2116 277 2018 883 1865 479 1978 798 1601 157 526 1251 2599 2720 1978 111 74 294 2828 2577 777 839 2169 604 1142 2756 565 544 632 2557 2989 844 2742 853 2207 271 2930 2677 470 2203 1090 1679 2790 708 1036 238 210 703 1665 72 1155 2732 1165 2476 957 2409 2886 2582 1124 1806 1292 2956 1582 1410 222 748 2876 2502 476 1208 716 934 2110 410 957 526 2213 658 1539 1111 2864 1384 675 1995 2618 1701 2126 2460 1816 2939 803 2168 1562 1391 182 420 2853 1733 1238 73 251 2131 2537 1095 2295 1048 992 1465 455 534 2430 1909 547 1688 2058 1140 197 2861 747 747 726 333 1985 1273 2803 669 217 436 908 961 602 2329 1479 683 2392 1837 405 524 762 2561 2248 1693 1389 1532 1084 1727 2253 1278 2646 657 157 2393 2150 1797 2975 257 409 607 149 2196 1819 122 318 1216 2587 1039 1746 476 1332 391 204 345 597 2592 1797 322 2433 168 1594 1630 532 720 2617 2610 854 2254 738 1981 1723 625 374 1952 1786 1844 688 607 615 1721 299 2883 2776 1985 472 1448 1501 2963 1824 1438 2091 349 2867 230 859 398 2621 704 2467 2257 2430 1457 987 2270 7 1935 2394 1385 1246 315 489 2528 2341 1274 2689 1929 389 416 2006 2083 1852 248 2369 2117 2589 1014 1772 1424 438 1797 1018 899 324 8 1127 2142 2479 2117 2043 166 2374 2197 917 827 2357 1214 137 1565 1093 2014 2135 186 432 2486 2832 164 990 1752 2325 1466 453 2506 2353 1568 2803 2516 2653 2429 2148 260 1563 905 2787 2883 1132 932 1859 2213 707 2134 2541 2310 845 2774 704 281 2169 2225 1742 1025 2819 140 2662 11 1997 2586 1884 2907 2244 2114 2125 406 1126 2301 232 578 139 2237 523 1530 2830 1564 1144 1601 2165 1595 2518 2122 1180 430 1618 470 819 403 2135 2429 2 301 1960 2538 2371 2651 1394 1020 1264 1412 964 2399 1720 287 1050 1315 915 743 2986 757 612 2160 937 1773 2051 2449 2094 310 587 1492 2254 583 1810 1177 2128 1107 351 695 2087 939 489 2325 2289 533 2350 1395 2788 1374 2565 2756 776 2086 1527 88 537 1102 955 2981 1961 2355 2586 1243 21 818 147 2607 1582 925 34 1596 605 2436 1366 1693 2005 257 2795 755 690 904 1923 2335 2331 2406 663 1987 27 561 2788 2581 2230 2445 211 57 2360 1178 609 225 200 792 1379 1656 406 744 1584 1799 644 2483 2635 2281 1664 2088 2012 1341 1319 181 2848 2767 812 1556 191 1304 605 1822 1736 1177 2305 2852 380 868 102 1160 2895 44 2623 869 1700 897 57 703 709 2398 1818 2563 1720 2819 2972 1597 2179 763 2009 299 178 166 1039 2221 433 148 786 2136 1599 1193 64 840 844 2725 2958 986 2210 1728 2436 1499 1863 671 2756 2274 2445 438 171 194 2035 1792 1290 670 494 2541 824 2803 2395 1958 377 315 1417 2990 594 567 508 2491 937 1517 2028 2997 2451 1853 879 1033 2645 225 149 1088 2416 2849 1671 2841 169 707 2487 1545 1935 2893 1714 392 2578 172 1792 2233 668 327 1738 2216 1193 2832 90 2213 2330 282 2721 2982 2515 1028 284 1135 975 190 232 1907 1954 2399 908 1275 47 1899 2758 97 2000 1703 917 2358 880 2901 2460 2493 622 2362 947 2522 1728 2557 1705 1652 1881 1195 577 1245 1403 1518 1854 898 2252 1818 79 2764 968 1955 2279 769 27 1363 2555 722 2087 2203 2994 553 2124 722 41 1586 444 1778 1593 162 2535 615 2882 2885 1790 1982 749 1029 390 872 243 901 30 1257 811 381 2544 2608 762 1874 1979 2744 1489 2329 2660 2243 2672 164 2435 1095 1343 2718 1950 802 2225 1002 1396 1874 2588 1378 1065 414 2454 2112 933 348 2007 2365 835 2024 968 2389 994 2017 158 1247 1358 2636 2103 328 2334 750 2010 2820 151 1648 2004 736 909 1167 34 1619 946 1062 284 1009 2910 656 2066 285 851 1369 2219 1840 508 2973 695 1779 2131 1153 608 2487 1006 2621 2311 1971 1694 1887 834 2256 2974 908 1246 1884 2226 2850 950 433 2161 19 1713 525 846 1457 1027 903 2607 485 2533 156 1193 1568 765 2535 2147 883 458 690 2254 2236 2413 1925 2456 245 1109 1673 4 326 1365 2826 2820 1413 2905 2159 1463 2306 1793 1880 2152 2156 2212 2077 1768 2324 450 2601 105 1725 2179 210 1168 2824 198 951 807 313 2144 1557 31 1594 913 298 988 1171 1917 852 2618 1832 2070 2966 2579 757 2260 1047 1312 2138 159 1308 1251 1311 2729 1877 737 1580 259 562 549 1215 629 779 1803 2265 1824 917 2544 2098 2500 140 2676 1753 518 2094 2958 1798 42 1962 311 636 726 1631 1119 834 707 1227 2152 2320 2512 1326 2609 461 60 456 2597 2720 831 2036 162 649 2514 1314 2992 2472 1328 2647 339 1453 1156 739 1139 1949 1486 687 2725 1873 62 2959 2143 365 2415 1874 2734 1966 1030 2467 746 2435 1946 1097 2654 2113 1051 2838 421 218 640 2433 2303 2803 2548 164 1198 561 2427 975 2592 372 1186 21 2969 2847 618 1721 1376 2124 1705 1862 668 2139 1426 10 1140 131 2507 458 1620 2137 188 2277 234 2313 1352 189 542 287 408 2506 2783 2614 2935 1709 316 2216 1453 1418 1537 404 506 1419 551 2082\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 139,
        "task_id": 559,
        "test_case_id": 28,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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1679 1835 2655 2139 838 2097 2916 274 2689 1942 1141 445 802 2561 94 2819 2968 2608 2647 1166 290 2428 1969 2734 217 75 2977 2427 589 194 262 537 83 2406 559 959 149 1875 2376 2582 1291 2195 1055 1632 861 2082 1812 1519 2382 532 2718 1051 577 1963 861 2714 1648 1108 195 2385 2928 1414 2778 2307 758 2811 2273 1513 1108 172 939 1115 2260 2572 1254 1425 2845 2194 1058 1059 1106 2207 734 2785 2607 2570 1360 1476 1720 700 1230 1261 2052 2680 1352 19 2271 1935 84 1527 1049 2347 2621 1923 1339 354 2326 454 980 167 1395 2212 703 2220 1764 661 1339 2771 387 12 491 1812 751 982 2031 2193 1410 1332 2535 922 1445 1548 2146 1592 1207 1531 2301 2283 1646 2896 76 2568 583 2775 2372 2100 2291 1461 745 1431 2890 2844 2956 44 2403 2850 1073 770 964 1175 2040 2974 10 1322 293 2539 1825 2463 2856 2702 895 1748 1944 1049 1129 410 738 2777 1705 1429 2992 2587 2789 991 2230 1859 592 870 2433 1921 2342 901 199 909 2678 1118 2954 536 2629 2903 2217 2445 2923 220 832 501 189 2775 1896 2693 2905 1738 1959 1584 2329 1330 1398 2800 2053 1489 499 217 930 1373 1588 950 1762 2910 118 1396 1234 638 1425 1228 320 756 1002 1105 593 463 2952 1084 2457 2323 1829 2307 1082 1033 1158 2470 853 2900 2266 1088 1074 750 137 933 2304 1594 287 1493 1610 588 1015 709 2965 1334 613 2044 1291 2738 1564 455 2788 1383 688 1158 1698 2954 2642 2855 2274 1199 208 284 1516 1394 1630 2806 1875 1740 1846 1497 1094 2812 451 1400 659 1330 1565 700 179 11 600 1286 911 2917 1963 1854 176 409 2872 1177 2293 2918 622 2346 1557 605 2043 2117 1868 1924 59 292 2316 541 1577 1337 2592 939 1852 5 788 1024 1208 2427 686 370 2736 1046 1030 2406 2683 2808 91 2064 390 2233 880 36 1082 1654 2651 1319 1391 1043 2837 2890 1405 233 1250 2560 629 1281 176 42 159 2750 2494 818 2934 704 866 2869 1569 2546 39 1126 2005 1633 2990 2728 1581 1089 2083 998 1664 1996 858 37 375 2445 2395 999 2773 2937 189 2612 1618 839 2800 2023 2030 2687 2795 2393 2537 1901 2345 2470 638 701 108 645 2244 2432 2697 397 1267 1227 762 2036 1943 975 1548 950 2026 1495 2939 1424 2504 2989 80 1103 1161 9 2952 135 138 1444 2886 2244 2911 648 824 2568 847 1434 1254 906 2896 2678 1704 704 2570 47 1592 2196 1900 2863 805 987 464 395 2030 2930 228 1914 1970 2508 2917 127 2939 1394 1350 396 903 2035 2791 273 867 121 1291 378 2668 1386 333 2349 1823 777 200 2278 1066 909 1749 1763 1974 871 290 1210 649 20 1693 63 1150 173 1659 1376 2548 2261 2590 667 394 35 1230 62 2795 540 763 677 2106 1822 120 282 1452 2456 1859 2174 737 2136 1860 2448 90 2754 2303 1265 1447 1290 340 1594 2186 2420 2199 609 1320 1445 1696 147 1000 1980 1383 2213 2255 1825 587 2651 1846 1757 1527 1803 1373 2118 865 2098 1284 2135 442 23 2100 2015 1104 2507 2992 1837 2531 463 2184 488 1408 568 1936 103 2584 986 321 1442 2294 724 324 182 2017 2843 797 2340 1988 457 1327 181 2839 2866 677 1995 2120 524 472 2661 634 2010 2388 1213 649 259 1302 1539 54 97 2568 1219 237 2689\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 140,
        "task_id": 559,
        "test_case_id": 29,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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1017 462 2412 273 175 1918 41 1402 20 2826 2881 2547 343 2128 809 1262 1614 651 78 891 2585 1299 1027 2034 2719 866 2417 949 49 1436 2920 2432 2900 2173 437 899 1691 500 1165 2694 214 133 2017 1657 398 456 448 1657 1542 1432 2141 1385 228 2628 2277 870 2847 407 2960 462 321 52 887 850 2939 1825 2557 2934 2929 1916 935 2504 2666 2111 2335 302 260 920 2098 487 532 89 823 2526 1639 453 797 1613 780 298 173 1875 2590 531 1775 933 2527 534 351 651 1238 100 2342 1195 2018 383 238 1381 537 2259 218 483 1587 236 2833 102 1344 55 893 1271 993 1082 1132 948 1331 527 2053 1142 2095 2447 2074 938 794 2548 1137 2607 2693 89 2782 1222 813 2348 2583 2628 1592 2091 230 2404 1750 2016 483 558 2694 1222 2617 1685 1463 511 1590 2098 1933 275 188 2857 1127 2900 73 610 1330 2399 371 2952 333 2226 2630 784 1576 2325 597 2769 1660 2438 745 2416 1913 1144 1414 2456 764 1384 2086 2761 416 94 575 2364 2220 724 2900 1709 1442 1587 1292 997 684 2682 1681 1740 2792 2353 70 1604 2964 2485 1762 677 371 1462 1919 738 981 1237 2383 83 2844 2522 1257 716 581 286 47 1719 850 2233 1100 117 904 2086 2462 327 2560 1980 806 1273 1341 2805 791 35 1204 2172 703 1290 2223 1082 1702 1046 209 2883 1424 701 1657 1279 45 1713 1637 1626 2009 844 697 2893 1984 1786 2724 0 887 1938 2609 500 532 1123 2340 887 665 2298 689 1180 1725 151 1313 13 2005 2861 860 469 271 164 2004 305 1858 2681 2974 462 2834 2754 1551 587 2035 218 657 1955 441 2781 1552 1501 1783 718 1770 977 1900 1923 2162 406 195 1420 52 2653 2296 2620 2586 1712 264 2128 2371 2238 1254 38 75 773 1433 1038 1913 459 1619 2371 938 1535 301 1155 2114 519 301 1952 681 1560 1122 288 470 2944 472 1542 81 471 2182 297 1466 1877 1196 1073 553 1764 500 2967 1448 679 1451 1157 2882 1503 883 1426 395 2979 1614 2672 2718 2072 2983 2990 2511 2410 1672 1873 2800 748 387 1672 766 1534 1040 17 1332 2306 247 1612 2170 845 1149 79 2852 887 1523 999 652 1151 1986 2653 2585 2233 1691 472 783 238 1342 363 2670 2398 2199 2220 1367 2365 1890 1058 2863 2607 2711 1774 2239 2223 2994 2111 1143 2493 502 2112 674 2740 2252 2323 175 1174 2389 229 956 1977 1284 2296 1195 382 733 1000 1168 2609 278 2742 2515 2556 1343 2431 1722 2797 1269 1116 629 2062 1341 2763 1925 1963 1531 2739 2162 1150 964 943 26 2239 1164 2942 1259 2397 2077 1512 740 222 2527 2698 2311 1084 1097 1149 2040 1493 2392 1476 2755 832 2932 2218 2397 1201 776 2531 1086 1452 830 1144 13 1470 1986 2709 2685 112 1337 2114 906 868 911 1892 2544 631 1115 69 1806 339 2963 1905 1084 427 2531 2678 1208 2746 377 1403 1439 1689 2818 149 1638 881 45 494 1231 2812 1049 1018 2337 486 919 986 1332 38 448 2940 1170 1900 2797 1710 1724 1832 1734 788 511 1762 1648 2020 175 1918 1053 926 2562 2137 2197 1590 2398 172 2750 2237 1448 2087 332 2888 421 478 353 2789 830 548 1730 262 1845 2039 534 1709 2241 2899 1410 515 2903 2137 2263 2947 1403 210 986 222 423 859 944 1673 863 602 367 139 2719 2065 1683 2226 1286 2017 853 2691 2243 2536 2886 2390 345 532 485 2844 2229 487 270 1845 213 4 1410 2413 2005 598 1066 790 660 2140 2666 1304 980 2108 770 673 1168 2888 1953 991 2143 1987 1781 1399 1055 1204 2486 1636 2106 1751 1911 1639 2890 2638 2809 174 463 2116 1938 31 1926 1869 835 2614 406 1224 7 411 100 490 2585 1075 2461 1348 2608 1138 616 1231 345 2297 539 160 1214 1488 1764 593 144 2204 1995 1718 1581 1694 2376 1498 75 394 598 1663 1901 2290 1746 1535 1092 551 408 2384 632 1230 1085 1100 1973 611 997 696 1618 794 1528 803 587 1362 1859 1090 1955 2688 2446 1037 2156 1341 2171 247 1376 1869 815 924 635 196 2283 2800 675 2263 638 1723 1586 1137 1321 2957 2461 2916 2868 163 2338 620 897 2276 819 892 2392 1048 2202 1150 1396 1374 595 322 1381 2108 26 2268 1980 918 2044 2478 1004 660 1968 1062 226 1231 1481 1696 719 625 1388 2371 1092 503 583 1351 1672 2509 865 870 1627 2497 399 1548 929 2515 2549 2392 587 2240 1548 1431 827 2488 994 2722 2713 2110 95 806 981 1780 518 56 1516 2667 873 1927 2680 368 1997 1444 635 2427 2379 1866 727 1435 254 812 1504 547 2639 641 1421 525 814 2310 1235 2617 2526 1713 1701 2678 2595 2561 1395 2070 1155 94 2625 114 2914 2880 667 582 2687 1966 2247 2810 2877 417 1519 184 1135 118 588 1068 749 2538 2714 762 491 601 1311 1631 1037 2408 1849 143 106 2763 2813 2113 557 2663 2957 1508 152 2914 272 2427 1368 2818 2542 1578 2954 1682 1262 238 2164 2546 30 1148 1091 2946 700 1181 2545 2808 330 2784 799 2897 382 480 1180 709 1759 1360 1820 2954 2030 1089 100 147 2030 1637 1260 51 2702 1532 2834 1568 930 617 2664 2656 402 2777 2847 618 1120 1158 1610 573 2233 2080 1751 2841 956 2881 1696 2145 679 180 971 2554 285 1823 2403 218 2146 1575 1568 2377 2194 2206 2933 2444 1586 949 2381 2564 752 840 437 1549 2842 2879 272 229 1324 351 2199 2994 422 2879 331 239 1846 2149 2217 523 1901 1134 84 284 861 868 1733 1793 602 2574 1347 1241 1246 362 57 1768 1576 250 2675 782 2572 1940 81 2814 59 2403 2274 1523 2221 2376 2894 700 2159 318 2265 2625 2520 2115 402 2954 2025 112 1828 390 1994 1432 492 799 1112 766 150 1 2027 1747 2048 2531 1717 2449 1889 2956 1261 1617 1317 2092 1165 1739 292 751 424 2388 1385 2190 1253 85 1502 1122 443 426 2374 2969 709 68 2031 2507 1442 2052 1225 2924 2511 332 2883 547 2490 701 2813 2452 1480 1081 2706 1701 2725 16 2688 210 2349 2715 1016 1669 2979 365 675 468 2439 2477 130 1824 696 1469 2681 1639 1128 848 1763 377 1627 2481 1069 371 2533 1979 1401 87 2857 1490 1498 1672 1547 19 2515 848 1769 1549 664 459 1389 115 1652 2058 254 527 1417 36 533 2843 324 1794 2788 2148 700 1032 1526 2690 1116 2344 2920 625 1935 2683 2264 2327 171 1058 548 51 562 811 2052 666 368 2138 1548 172 521 2795 1379 2683 730 1669 133 987 830 2812 1234 562 1907 101 684 2598 1303 2190 2919 1154 1843 1392 1950 678 1792 2732 277 2734 697 847 1211 2269 912 1403 1367 2757 832 1886 633 532 1493 1869 2359 402 2678 1213 338 1306 188 237 2420 2052 1252 359 2787 241 112 801 1811 2539 1096 1599 1393 775 2074 1421 30 1549 464 1010 2946 1825 575 223 4 309 1921 359 1781 1697 1603 2949 1996 1018 2848 873 503 1015 2 1307 2134 1209 2757 1931 1935 1835 1953 2509 1552 267 2770 2320 2144 272 1196 2767 92 564 2757 70 1908 2377 2195 138 1941 273 2203 2980 2403 2236 2672 1118 787 1520 1057 2826 349 1711 73 1195 841 1336 1443 131 1341 538 2720 418 1289 1007 516 590 288 837 603 1414 2126 610 2651 238 1167 156 810 127 1184 471 1281 832 2386 2064 1659 256 1244 411 1924 2696 2743 82 1374 2440 2584 2461 2466 731 642 2540 1350 1928 1752 1070 2953 2287 2880 2635 824 779 1303 1856 2878 935 1847 2256 796 1255 1568 313 997 2032 1419 2741 1690 2710 2607 2190 31 2197 1710 1918 404 620 2188 2531 2593 1517 1840 1153 530 80 431 1128 326 438 2865 478 280 187 2592 897 1624 2463 1920 1950 298 1716 1744 2624 842 1848 269 858 2439 1437 2992 2847 961 972 2685 1875 2230 1875 1589 2973 1708 1562 1523 247 726 535 1529 2748 1157 1052 2993 167 2645 2237 2076 1527 1213 961 1827 2826 1921 1238 837 2152 595 1402 676 212 857 1012 1530 2231 2368 1888 1409 2559 2284 48 2831 2986 764 2193 666 1862 2296 1764 1413 2533 1019 476 2571 1110 1340 1770 2645 819 841 2383 2650 239 2206 1185 2297 2747 2412 1500 1897 1323 2193 1287 2958 2372 1267 838 1882 2992 2389 1628 2332 2868 1292 2606 582 1848 1538 1463 2620 2875 1427 1900 1558 314 2803 2245 2037 1764 171 890 1347 878 1869 2577 1242 387 2613 2109 1573 2166 152 87 985 458 1134 1721 643 214 2580 1661 2736 2036 1944 1233 2799 1839 1933 1294 1505 2896 1532 2303 764 93 2622 1631 554 723 1878 1416 2736 429 2190 2275 2827 2180 1442 2605 247 2646 1514 761 1911 2955 2034 1950 2081 179 2533 1428 1107 1824 482 1291 2082 2968 1200 1730 1642 273 2649 956 1821 938 1110 1492 2078 2570 2190 1732 1725 363 45 1544 1108 145 1071 1981 2727 2756 1342 2965 1020 1053 1205 1394 417 987 957 667 207 289 1366 1604 2623 1804 2814 184 1360 2839 1357 796 839 480 1085 1164 994 2066 461 484 988 2043 1125 2955 681 1657 126 1027 2047 291 639 1302 1848 2580 2158 676 197 2865 2047 2465 339 1924 2838 2137 1405 455 343 591 1336 597 981 2852 435 2954 80 1196 1912 418 608 35 1365 1477 2491 1692 2519 1423 1338 249 2782 2388 363 1788 1078 1588 1162 2305 559 1939 66 1297 849 2920 2638 1180 2575 1535 993 1971 567 1669 2175 872 2413 989 2212 2171 945 1359 2725 1072 1006 397 2308 2890 2269 550 1304 294 2040 1514 205 2173 742 339 2 1167 1855 545 1689 1386 1316 765 1078 2093 2309 429 2318 2891 719 1376 20 1795 2139 2583 1385 322 1196 2306 1472 2864 2180 669 2295 1595 1782 1391 2985 887 139 2698 491 2531 1462 1589 920 1023 1397 2956 2987 401 2283 78 2909 2153 199 889 1992 1464 2051 1625 764 166 274 497 825 439 307 816 349 189 1659 731 2403 931 28 1580 26 560 2091 2913 972 1868 2202 2379 284 1167 2926 2850 2904 2690 578 2209 2476 2513 2012 2604 1768 2896 1579 2226 2261 36 1134 2922 2700 1532 613 1434 1492 808 1055 810 1273 2823 2932 2909 2819 21 1788 1882 544 307 2112 132 313 2466 2955 2075 813 778 1297 2144 284 741 2850 1088 353 2733 2766 2961 1348 857 1016 598 2138 1307 1928 2558 556 2595 551 954 1927 1692 453 2554 1111 1183 63 1101 309 1815 1649 625 2058 2239 2742 2848 855 2259 1351 697 2126 2879 2567 2535 2823 1302 2743 2945 634 2098 2265 213 2637 1587 1423 2029 1165 2965 800 1284 1918 2355 107 1176 1481 711 2232 1781 1914 2885 952 330 316 1210 943 119 1016 69 1032 2167 1663 1213 1266 1560 2980 1931 2595 365 2366 2725 1734 497 1678 2536 2075 1536 2291 92 2924 62 1717 1797 2289 1722 2919 1875 780 2453 1634 1197 2643 1173 1005 715 1149 2720 742 1141 1036 544 207 771 2709 2848 234 636 1631 32 94 938 1892 1308 2370 1475 2629 2584 1876 2106 1462 1621 2650 320 1145 1919 2201 2313 544 1894 1381 2631 2757 1907 1877 2944 426 1360 517 338 2853 514 673 344 767 1421 1957 1874 2759 189 2441 1799 2795 799 252 931 163 1279 2549 1395 1251 55 825 2687 2371 1828 1999 2522 2958 1579 2772 1522 496 264 476 2207 2949 701 2761 2766 2229 1997 728 2949 176 2523 1356 2774 1030 1767 256 692 460 803 1250 162 2345 452 584 1064 1476 249 2924 403 132 1365 571 2490 1184 1116 2118 132 367 2601 1178 893 324 1171 2932 406 1255 1695 2096 2384 166 2591 338 1926 2412 16 1645 2447 2121 1658 321 450 2132 1021 2691 2983 1808 2974 2977 1612 1981 2325 2905 2564 2690 1854 2981 1870 1899 1457 2730 2886 2038 2968 209 143 183 487 1085 604 341 58 396 2895 2399 1478 1914 2677 164 2588 499 684 2128 648 663 2950 1831 799 1933 1580 875 2454 2073 872 1616 632 400 2405 2732 569 615 1364 2567 1716 735 582 949 1472 728 2610 21 152 1568 36 2735 1479 2664 1 2019 1515 1604 1032 240 2609 1333 2741 485 431 2345 2889 2339 63 1051 1697 1048 953 798 337 2242 1870 2286 403 1758 1136 2849 299 1590 2632 2628 2294 1133 751 654 1014 2893 643 1011 1122 943 202 2188 1271 463 95 2955 113 1140 2798 2379 95 1333 32 1060 760 228 2650 2834 2929 1763 531 664 1064 2862 2576 203 1545 2319 929 1517 860 157 1154 896 1258 224 483 1831 2048 2158 610 369 2947 2660 1096 1149 2345 2523 268 2539 2872 2739 862 2297 2036 2030 715 2323 1057 1602 205 2610 1985 1620 1469 769 1694 2578 134 2150 1412 1397 2682 1717 2557 1227 1306 2474 2119 1464 1256 2399 1459 1964 1499 1195 1210 2909 876 2674 1849 2662 79 1055 2315 701 369 1083 2175 2209 275 1152 18 1357 84 2493 2801 2361 1126 779 2967 382 855 890 1189 1028 825 2362 2448 1205 492 2152 856 1108 138 2818 1315 2233 1947 984 1301 1817 1995 853 155 1899 170 638 2607 2595 2860 1427 2893 1166 201 2073 641 1250 1512 2789 716 1034 1800 1885 2281 2215 998 1512 2627 89 294 1365 837 643 1188 1876 2116 724 2761 2515 653 1907 990 2666 1859 2742 886 2991 2313 687 2586 2972 2054 1288 382 730 69 1355 923 1478 1184 2582 2011 1301 2712 2909 2627 2335 663 2626 1925 1781 403 676 2169 81 1059 2242 2798 2315 1600 644 2876 40 74 1074 1208 2270 876 62 948 38 1271 42 1058 1976 1070 544 440 2437 1039 2433 2262 2011 2076 970 1989 792 2422 193 2337 530 2224 629 2511 963 1388 1724 2923 682 1986 2314 2077 498 1781 1786 1678 1362 2922 1381 465 73 93 29 2859 170 88 2812 1698 911 2297 402 677 2567 2171 241 1172 2278 1529 2941 1657 135 1844 2892 967 2097 891 638 2470 127 958 496 2031 2640 1528 2878 2990 977 1003 1052 2070 725 390 1733 1069 2830\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 141,
        "task_id": 559,
        "test_case_id": 30,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
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2793 1307 580 1425 787 944 245 2181 487 2923 1006 239 630 387 2197 1382 2173 689 1260 2452 1301 2785 430 777 2068 1957 2514 1605 757 1227 2892 807 861 125 1235 2762 1408 248 2025 690 2041 2989 1904 2767 464 427 1782 1203 484 474 2991 1481 131 784 2028 1465 1124 538 1500 657 579 2820 2888 1550 2059 1759 2538 2997 1419 1567 2814 638 1721 2877 2596 2096 878 1953 2006 341 2791 144 2046 941 2591 1921 833 2222 1423 1738 1812 930 1351 2253 1955 583 460 1693 2145 166 1623 388 1984 2064 463 573 92 1019 1685 2997 51 1369 2779 2832 1705 2495 209 1397 2236 1511 1005 1046 45 1227 1558 2331 717 2480 1319 1821 860 1512 1484 489 2561 255 531 2427 2036 952 1972 1173 1495 736 1673 1636 2045 958 33 1687 2642 532 47 1092 2555 326 2080 1078 2741 2062 2504 772 2689 2784 684 1472 1946 1515 2571 543 657 2874 1311 2126 1303 2636 730 2506 449 1336 2415 124 1373 1446 157 1191 2695 929 2080 2968 48 2188 786 1698 1480 363 22 2014 1572 1376 1518 655 1265 198 481 5 841 2189 1694 318 1592 2896 2899 2164 1302 1317 507 1968 1634 1224 2337 2503 2443 2730 1058 1602 2712 726 63 1538 849 2503 1336 1281 2408 2532 2636 2634 129 2755 2577 894 420 587 2954 2759 1720 2282 1659 1546 2279 2863 713 1902 1216 1893 242 2446 1094 713 2005 2822 1491 1629 177 931 2328 1202 1929 1660 1110 634 456 742 1955 1463 1813 432 165 539 2856 769 2633 68 2905 114 2949 118 129 1321 120 274 886 2172 1081 341 296 1399 2293 2468 507 2477 2019 2158 727 2923 1870 2449 280 812 642 1359 1202 261 435 1627 2025 1223 2206 1137 1906 2066 531 2008 1485 1135 1132 1677 1918 642 1809 1629 1793 2299 1369 1276 219 2033 652 2480 831 2742 1494 432 633 2604 590 2885 1403 2703 2288 347 1424 838 2478 399 1902 697 2556 2759 2613 2557 2877 604 2548 2334 1593 1068 2941 2173 1047 1946 1519 828 622 2573 2085 295 2727 2331 250 952 1029 2463 823 2057 1965 836 1356 2926 2805 2533 2525 2095 1985 2004 38 944 1395 2709 1441 1596 2255 2834 405 1656 49 2344 107 134 590 2421 983 2329 560 1924 152 178 1463 1787 2077 2945 846 2436 509 1317 1411 1652 1909 661 2518 651 711 1599 2069 911 2486 2994 1106 2444 929 1276 2105 283 2774 2760 2820 1079 2396 1163 11 2070 1762 531 785 2170 2954 461 257 1776 189 2534 1968 2267 2838 1625 2196 2525 2412 242 2021 986 1420 2504 1786 2465 1713 1654 846 2817 793 2668 2260 2167 1029 469 1472 149 1229 2318 1812 2034 2426 866 1168 1761 144 2771 402 1469 1504 249 198 1431 128 2534 1312 330 2783 390 2649 1246 1953 1358 2012 202 930 513 2452 1203 1561 1207 1052 1115 1261 1216 1301 1453 571 2576 1487 1305 2512 1159 92 943 617 2098 2507 2004 1871 2741 1769 90 499 2120 2596 2597 1883 553 2252 1725 2365 1447 1713 1628 1392 2249 449 215 572 828 1544 1515 1759 2951 939 2236 1174 331 411 2648 736 1240 1948 1044 2868 2986 1105 1953 1538 1709 2303 2707 651 1430 2388 1219 2143 2167 967 2837 1074 467 2029 1871 1658 2608 2239 805 2590 1355 2808 599 1158 1186 1480 2958 2182 584 2856 1187 2503 2048 1069 1420 1855 196 906 2973\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 142,
        "task_id": 559,
        "test_case_id": 31,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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        "output": "0 2995 849 2241 1287 58 2371 627 1336 2924 1270 1688 2230 1717 1884 2877 2540 2218 312 1872 2803 235 289 423 2395 2547 2553 1738 1272 2046 1222 1969 1075 755 213 2641 197 1759 86 573 331 273 274 2371 2227 595 2429 2698 2567 514 357 832 2681 2407 916 2873 2745 1598 2182 440 2508 766 1497 2145 1831 2660 2948 1654 1471 376 1887 1620 2329 2289 449 1954 2920 1300 1667 2208 401 2712 2704 824 1632 1035 762 1472 960 86 532 1319 2311 1277 2444 1992 1528 776 1208 1728 1154 1362 2597 548 2601 546 1204 1958 215 1104 2512 2592 201 426 2976 2660 1746 1449 2548 81 79 2318 2089 459 2205 1989 2354 2815 366 2102 594 1626 1729 2925 1322 610 1903 990 2909 2238 2270 660 833 2388 2266 504 1664 344 198 2240 1543 499 2179 882 2546 397 1206 1687 1888 2583 1612 8 1198 91 623 1301 2221 325 486 1819 474 136 1871 852 266 790 839 1318 1339 2411 2477 829 2257 2143 1412 1702 1718 2784 2574 1183 2260 1869 2978 1487 1659 2181 753 2904 1014 1742 830 1698 2962 1653 1101 1375 650 1033 1628 1822 1391 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1326 43 1305 2117 383 386 2441 1564 1178 999 1423 2542 2052 2094 86 601 1927 337 2366 235 1075 293 2073 1526 1262 2718 105 1092 2737 193 695 2934 2438 2589 988 876 1081 328 1886 1562 1513 2671 906 742 128 432 2617 646 2394 1373 1279 1399 442 285 1396 2293 1622 1692 1740 950 6 2237 1163 126 2602 150 905 2197 1586 2956 2074 907 156 2269 94 936 978 514 1315 1955 1138 523 1441 424 1381 1833 148 723 1250 2789 524 1968 1529 127 691 457 622 2872 1059 2403 2191 1096 1343 2658 1823 1462 2570 506 2057 1914 223 1348 1736 0 780 856 528 57 1268 1471 2546 385 2379 383 1204 228 1867 1976 2599 2553 460 205 864 1471 548 938 2387 2011 2658 877 2822 933 367 2210 1064 2013 1467 1338 805 460 877 1099 339 945 343 2076 1665 2375 2402 2619 1175 153 1611 64 2641 225 2445 2533 1791 601 821 568 2380 1169 617 675 2076 377 2127 2204 1277 1697 1159 273 1183 2822 675 1091 1958 383 42 390 228 896 2557 914 2601 1575 1099 533 2667 1478 289 6 2255 789 1094 369 1682 1784 876 2563 2763 1037 893 2394 23 2016 2500 2970 393 1166 36 2879 2106 409 2568 2716 2326 780 454 957 363 2249 1905 1174 2404 2648 1177 2969 2139 2522 735 1944 694 1120 2822 2082 407 2959 1906 2105 1441 465 245 332 606 2593 1697 2965 1792 2842 2039 1525 412 1761 1127 913 2017 2160 2872 408 977 351 1289 1391 1324 384 1559 1124 2047 285 2840 949 386 1299 1505 1547 38 2094 1871 994 2523 1092 1321 2595 1300 341 1812 2860 2453 2238 2690 1165 2002 1915 2973 2958 737 2176 1128 1358 2321 436 1508 2850 1185 1731 2285 2658 1530 1905 1366 1723 2475 2279 2633 2507 1818 2886 1918 1496 605 1379 1454 2489 1105 2149 2010 2232 1101 1666 1834 1700 434 1716 347 1764 2246 452 1363 111 673 812 291 1150 105 1089 2778 1669 1709 2147 2913 2750 1175 1293 1329 2717 2539 2652 2732 2757 1604 692 1173 2374 1239 391 861 332 1160 2395 433 1125 1017 829 1770 163 1260 2852 1558 765 2852 378 796 2599 693 246 1740 5 877 2028 1537 1951 2128 469 65 1940 2258 197 1236 1816 2978 2602 2891 2278 1833 2562 1478 2255 2122 2027 1014 1135 1312 1525 815 2959 1553 388 1082 287 1581 2066 1619 180 1773 797 2275 1921 896 2672 2772 2673 1154 1540 1611 371 1781 1649 2352 2812 667 924 1208 2002 2041 198 1246 1991 2031 2739 1707 1025 1542 1713 2166 362 769 1542 994 1847 618 1789 854 1171 2643 1420 1812 1636 2603 301 330 1152 2069 2789 1119 648 2326 2661 1492 447 1584 671 540 2603 107 2670 167 1005 1838 637 83 1039 1619 795 1062 2613 1498 2989 2421 866 1850 2634 1771 1363 890 118 1774 1067 1381 197 1500 1159 1345 1905 2464 1045 2388 1696 2930 2598 1053 560 1223 2405 2735 1776 109 2082 849 1634 882 2076 775 2352 1385 904 1414 802 2741 2987 2360 33 2196 2907 2794 2886 2215 1068 2647 779 2903 1210 8 1372 1428 2929 2899 997 518 1619 2094 1549 867 2228 1439 105 349 8 450 606 138 1654 2493 2966 229 2055 948 1077 2661 2909 903 2200 620 2410 2531 269 2237 523 1247 1252 1269 722 1883 2837 1406 391 272 1422 314 2297 134 315 1694 1470 2198 152 2488 185 1448 1285 316 2540 1639 2346 1356 24 2016 2919 1974 727 1741 912 2330 2551 302 477 1474 2947 1686 610 147 834 2010 232 2637 280 2872 2545 364 2584 2352 1535 1437 2873 1095 1871 70 1 2897 1041 2435 1545 291 281 726 2147 1233 575 626 2980 208 830 635 467 1946 2200 2527 1469 838 1651 678 2560 1998 1581 2049 771 1267 2642 1865 1906 161 2716 659 1351 2047 785 2536 490 2378 2971 1949 1255 1936 895 2948 1526 701 2662 997 2410 1407 996 100 971 344 2832 382 485 1874 2988 2987 1156 1391 323 830 19 275 501 1426 2838 1052 2569 597 2923 2078 1340 69 345 2397 847 2726 132 2065 222 2847 36 1404 871 1344 995 127 566 511 1900 2100 2413 2344 1284 697 860 1651 2050 2974 1786 106 61 423 1907 2750 2435 450 292 398 848 2006 2542 1784 1455 488 2742 842 475 2145 2937 2653 1504 171 2491 2699 341 674 2444 2698 2059 2962 1749 918 2819 1884 1582 1836 2403 2362 383 277 2300 1410 706 829 2713 2764 1178 288 184 168 1835 127 1964 2864 634 1188 2054 2598 2942 854 2969 1581 1176 2930 1158 2535 16 1673 52 2695 304 2214 855 1827 2220 2502 2138 261 2397 2992 2946 271 2737 2805 1829 1338 2318 2448 1198 2453 1744 61 1706 973 1119 282 2181 1662 2210 455 665 94 1267 1576 1156 978 1575 1515 2699 569 2828 2131 1374 1708 991 184 1159 1071 2502 1751 1492 2258 2401 2558 900 746 1477 2879 1677 864 2905 1729 2572 178 713 2832 2720 2176 2437 798 2038 1660 1409 2405 62 9 2291 2039 708 1452 2392 1133 985 901 2899 899 422 2170 584 2622 1317 545 2315 1847 346 1060 2498 2640 1107 544 1681 2779 587 1510 2670 2929 936 2344 520 462 1972 1855 1797 125 1799 981 1335 2935 2928 1672 606 818 1648 1821 1004 1725 478 241 2487 354 1704 630 704 2426 2567 1340 2879 2005 2365 1479 2500 2639 478 1344 1251 1902 2550 1063 2952 303 593 2077 156 2586 559 395 2325 1998 1932 2612 2603 478 2574 2939 885 2394 905 645 2142 2977 512 244 579 817 2725 1428 2669 2829 1419 1093 2008 2899 2544 2785 2509 2350 2246 972 1862 939 624 1634 2504 2062 288 2334 2513 2038 1710 2881 2205 2525 1616 418 1292 1156 25 2140 762 942 192 304 1165 1271 442 187 1713 1752 2554 2058 2586 2466 1122 620 2030 1974 115 1203 2018 2868 2431 2372 6 1984 2159 2565 51 409 963 761 1015 1763 1511 2614 2200 900 951 1024 1713 1947 350 546 222 2261 1157 1398 2919 270 1013 1985 537 265 2349 2481 2160 1651 1110 2706 205 565 1529 160 2982 2040 964 1510 1348 830 27 1261 1875 1178 2108 435 2276 812 2966 1508 1025 1025 2806 1982 1004 1058 869 986 324 1443 57 813 2946 2005 824 1249 4 1260 1430 1316 2105 2286 2746 804 1612 2239 157 1857 2345 721 2208 1146 1874 983 1225 1239 54 179 1810 193 2303 1493 368 458 733 2737 425 1494 658 1902 1620 1225 2385 1986 403 91 1307 2387 42 1056 2436 2606 2523 2891 2863 1494 1647 1388 893 2617 1023 287 1598 1297 1741 686 2899 2093 2013 1635 2713 2423 2664 608 2034 2464 194 1229 442 1111 880 1466 2260 2939 1225 2220 2812 2269 9 988 2451 2132 928 1454 1889 235 2918 1714 812 362 525 2297 1149 222 650 2015 43 812 2342 1567 2615 54 2826 910 914 2076 1920 509 2371 1734 2296 1446 437 2176 528 1586 922 885 1390 550 1670 1288 2857 1032 2927 2625 273 347 2271 804 1593 726 478 343 1423 78 2793 72 1357 1980 1449 6 2150 1732 2710 668 2074 317 521 682 672 1859 1939 1276 1925 711 945 1675 1649 133 1084 1464 1895 462 1300 2358 387 2914 266 2987 1441 2844 435 1207 2229 2874 2452 2259 1268 1022 1649 159 1790 677 2233 1104 1655 1500 180 1650 2163 1939 2304 636 1658 270 2189 1644 2634 1072 2465 1689 1129 1462 1399 1306 2461 1883 2772 1435 1079 227 289 776 2059 653 1994 1185 2041 2361 2099 1827 2030 2719 1022 872 86 1928 2958 2788 1187 2317 1263 2036 1644 126 805 1912 138 88 1735 1261 1028 2164 372 2782 1663 2383 241 197 1367 2346 175 2490 2885 2674 2681 1207 240 2944 121 42 542 275 2845 81 1075 284 252 372 646 435 2408 2098 1321 1571 64 486 1077 1065 632 1166 144 2865 703 552 2302 22 1545 2624 1012 1689 2191 2045 1325 1529 1122 531 393 1638 55 631 2738 575 1845 2234 1837 1128 1006 729 2012 298 1040 138 2573 2336 941 894 31 1854 2031 2768 2354 50 561 2086 2235 1409 1682 1924 1898 559 455 1089 939 773 2763 2557 1092 2570 1871 429 2327 2294 1283 47 2774 1522 158 7 1096 1462 2523 1341 2506 1140 2754 2737 583 2418 963 1397 68 1912 702 1017 1587 999 1491 2872 1566 1403 132 977 467 1242 503 1841 1523 2402 1860 2821 1228 2840 1609 2840 114 190 1267 1841 1206 385 2109 2490 2954 2523 839 2153 989 2158 981 2758 1867 2914 2006 1910 1817 648 1750 663 1155 439 50 1105 646 1223 2701 1206 1407 885 2064 1092 278 2477 2206 2520 1836 1630 1807 544 1839 666 314 1287 874 2638 1720 208 50 147 381 2223 1734 1543 2161 2767 690 2279 2853 1067 1171 223 844 918 125 1123 2423 805 638 2542 542 536 1939 146 2592 432 642 2205 372 1828 364 2558 1762 2724 2282 1917 2744 609 997 267 1535 769 1678 1868 1124 2452 594 2805 582 2025 2008 71 1997 2401 88 1821 689 2140 2744 2636 2583 27 2717 1428 1502 2811 2200 2074 1399 1748 1809 2718 659 1058 2515 1224 935 1662 921 1167 902 2231 322 424 978 2391 2421 643 2169 428 754 616 2012 1398 2029 317 1433 858 1788 497 1018 847 187 1373 1882 2529 2950 648 2703 874 2297 1021 1648 1284 2122 1641 41 2233 2410 974 1430 55 2320 280 2298 2189 1120 723 2075 2513 658 1895 2599 2487 2684 2647 1414 1498 1929 2280 2563 2742 784 2853 6 502 1452 2334 1904 605 1837 157 2791 2184 2406 1991 503 2394 2572 2186 1229 1821 92 375 1368 2251 1144 1136 676 1303 2197 1510 703 1662 1230 436 377 536 720 420 2927 659 887 1147 1264 332 2382 353 498 2662 857 1314 1602 829 632 1439 1859 945 67 79 511 2393 1800 116 1696 621 2818 1539 304 626 1956 1312 2805 1018 148 1756 2774 25 882 2219 2128 199 1258 2972 2875 602 719 672 1896 1949 2352 670 2754 1057 2477 948 2112 1609 2127 776 1367 68 461 2495 2437 811 1975 1261 275 963 1180 1780 864 2037 1528 142 1603 413 2190 2907 524 2279 789 201 1998 377 2380 1892 2838 2945 1928 1942 2924 896 1471 1319 1495 1181 2252 2916 1348 1192 2973 2673 1770 510 2014 2414 1277 171 2821 2627 1245 1720 1200 1868 674 1772 912 106 360 2056 2904 2056 1348 1398 780 2473 2810 1989 1654 2813 1264 438 1227 2905 569 1666 2544 1678 861 2446 2257 2475 1182 1627 2631 2866 2780 319 1032 2158 2852 1543 2389 878 847 2289 289 1651 1879 1921 1363 933 865 1008 1529 992 2680 610 2118 1340 1983 1026 133 951 32 1922 288 951 975 178 35 2558 2378 2529 2277 194 477 1010 1482 2159 1302 353 2395 994 2480 1898 156 1353 1727 1695 2860 477 285 2789 1753 1630 2319 2948 1483 90 2007 1035 2674 2330 2364 2852 1157 88 1683 53 161 2163 825 918 168 1433 2632 1174 2129 2165 2276 515 346 1231 2110 1943 576 1816 2190 2435 1573 1519 1105 2645 2144 471 1576 730 1357 19 2172 0 2740 1440 896 1663 358 1022 2168 1023 64 950 1427 628 324 248 369 2828 1206 1765 2425 1376 161 2549 789 209 1368 966 828 426 1062 2141 1323 1546 2141 1628 2023 735 1158 1420 2870 2365 170 2360 2584 1323 2478 1210 2574 836 484 2033 2688 2834 1935 106 858 2993 936 139 1109 817 1460 2373 1884 2193 2940 951 1911 584 2875 1738 1389 1233 2692 1410 586 2484 1460 1102 2635 1606 2613 1558 2151 1475 100 2912 1646 48 238 916 1008 649 1424 2343 199 1233 2627 1146 230 2193 1263 1412 2012 550 371 713 1403 956 1944 2888 21 1801 1755 1739 893 2522 2488 1180 350 2425 1600 1753 1868 2304 193 1684 2427 2406 2662 2263 699 2817 2350 471 1316 801 2953 684 1162 2294 1873 1027 2310 2007 1297 2210 279 1107 1325 1540 2625 2995 2463 834 2441 2944 1037 1199 1566 2568 200 1613 2232 1395 680 1345 1621 1662 1950 1751 1075 239 916 1898 1412 1412 2733 2426 1792 1636 1483 1325 322 2817 1881 244 2354 1464 608 508 2744 2742 1767 2300 1507 1232 2823 2811 1537 1824 235 1348 2249 776 2288 2085 2774 1182 2085 1184 1609 2964 2633 117 1227 83 2350 1624 2942 679 202 2723 2715 375 1068 1056 2181 1139 1516 1374 2393 188 1541 2423 2722 2589 1495 2909 2152 2688 2425 2264 2450 2526 2943 2743 1779 1200 2157 887 2172 1108 2483 1077 528 21 163 1619 1460 1967 1863 97 1098 721 812 1717 841 2397 703 1704 2600 275 390 2313 2795 655 2933 62 2031 991 1149 2526 37 989 2021 1612 2936 2124 225 511 416 2447 1497 1699 2700 622 2208 2094 2247 1606 637 2447 2017 1299 1294 919 811 1344 2405 2846 1804 2320 564 2101 2328 198 2104 2051 716 527 803 2350 1813 2246 2055 2763 2794 1656 911 161 579 885 1525 1881 784 1398 2074 2163 2494 802 1357 1838 1340 300 2024 1054 484 1724 1089 2348 813 2504 1094 1072 2627 1343 610 2576 2494 2366 1631 381 2010 2657 918 1855 2759 2572 278 1810 2673 2439 1268 85 356 489 2397 2039 625 1317 674 2298 1228 590 1982 1410 1119 2442 1126 2397 2824 1691 370 2948 2559 2780 1076 836 2169 871 2090 1964 12 365 779 2867 2082 1813 586 322 1691 2375 69 2006 2539 2076 1495 1862 1936 539 2549 732 2128 830 534 2440 2040 2193 2750 2835 1670 939 1222 239 2816 941 1714 2778 466 1835 2289 829 827 1956 2043 2419 2207 1240 1369 963 593 1998 1516 1 1536 762 799 2994 1891 381 966 745 1977 257 1225 2837 2689 284 2386 626 2183 7 950 1940 435 419 2995 931 2325 1804 2108 86 308 2312 1333 2146 2554 309 969 1944 86 2516 1030 1547 1049 1611 880 2521 1633 238 2482 957 2588 1137 1497 1162 1782 2146 2263 1642 2121 2911 2376 2026 2661 941 1963 147 1178 2342 1984 301 2799 2765 2262 754 348 605 2615 556 2708 2063 2467 955 1890 511 583 1719 875 1917 2433 1301 359 797 1187 1032 559 351 1613 2981\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 143,
        "task_id": 559,
        "test_case_id": 32,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
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494 1621 1752 1724 2552 420 596 1434 1222 1290 2494 995 965 2921 2023 1733 1484 673 513 1233 500 2714 2484 1585 2695 2087 950 2700 1035 35 199 569 1881 1163 1822 1638 410 1225 2026 2098 2195 2072 2024 701 227 400 124 2687 625 561 2953 639 2468 1637 98 2043 96 1534 1070 2265 433 457 1486 1900 1185 56 376 2802 2100 2076 1728 1785 2349 478 1343 1574 1463 1489 188 1869 1531 1136 252 300 1638 1849 92 756 197 2539 1063 218 2339 2366 1748 484 165 94 2387 2596 1863 1268 2737 1774 1772 2292 1494 2342 2563 2654 332 2731 1759 1032 2177 356 1125 92 1770 2216 1976 2871 997 1170 212 2424 2481 2821 200 536 1454 109 405 1850 307 739 1453 2233 1450 116 984 2163 10 90 2733 2458 2005 434 2158 2015 260 159 1111 573 1163 51 207 937 717 1312 471 2963 2298 20 308 1442 292 1751 1462 350 2177 2454 2179 1288 2814 2127 1195 1672 1897 1502 2159 745 1867 71 695 1722 2390 1919 116 2186 1445 1845 2532 2572 1997 236 2611 923 747 572 2737 1063 2846 700 1743 1488 1011 1751 1365 800 1055 1711 588 1606 1417 1744 640 2447 1533 662 646 2459 2038 684 2089 2349 1505 1286 811 2243 2307 1620 284 524 1808 374 2802 725 1876 2202 1136 449 637 435 258 833 2963 2901 1491 2969 1877 2786 2525 1542 2508 290 2834 2477 1427 829 1160 1686 1183 1968 41 2564 1241 2909 2037 125 707 2041 1048 1097 2962 866 2219 2675 2653 2399 138 2304 2702 2305 1735 159 315 1560 2387 1597 1010 2669 1099 2456 588 436 2019 188 2709 1412 1072 708 247 1966 712 2942 2843 2965 1104 310 1872 1118 1943 1829 27 2613 161 1676 2988 419 616 278 839 2077 1690 2051 283 1555 1891 596 2379 1620 376 2429 15 2497 1514 1815 1903 2704 2 1521 124 2775 2979 2260 1530 1539 2933 1424 463 2945 2750 2445 63 624 512 1733 1354 2049 474 1387 1081 638 758 2426 256 2859 113 2688 232 2448 345 1114 1063 766 1763 2127 1417 980 1763 2503 2116 1189 2062 2928 454 1050 1435 586 1956 2812 95 1522 2069 1403 568 2771 727 2615 1497 547 1953 1433 1762 1727 2371 119 1516 2428 977 844 1486 1184 1238 2843 31 2929 978 356 1838 527 915 1656 1305 2085 1987 2662 176 1558 753 1967 1719 2827 2460 2671 2245 480 1294 1049 1006 2490 409 2898 1350 1965 2914 1085 150 1536 416 32 27 1694 2240 697 1119 20 2733 1619 2607 530 1696 1671 1002 282 201 353 1955 795 1756 562 880 1667 1134 2870 2601 1234 2844 467 500 2685 1103 1538 1180 905 1425 643 2487 318 2595 1476 2664 951 2117 456 955 1286 615 2611 1339 382 1813 2063 827 1963 863 349 2879 510 1564 2254 675 1150 931 122 384 2132 2432 44 612 1938 1988 1909 2369 1976 1420 516 678 313 833 1992 2133 1613 19 2598 2172 971 1002 2001 2454 2816 157 1600 2406 188 1932 2327 1352 1616 1584 2429 1011 467 468 632 747 657 27 1538 1493 1875 2515 559 2572 2216 2413 2031 448 760 2763 905 1149 1818 1554 1897 2099 2636 2611 1632 1235 1627 1235 2848 1768 2890 325 2095 277 2248 670 653 1305 2096 2300 2972 2090 2453 642 1361 2072 1989 259 1912 2044 1908 1899 2150 2951 2964 314 2418 1524 1623 2655 1734 1229 1471 2828 1399 1606 1378 1228 2834 1076 73 2347 2197 2996\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 144,
        "task_id": 559,
        "test_case_id": 33,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "7\n1 1 1 1 0 1 1\n",
        "output": "1 2 4 1 2 4 1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 145,
        "task_id": 559,
        "test_case_id": 34,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "11\n0 0 1 1 1 0 1 0 0 0 0\n",
        "output": "0 7 1 4 1 0 1 4 1 7 7\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 146,
        "task_id": 559,
        "test_case_id": 35,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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412 710 1692 458 548 1624 2422 2150 2342 1098 2575 510 815 574 1264 1061 2852 646 484 2944 1260 2827 1868 802 2490 2893 1447 2956 1194 1016 937 2883 346 2836 2952 2397 519 1675 1537 2524 2725 1191 2696 2930 2489 2652 63 1317 2396 598 1054 754 530 2822 2023 1035 2000 2018 2330 203 1201 98 496 1108 2824 393 605 1500 744 1309 577 450 2049 1706 582 840 1717 876 1494 73 517 2104 1959 1225 19 2112 508 899 2708 1432 1116 1966 2057 859 411 751 1264 76 696 18 1053 150 1499 2811 2029 2938 2350 501 3 2859 2763 1043 2776 1422 1932 2285 1608 523 610 922 1112 2668 1603 1695 1692 2901 576 1125 411 227 625 1177 1580 2268 1730 1695 103 1170 729 2808 2038 339 602 978 1798 341 2899 3 1618 2385 2661 1537 1521 2051 2547 1413 867 2301 1246 2206 797 922 2920 2859 1569 1190 2546 468 210 341 876 2360 2910 264 497 1901 1988 137 1428 1036 1495 269 1655 2529 2023 2091 1996 968 2454 1985 1582 1893 1199 895 2754 1329 1612 2852 2347 1173 2072 780 32 1543 1802 1820 2597 1229 1736 688 794 2200 1566 1481 212 1723 1758 1422 2082 412 1901 519 493 2273 1715 1139 1502 164 67 2798 1 2057 2194 2171 1289 1885 1573 32 2873 61 2018 101 1404 1163 350 1806 878 21 686 2176 819 666 1769 1978 927 2594 1441 2849 2756 2339 2350 2479 1020 742 845 2442 2528 560 1401 1543 386 2414 1740 1116 1144 613 1132 1451 1020 1560 2950 1658 2383 558 1421 36 696 901 2776 2544 1482 1304 366 2617 148 1582 606 2413 1344 1960 2123 1120 2826 1392 1271 214 1968 146 1162 1635 1610 1563 735 241 86 385 2737 931 751 237 2522 1039 284 2329 980 2854 2625 2418 537 2756 99 1925 1229 1907 69 2194 628 2807 559 229 361 2044 21 37 2846 2442 1311 732 1227 143 1421 2096 1962 1113 306 663 2490 2818 388 1639 182 786 2898 2235 2164 249 1992 1038 2395 2922 2789 539 2469 1831 2864 2818 2801 2316 265 621 2148 1714\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 147,
        "task_id": 559,
        "test_case_id": 36,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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859 2417 1394 1921 2459 1186 1158 2602 2246 1156 701 2951 1632 1996 118 2419 1399 2614 2958 1376 704 2521 1830 1658 1066 1797 1188 1318 2316 1978 1967 1169 739 1948 2214 65 1155 444 1436 1557 873 1010 1169 592 364 1781 1972 1031 468 995 1652 2143 2698 2636 2897 1850 286 2380 2075 1961 2359 2850 1297 1534 2262 2164 2043 2885 1821 1090 981 1327 1020 2700 1215 731 1866 161 1720 2913 140 217 2354 1565 1653 967 1274 2925 1447 860 1220 608 1720 1869 2151 150 976 2431 762 276 18 816 792 556 227 1284 2743 2542 186 1754 1837 1339 594 1387 2962 2248 894 307 2285 576 1594 721 2628 715 479 107 1310 406 455 1196 767 318 1678 68 2357 2775 337 1719 998 548 2679 2462 2657 1000 1093 1630 1302 1004 97 1233 425 2493 1494 1037 1050 1839 382 635 2143 1154 2269 2765 1319 1381 978 559 590 2261 1236 1235 2668 112 984 2213 2505 1775 139 322 1854 2002 2063 2834 1158 2515 989 2146 1590 1719 929 778 2369 480 2325 896 207 1548 291 2089 934 2757 1148 286 1416 685 549 2915 870 2834 291 185 2531 177 284 1235 1889 2137 2321 366 931 2462 93 2284 660 1112 2676 18 2387 2039 2194 553 960 1011 121 1066 2279 2296 1960 394 438 2458 2227 480 826 2603 1412 2730 492 453 1286 2460 143 1747 1432 2424 298 771 816 2515 1760 453 2961 860 1173 1491 1917 2406 1364 2506 2532 2911 1679 1538 1 2240 119 299 2321 1606 1134 615 214 2630 165 2099 2868 2626 2418 1980 2594 2899 206 1117 2182 2872 1879 1206 310 1035 156 2759 1715 2061 1013 2279 949 848 2557 1760 437 1114 991 2179 1664 5 2452 1914 2001 205 2675 2121 1947 2273 1605 2848 2767 2650 665 1549 2348 486 1806 2949 1275 1107 901 1317 1637 1031 786 938 118 2162 2055 1222 263 363 139 1275 1594 2405 699 588 102 1899 1419 1758 172 690 1069 1130 2314 2278 1835 2204 960 1932 187 478 2216 2358 2927 1095 2381 1669 147 1674 283 2562 1044 68 2602 2175 2370 492 1147 2255 1028 1261 1113 2787 879 1809 808 2072 1817 1013 1669 1625 210 2125 2776 1871 2757 2623 389 2086 2877 61 1798 846 1071 2597 1654 864 2037 2245 1114 1704 2963 187 2136 1192 393 1275 2160 300 1133 1726 1427 1354 634 1131 2436 2325 2828 2173 2244 2285 1905 335 2513 1020 402 2291 1764 1220 1994 2428 1245 1465 2111 1699 1534 1319 1269 1748 1464 1393 92 1410 193 2212 2007 2342 1360 1950 712 834 1773 1719 2770 2333 1506 54 2292 2570 2574 351 2381 890 81 1166 2827 1445 1018 315 2259 2592 1563 1318 1429 23 2115 260 664 1956 2704 1686 686 1915 2131 1156 2014 463 1622 1717 1845 1484 1891 1622 1026 2647 1332 311 2273 561 1876 1982 2310 280 509 2657 468 2576 2763 616 1104 2943 1599 1267 2464 980 1431 2202 770 2490 2470 2763 2767 1638 1142 2954 1455 1986 832 184 665 2638 1587 2634 1710 2293 2107 253 1464 1045 2535 57 942 2398 516 1948 823 1973 1973 1363 1676 758 2420 2272 732 2071 1720 809 2152 1491 1092 254 1533 698 1731 2947 2309 2721 1387 1664 1532 2385 2125 766 1640 2674 2490 2397 870 1463 2205 222 1246 2688 582 2421 632 359 1597 433 730 1069 1527 2648 1623 2332 1982 2640 1921 235 2237 1441 1026 2912 2363 166 513 758 1188 2176 1785 2737 676 1782 133 480 1952 2487 597 521 2229 1990 2013 1388 80 2644 2373 177 390 2754 2722 2030 49 342 1102 1427 2743 674 500 1335 1529 1884 2951 2623 2740 2793 1487 2795 466 351 2428 1372 1462 1985 582 820 39 2340 1138 175 832 2620 1578 650 895 2620 2375 1925 2632 145 2477 270 1952 2653 1538 938 2143 2532 567 1131 1702 1436 857 968 94 444 452 2257 2817 1879 391 1397 1271 728 818 456 1010 2786 85 2155 1838 2779 362 1646 2562 1572 434 2702 669 636 2230 2039 1214 1960 2124 2016 2116 435 2604 2282 2498 2450 369 2465 2437 1697 725 1022 1991 960 1625 475 129 35 917 1386 755 138 2855 868 2862 2186 1152 695 409 1925 455 717 374 1945 1656 655 1603 2612 1183 2481 231 1263 1530 503 2224 2949 2648 1766 116 942 2646 472 184 2700 1916 1777 2372 2959 149 163 2893 1787 2674 1493 1205 2569 164 2017 136 670 384 1977 2192 599 1960 2195 820 1661 722 114 1341 537 1471 2658 1602 1398 2 1312 760 2073 2596 799 244 740 2937 2152 728 185 1134 93 190 1153 756 390 1747 1342 2196 1746 2842 1448 2273 1346 2455 1916 1910 1911 1308 153 2586 824 1152 2927 2022 1956 1679 2626 1934 2717 747 2181 1814 2630 949 418 977 4 2707 1180 683 417 2326 261 2705 1229 1166 2688 1181 1385 487 96 1117 1713 681 1707 1235 263 1164 920 2745 225 2094 1952 659 1711 918 801 330 747 1825 2807 1145 2695 591 1504 987 2665 1638 275 1563 98 2192 1260 1202 1893 1802 2928 1960 2783 2379 635 2163 1126 1251 589 2478 2077 2380 948 1399 481 1733 2089 1958 1708 1780 1552 2588 2076 2491 1106 580 2259 771 92 2729 671 2672 2286 2508 39 523 2336 2139 615 1613 2041 1040 2953 1986 751 2745 2694 1227 2596 555 781 519 212 2225 2274 1750 2343 2956 2637 1490 412 1069 2128 539 2489 725 241 32 1655 2898 201 2181 723 145 54 448 285 639 1695 1593 960 2818 2633 1784 2137 2548 430 320 1486 2611 2068 1595 1980 2745 2905 1773 1992 2884 1574 1190 600 680 2954 1200 2844 345 850 1469 2608 881 2789 2685 763 2311 2357 1811 90 2446 683 947 1640 1738 1223 2190 2248 689 174 2422 422 2835 92 2790 1378 51 276 921 2158 2695 1816 21 1498 2650 2681 1976 1410 1819 829 2680 1602 1453 1222 1474 2098 2107 2161 847 588 156 973 46 467 945 1953 1882 840 499 702 2667 2335 2437 2692 1933 2642 2414 714 520 105 2414 1829 1874 590 1485 2219 1983 2206 1114 837 558 936 2345 2113 2465 1314 754 2497 374 2911 400 501 2831 1887 1658 904 205 1327 617 1696 2947 2613 1682 2844 2066 2615 152 342 1012 191 852 2931 2397 2144 2680 939 2369 2155 535 865 2506 2140 428 363 2062 151 2241 927 2708 1945 2871 1927 2077 1782 2033 1900 331 898 2544 2371 712 1704 2073 1928 209 1261 898 2423 2793 2540 1078 1294 814 1234 1919 797 1838 2742 1583 1170 118 2303 475 1184 1027 1901 185 1072 1240 1239 2737 925 488 2565 2178 102 2872 2824 2382 1643 2303 401 450 2022 2692 2609 1715 2126 1888 171 693 1036 2704 820 62 2391 833 416 2226 1655 2778 1161 2562 1884 2640 1634 572 146 344 1918 1785 846 2662 2785 120 1583 602 159 2328 2438 1630 2388 478 2027 1313 1520 243 2748 2599 504 300 1153 1030 2418 1644 1285 2124 2141 2959 1221 1871 679 1486 2542 1037 1792 2303 478 2412 2316 1829 1214 1666 1038 1209 1472 2598 36 2295 2260 900 1192 374 966 1 2681 2082 1245 122 2329 1703 236 1353 1566 2925 2314 150 2464 535 2842 2607 1339 1899 1834 972 1147 2381 376 1929 1408 1886 1687 1372 1633 2599 1613 991 988 2298 2313 2563 1134 687 529 386 2050 2930 1774 183 1851 1861 2609 2038 1401 1460 2596 899 2173 1914 1463 651 2613 1835 2737 2366 1136 1466 590 309 1083 1717 854 55 2068 190 584 1642 941 2876 1647 1767 1383 2649 2916 2391 449 82 1432 2435 1109 1605 2683 1774 1841 2876 2887 278 130 2467 99 505 763 1951 1974 988 1795 2695 937 2960 1079 774 2515 707 2739 2162 965 724 777 1325 2645 2045 213 783 2669 1934 936 259 1577 814 1450 2471 1202 1538 286 1041 1475 896 1922 1749 1473 966 728 857 2172 2674 2569 2796 1590 2693 2065 1489 2883 2315 1230 2047 1151 117 2402 2578 2092 970 2466 1872 1925 350 2642 2933 1289 2802 1465 1241 1401 1890 2536 13 142 1775 2770 2967 251 1757 2444 1590 1701 2288 924 2533 664 230 1250 2548 359 994 71 1397 1587 2766 1338 2162 2420 2855 2950 661 2466 1998 2870 821 1053 629 8 1414 2626 628 2439 2551 1382 2913 197 1494 133 2028 688 382 2155 2609 2003 2348 1629 2382 497 1530 314 1647 243 532 838 2219 328 1440 712 467 2165 561 233 493 2439 759 2072 2552 2170 2007 1381 2251 1161 1396 2745 763 1529 1984 1751 542 1804 2080 584 1501 2677 479 1048 478 2744 1298 1272 2033 214 716 862 2457 207 275 2415 2531 1211 2844 2518 2563 1696 2404 2232 2661 2861 2228 112 260 1348 2122 865 663 1202 1861 439 2656 2327 1424 1842 2515 1204 840 1613 1185 1221 1996 613 511 2057 2518 2724 2969 2497 1524 99 1 2831 1215 1245 1236 1118 1910 2057 1054 2887 187 605 1626 2681 1522 1573 2362 2022 568 434 351 2285 904 2842 2442 2798 2090 2482 2390 1743 699 1266 49 1900 2683 92 501 1507 1895 941 788 405 462 2687 546 2881 2231 1926 2402 2234 2689 699 1732 2751 133 1794 1027 1231 843 1273 772 2126 394 1528 998 176 861 152 1348 564 1091 522 386 258 518 1993 281 1795 29 210 1394 379 1771 925 2841 1680 169 2377 1105 126 1425 2060 2565 1164 2644 729 2341 839 627 2509 421 908 811 1521 1376 400 2240 2304 1215 911 2940 2600 1261 1262 2520 884 2609 2357 938 2771 1249 2685 664 907 1123 2805 588 2237 180 1759 2091 1761 2171 2752 2687 1643 1239 1213 1939 2603 1922 946 1472 357 1907 1787 2747 1139 1836 2930 216 199 1965 1033 819 2044 1721 1329 984 2095 92 1317 532 601 2423 2786 1326 2831 488 777 260 1914 327 618 1702 1161 202 2263 1362 2945 856 1768 1980 1562 2380 2650 2556 1961 238 137 2697 2693 2925 1337 711 1086 2086 977 2268 916 1819 876 1773 869 2248 2315 2840 1738 1551 241 2360 1900 520 760 1049 754 1963 2913 2329 267 944 1857 2869 2854 994 2440 1052 1434 2536 497 632 2207 1387 2506 821 530 577 337 2494 2127 2772 2817 849 292 2858 1549 1008 2537 1258 1996 1627 1203 214 787 1598 2160 149 1180 780 1424 745 1662 2237 1098 2816 1970 258 760 1160 561 274 2652 2856 2383 794 289 1206 993 2771 568 1882 1369 2146 4 993 1405 2783 209 1503 2124 460 27 956 138 1973 2540 1 2755 559 1089 2961 809 157 1371 2664 1940 412 943 232 2957 2062 1901 985 1725 2663 2779 1336 1656 2626 2170 1163 502 2851 2606 469 1094 300 2611 2320 2500 0 1039 1377 645 802 1790 2512 1179 1992 1189 2333 2168 271 665 2944 2139 813 1675 1200 2508 220 2582 1328 2832 84 2388 98 717 94 2265 1789 940 1052 1460 875 615 1698 919 170 2249 1470 92 2907 2560 2407 1534 92 924 2711 2134 1882 2618 2498 176 2150 2137 1032 4 2638 941 956 1986 2539 2222 1802 162 1019 2847 920 1005 1814 1118 2744 1075 2941 985 2924 1969 284 2689 736 196 1713 2529 2729 837 2682 2109 1430 1909 2624 1707 2190 12 487 1806 2712 2455 1418 2284 1216 2658 2502 2816 1115 209 12 630 864 143 1956 869 925 1109 2068 620 2542 127 764 752 1088 804 2526 1604 1213 2131 1978 91 1374 232 2314 1718 1422 1135 1718 1866 2208 272 2378 1218 2689 1080 1228 741 114 2232 2401 2639 2335 213 2402 1718 813 2316 1485 985 1869 1535 929 1436 2550 2869 117 1424 1267 2028 2198 986 968 2020 409 51 1657 2556 361 2151 2810 880 2871 2133 2431 1336 14 310 1356 2614 2725 2874 94 2922 398 1223 1564 881 1009 629 953 2540 2315 457 1622 1453 1841 31 414 492 318 1821 2954 1418 1118 2850 2484 1296 969 1768 2505 357 2091 445 2789 2938 1054 1187 2687 1647 5 2386 2474 2080 1903 998 1298 752 1562 196 495 898 2638 555 1280 441 513 811 2751 2283 2515 1895 1329 2453 816 1106 725 2496 2404 367 1938 318 1962 701 1080 558 888 1375 2905 1485 1570 1249 2221 2531 932 1575 1058 2681 1204 216 68 2002 2632 1529 1882 2092 2597 2664 530 349 444 2528 1615 765 2670 634 708 1446 322 2953 915 213 982 39 1421 676 654 5 1144 2134 2940 897 159 1388 218 1044 1495 1238 459 126 969 2948 1083 1023 1666 1596 50 2395 1596 1646 424 2458 2168 31 548 2870 662 214 2162 1962 2368 1743 1786 1455 1588 813 849 2197 1825 2478 1908 1509 1376 1934 846 2594 242 310 1102 1776 2164 1433 237 1351 595 1584 297 1714 301 1112 256 2179 782 2050 2798 1906 2135 2427 2495 2050 1083 515 1600 2625 2472 2287 341 952 73 1893 2394 1879 2557 360 2944 2363 140 2271 599 2848 1004 1902 1298 1461 2705 1737 1658 1888 2171 1667 2484 1232 519 1380 2059 550 1414 417 810 245 2184 2383 1019 2741 810 233 2554 421 883 1377 1990 1909 1822 608 1835 2269 1598 22 2035 459 1370 627 1124 375 1179 2664 2436 2332 1336 2134 32 71 710 1916 1511 218 1424 1305 430 929 1361 2754 2785 1131 2509 1756 1238 1744 2857 1700 1450 351 1361 17 1710 2078 455 1231 2276 2631 1784 2053 1829 2712 1337 310 2316 2697 463 258 2325 2237 2173 2082 1667 1098 2516 809 1453 1496 85 1084 2015 361 947 1043 2682 651 1515 666 2225 550 1822 1847 1586 1384 1684 320 1276 1365 1489 712 884 981 962 2222 2225 2931 330 2160 772 2914 2467 261 369 17 2005 442 159 1943 336 672 1900 448 167 1296 2458 2210 2018 1314 1819 1864 1426 2204 1153 2724 650 2905 2670 1692 1678 187 1625 87 279 1345 655 2313 820 810 396 1179 405 2262 490 1580 2333 969 2375 1397 557 1560 1515 223 1011 2345 605 967 2959 1683 2804 7 2239 1540 2897 2473 285 2294 2341 2797 660 2290 856 1835 1364 1640 755 772 2672 582 2716 749\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 148,
        "task_id": 559,
        "test_case_id": 37,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "1667\n1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1\n",
        "output": "1 1563 15 180 1433 219 651 1380 1213 472 92 514 523 1181 1230 469 947 808 388 204 741 1492 1555 693 1162 996 690 203 1224 179 1459 1383 1610 754 1020 1051 799 666 144 615 871 524 1120 291 1283 708 814 492 1636 916 1000 81 1206 1080 1461 1329 1355 928 70 1269 348 486 1484 418 443 1132 459 284 1046 276 1442 506 1276 784 1295 579 1449 46 1048 300 58 951 1412 865 725 1069 370 1460 1032 725 1144 1242 979 435 1305 496 595 1441 158 338 1027 1272 1378 1543 560 1257 466 812 765 998 1038 74 748 617 324 1041 1556 912 752 946 253 1592 398 823 1513 401 1629 1495 812 1565 1402 1214 696 193 238 225 1290 352 860 898 324 1507 382 686 905 678 41 86 1407 1442 183 578 857 774 1151 1592 1589 185 1355 151 874 1056 149 760 1350 1638 383 1579 673 468 842 1302 258 550 1318 810 1652 1095 518 486 226 640 579 64 804 1447 755 950 1337 679 1168 922 405 1523 655 1488 1521 319 788 431 229 1366 738 665 757 722 814 936 349 1422 588 367 177 1322 89 1034 35 1395 1129 686 1581 960 649 426 1503 1182 1355 846 56 920 17 41 107 861 1386 1307 587 1402 1621 206 317 713 233 472 1429 272 84 1366 30 1449 244 748 1299 1554 596 838 1504 1238 553 873 1162 644 544 75 263 386 175 56 1284 69 1628 1172 1514 732 681 1403 905 1037 1324 1171 928 1422 580 74 458 625 1474 696 1011 497 1217 285 469 811 1214 977 841 1463 1213 1359 996 127 197 1140 137 217 945 1337 1377 219 51 667 1134 1224 1056 475 1339 138 503 265 249 1289 630 604 600 1587 592 633 422 787 685 1150 70 1243 1603 687 1619 269 1546 377 1529 131 1517 795 186 594 323 52 1330 1241 646 204 420 952 1327 1575 1619 993 956 28 1524 88 1562 1302 1448 509 374 1019 1209 1313 783 1463 1353 541 1556 878 313 522 948 1262 1067 1280 165 813 164 1654 658 342 673 739 122 687 702 748 1658 75 73 1266 156 756 867 1082 842 1320 485 81 742 1034 54 1463 577 1262 308 1501 1559 865 57 254 106 253 402 294 1274 1334 1124 1574 1387 134 1064 1587 396 1242 271 1185 1500 106 1568 1620 1516 956 1614 959 224 1306 1387 1031 1141 144 501 1247 604 368 960 198 1570 246 667 1084 1570 1110 143 147 1067 399 44 73 409 1218 147 1313 1600 1658 903 443 411 147 1172 35 29 786 1023 78 539 1416 1605 618 750 1076 441 1083 33 1347 1077 1494 235 1665 935 446 52 1649 231 1449 960 1230 1304 786 1136 1177 1139 1534 1098 1129 1236 583 1070 1268 261 1417 35 1167 1361 1259 708 619 582 184 161 1556 1496 465 775 1012 719 747 1638 810 1057 954 1597 129 331 471 766 300 1338 1315 1068 632 533 1051 415 1427 458 1152 23 1392 1137 643 874 511 70 362 1033 1237 1658 175 1567 1512 669 648 1382 735 686 368 389 1628 910 678 313 1420 760 1618 23 623 1024 127 1532 948 1578 235 1291 468 445 1045 815 417 567 701 1253 197 189 449 1398 388 979 341 175 142 989 1325 866 1431 1217 1442 385 1438 1626 908 1646 1164 1660 675 1530 547 1268 1346 558 1041 162 876 1167 1491 255 988 553 182 1261 723 1496 176 1412 700 731 1301 457 129 240 959 27 153 1546 1580 1173 1037 1397 1175 1004 832 372 32 17 463 915 636 1148 336 27 800 45 410 1372 513 474 906 1355 844 1438 93 1503 179 646 1610 1024 327 842 1459 1252 52 338 673 520 1061 1572 1192 160 882 1007 1329 1003 1345 791 69 538 1099 1266 1117 1144 373 1089 1333 635 1003 67 1124 1189 467 1300 816 820 107 813 1661 1464 554 481 1504 729 1159 1323 174 607 675 1571 832 1091 781 317 387 999 40 944 1553 529 69 11 1126 1578 309 188 177 57 44 290 1183 1157 1602 641 1058 411 1383 1575 1479 1439 1185 1103 1178 1266 1576 644 1432 422 612 1519 528 178 1394 252 1232 882 1397 1582 951 1235 826 1006 755 1504 1021 1376 55 1395 1127 728 887 153 1093 1578 554 760 1538 44 196 530 526 191 343 919 910 782 467 157 338 897 1449 122 188 918 1286 1330 53 525 307 1444 532 513 131 1337 196 1079 6 165 1124 661 4 250 1280 1256 398 97 1163 1624 166 910 586 1461 1453 344 1514 717 540 1184 263 396 433 578 1154 141 1436 1306 382 1125 131 1327 1401 95 1626 746 329 89 1303 515 1006 1007 1437 140 995 144 1323 305 1073 139 1563 1595 660 99 1288 1026 204 1204 243 328 1598 821 1287 257 1585 1398 429 1601 894 1248 1081 998 50 706 361 281 814 838 1258 608 1200 390 892 1550 1381 1603 111 1594 1577 761 1101 959 220 1071 970 997 865 1489 201 180 639 1499 612 339 999 324 1078 1004 3 167 1290 765 168 1436 269 437 1243 1026 651 1620 798 735 1492 498 1494 903 193 1412 1106 1632 593 1498 892 814 697 1593 740 1243 1656 1122 1601 1306 62 990 1229 1660 586 635 307 1214 1006 1401 485 841 970 812 957 1163 280 441 1397 1568 146 80 1434 1613 39 1041 15 134 633 1131 332 1196 391 1313 1302 995 715 101 1635 1632 351 245 119 1544 445 1297 188 1397 178 732 1311 1555 772 1149 80 1188 258 1567 390 360 451 1319 1154 1135 1505 987 1383 224 939 1231 21 1284 208 36 1215 629 1153 835 418 1469 303 37 731 85 1323 328 1184 580 262 1616 123 18 1639 1222 112 728 1396 335 1359 7 451 870 426 220 806 673 1016 1479 1613 370 1253 1568 443 557 1632 600 1227 655 505 897 240 184 1049 460 1224 1267 330 1569 917 894 429 1492 17 1526 807 583 1570 465 1396 442 241 1054 1292 261 905 1572 725 793 999 1456 1076 1240 109 249 828 1502 1626 314 1662 1292 1069 1373 660 884 805 1460 1098 1132 1172 780 1398 341 387 508 135 1414 680 1645 466 377 955 452 413 1030 1461 704 915 1664 678 944 791 639 772 741 18 530 869 796 786 1628 180 1541 974 393 72 1441 1416 1480 1094 1269 1604 817 1584 1065 619 3 335 158 502 736 1077 1536 1128 1570 1152 1289 207 422 1081 1449 918 1017 1143 1094 923 1052 1224 1525 612 697 827 1464 1093 410 1609 403 235 1165 369 685 793 731 623 717 23 805 720 1516 1305 1 431 790 1184 468 1467 484 136 1577 391 918 1060 679 119 372 1148 1532 364 173 1526 691 685 1584 558 163 921 709 1654 747 1485 1169 1014 1435 39 626 1099 297 107 1284 337 257 991 1173 1464 734 1400 1389 96 938 322 235 1075 1438 1077 118 405 200 1283 933 348 785 746 1095 533 1489 156 214 1379 681 1082 766 287 72 1390 56 1650 1520 882 87 1179 198 721 1414 6 322 1662 73 302 929 219 597 846 503 945 800 332 742 29 1611 329 746 163 561 356 901 1571 16 939 1413 727 237 1080 1319 358 758 1147 403 584 560 104 1236 1382 831 1570 1449 1629 1282 1047 930 1196 1601 1387 967 661 1482 1317 260 518 363 463 822 723 507 584 231 928 1660 1249 707 1363 1545 1634 815 371 1255 1524 712 104 937 1115 640 831 642 836 232 1158 1602 679 1101 867 124 722 550 1664 1336 1377 1452 522 316 854 707 152 1176 192 1101 1007 88 244 128 1076 1043 707 1546 1664 115 215 131 1496 1211 881 802 921 1191 1058 1422 505 772 20 1468 744 1595 1295 1208 720 471 466 577 1549 1203 71 1101 258 422 874 1439 167 1585 77 299 193 579 1542 21 1176 468 1044 841 429 1446 188 516 961 851 1647 264 507 802 1343 654 1025 1186 1453 1332 1168 1436 50 281 926 359 669 1309 333 1022 709 237 1239 376 877 551 745 1109 15 1125 795 300 1089 1378 920 432 1642 95 217 1282 309 907 343 727 1051 1509 27 190 478 1577 1558 683 201 1181 1420 94 390 249 800 1588 930 350 446 1387 894 1447 777 1274 849 509 597 1479 449 716 1516 1395 1643 940 113 1492 1007 999 1024 1267 730 24 380 1572 941 63 119 668 510 121 949 1077 1615 1215 868 72 1057 187 674 222 1360 172 300 1188 924 58 1589 435 600 842 50 921 496 1091 1217 505 65 85 1064 1470 862 216 351 896 1209 456 1592 648 556 427 1262 0 829 1071 432 159 1517 433 84 1525 1076 879 790 852 91 1452 1311 1043 1402 351 1141 933 1482 242 1644 1583 1079 815 1010 44 69 1379 936 124 415 367 22 506 1052 1391 1615 535 513 323 1606 1603 491 107 86 437 1500 1307 1343 1107 1284 926 1047 408\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 149,
        "task_id": 559,
        "test_case_id": 38,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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        "output": "0 2026 289 71 2174 1528 535 1676 710 852 1541 991 2051 1351 1782 1331 1101 1160 284 382 1723 1901 1046 1014 1800 340 2215 568 851 363 1952 2204 1587 1503 575 1742 816 869 693 1381 1447 1526 883 164 1510 244 216 107 1866 578 173 501 914 575 432 287 1988 1761 1397 1352 1312 2234 624 883 1001 772 510 855 1630 600 1394 147 1637 749 2155 2042 811 520 685 693 1723 1301 301 70 1555 887 75 2247 914 991 315 122 528 918 484 1896 1434 1739 404 1518 1663 430 1831 1610 1512 2211 875 934 602 2212 1290 458 939 890 846 1917 478 696 798 1468 2029 881 1974 1106 1885 1520 283 1963 845 570 554 1866 233 1070 1776 440 1062 1892 519 1951 291 121 741 838 741 144 662 1101 1840 1846 1750 170 136 2057 1506 2092 359 1286 560 1849 1164 2120 436 1247 816 1699 2022 1666 824 813 421 641 2030 1009 1291 1004 981 325 441 1473 147 2169 512 2067 1320 476 1032 1444 8 1800 272 355 114 1213 1230 2228 1420 1939 907 1856 1693 535 1304 1210 2165 2168 513 2150 1051 1294 1105 910 2212 1471 725 273 1779 298 555 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1070 1370 1138 1254 2027 121 1056 989 946 1797 1949 286 1251 2144 543 282 618 1836 269 1033 2123 982 1431 906 2005 764 57 1932 1603 1198 1681 477 1863 409 58 1684 224 369 314 1380 553 568 1767 36 1926 869 1562 1962 1432 727 1078 1828 385 852 1111 1866 1669 615 1361 550 2174 1959 1677 1123 359 1977 2170 862 289 2095 22 1889 1736 1461 1689 1506 722 1974 1217 2109 898 1073 1036 515 1299 1849 2198 71 1752 1797 25 1114 1116 746 690 1988 974 154 1136 37 1019 1970 1467 2125 909 1573 602 465 2205 2141 1568 1146 1025 334 680 622 1786 76 1256 1041 2017 1840 527 155 882 290 1281 996 439 1304 665 1 667 1239 999 66 1721 395 750 912 1702 840 1890 1548 575 1152 380 1795 524 1729 804 219 781 818 1067 754 391 536 928 1283 556 1823 546 412 552 1121 212 1441 1371 282 1502 1496 1592 1912 972 86 1061 525 1038 1883 2031 226 1220 1912 1483 1591 487 1979 291 867 518 530 1477 199 2214 1150 1013 639 1008 0 812 681 511 1002 577 2208 138 1775 1088 25 1236 2176 646 1740 1440 273 1189 280 1583 2020 1088 391 1238 1127 139 1845 857 1691 336 60 289 203 931 1318 1688 1636 52 1030 1409 1861 370 1890 1347 1436 1974 1153 1726 62 53 41 94 913 2090\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 150,
        "task_id": 559,
        "test_case_id": 39,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "61\n1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1\n",
        "output": "1 19 33 0 3 35 28 13 53 34 8 0 4 47 9 27 6 26 5 51 30 16 2 7 55 16 8 19 56 59 1 38 11 50 21 54 14 35 39 18 23 27 53 53 45 44 16 60 47 57 55 2 33 40 30 19 30 44 58 5 17\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 151,
        "task_id": 559,
        "test_case_id": 40,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "2003\n0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0\n",
        "output": "0 366 1322 58 1630 819 584 747 1479 145 477 1559 645 1229 16 1192 62 1851 1834 1139 170 1627 1270 590 1490 1541 1841 1771 97 1413 277 1 1949 861 1508 1930 1859 1189 693 586 645 1457 218 973 1861 642 1493 301 1983 879 775 330 1991 1558 434 56 1178 1978 1637 431 905 662 1133 1052 1424 613 1891 1752 1585 255 957 952 354 612 1614 989 545 1630 900 244 612 1835 1658 116 1054 690 1242 1114 29 1201 779 606 1268 558 755 892 626 719 839 1657 544 1151 411 1777 621 49 1383 1030 79 1244 913 1353 1876 832 1214 1660 702 982 1218 1606 158 1570 104 84 1954 1856 308 1994 814 1278 1304 1352 220 1447 1715 720 793 1466 2000 250 1731 1499 1869 1264 1716 1870 548 1859 1941 1073 71 1545 1773 1485 18 698 720 199 425 1846 575 1367 539 418 1703 1825 1057 92 17 1535 640 902 1320 1499 208 1404 23 686 1759 543 1425 1175 644 1915 791 582 1220 448 1894 458 887 14 56 845 1474 717 334 439 963 1972 110 1535 1895 498 1501 848 1825 1550 1266 274 376 1814 1066 1002 1441 1350 258 171 538 902 153 57 681 203 465 1189 362 308 226 1343 1099 1518 586 92 1305 672 1048 999 1151 351 1039 1162 1536 1672 1709 767 619 507 1981 82 793 173 416 1440 1480 911 763 1226 1527 240 581 690 571 1220 1788 339 1774 177 356 715 46 1009 1777 755 1248 195 1691 1695 502 1888 676 1188 1317 1754 1809 256 322 82 907 1929 150 1716 584 835 462 46 841 184 1042 1382 60 431 839 873 620 86 1672 762 1786 1665 1893 1607 395 1795 1928 1504 1621 1330 1956 256 631 431 1456 1330 1773 1711 164 1629 197 1671 262 858 528 1717 278 711 646 1100 1555 1187 347 946 719 1710 493 121 1280 907 241 1593 1892 1569 1137 1875 1788 1248 1320 1059 1996 1335 394 333 927 1166 588 1708 856 1528 1989 85 1698 1019 683 1451 30 1117 592 489 1526 971 318 1984 1816 320 1747 1195 149 543 1000 338 1134 1867 1648 449 875 56 196 1383 426 1454 266 1863 392 1479 679 861 1820 1239 890 527 1395 1010 14 1777 1034 1969 101 123 869 694 413 1601 704 429 705 1893 672 994 0 1561 1803 1458 304 1683 363 206 1013 551 1986 1439 19 104 711 1972 1999 1859 1274 1361 1274 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1297 561 1099 1647 419 1145 540 756 261 1492 1595 976 920 1824 1629 1824 1446 1867 1702 1632 1993 1553 153 1771 1597 1202 1562 172 1872 1005 1031 1245 808 994 266 1855 1613 446 98 617 278 1614 835 1106 826 891 1356 1558 904 216 1186 989 1127 1117 201 505 407 731 3 1704 876 1435 1423 1804 56 1661 570 1900 1037 729 375 605 1450 502 1925 308 321 1633 60 1177 1161 1440 159 1709 1123 1267 1034 354 202 776 1282 600 104 1582 1322 516 1615 117 799 1673 1981 255 43 1527 1789 470 118 527 65 338 1763 335 1930 338 403 520 1746 433 1412 1620 1631 969 1913 779 1994 605 482 1824 159 1270 633 624 1863 806 403 636 575 270 1356 1157 1147 107 952 253 1371 570 1540 270 1769 1404 994 1014 751 891 1840 1118 239 1595 69 327 419 1918 1166 324 747 762 1046 1992 419 976 1112 1866 1006 1221 1725 1613 361 1863 1404 97 843 318 936 1318 1261 1899 1675 194 1087 1608 472 656 158 495 355 601 727 318 158 79 506 959 1565 1741 1776 856 241 1120 1570 627 1400 1837 1125 524 336 1197 833 1433 1051 357 1618 1728 622 456 945 794 1284 1945 1162 249 1715 865 1190 1210 1073 492 406 451 1847 397 1256 1752 1117 1852 1453 1150 1190 1240 1719 214 1575 1288 1328 1999 1129 715 312 172 203 787 73 437 1726 1043 1190 85 1649 766 29 1875 1884 228 816 1818 284 1756 950 123 761 792 187 272 1140 654 1210 1323 342 1243 1412 1453 1093 326 1397 692 1142 583 876 884 1323 1189 597 1500 1168 127 1277 1416 50 1352 1070 1071 1030 567 659 1099 962 187 612 195 678 9 355 257 5 420 100 120 1724 279 305 335 16 559 1519 1536 85 48 1707 750 1688 302 869 994 1085 136 1849 268 204 866 1014 1947 1750 1120 1168 1228 485 311 1964 871 582 1727 1960 1882 920 71 1481 1759 1140 1667 1247 1612 232 1271 477 1114 1959 1013 1126 330 1024 1585 754 462 1749 1912 1210 1946 4 1979 80 1934 657 85 1658 1960 1418 1948 14 1668 742 60 1331 954 219 430 688 1081 1083 951 336 1430 145 1510 753 588 967 243 1408 292 1682 725 1323 918 171 1683 1096 2001 1907 597 56 1234 724 1634 80 736 1112 161 531 1320 74 1579 151 1347 866 678 1388 1434 307 1516 1014 1724 1550 1141 1993 203 65 695 1033 448 955 389 1824 319 401 531 1033 618 1558 1109 1803 1464 225 260 132 1374 1774 578 1430 1808 679 1767 17 750 1680 546 516 1635 1316 253 1826 660 814 1252 65 1278 1364 1288 738 1621 1116 778 1689 1432 1475 1836 198 1461 691 1234 257 369 1888 1709 610 471 607 36 1183 955 1782 1393 496 1411 258 451 792 429 237 274 372 1068 965 1275 1094 1061 1926 1882 218 1608 534 1286 128 108 909 1387 1613 1665 1133 549 877 620 20 1451 1449 1387 402 346 496 28 1406 456 1128 478 372 1053 1371 1415 1144 1792 1301 217 903 162 905 1365 864 961 1836 48 1195 1964 1346 235 352 1669 1285 1460 1328 1518 963 616 1843 444 824 1113 1391 1811 1839 898 1614 1827 1489 579 904 1228 616 424 37 96 607 323 933 1477 375 592 1953 1763 475 1317 672 904 370 157 399 1526 1717 256 685 789 1967 1426 58 1225 1359 149 1268 388 95 82 1363 941 1443 1492 1403 567 450 295 1151 1186 68 1741 1711 621 214 923 1988 1758 616 1112 158 1736 1936 3 1203 461 1513 328 1682 1982 225 381 1707 297 306 645 20 1379 906 452 653 408 505 731 476 1354 1370 1763 1288 265 1187 1379 1229 1955 93 1955 1732 436 162 156 1744 27 756 325 130 486 1054 1166 43 1081 19 1618 1662 288 383 1871 1398 1084 396 71 4 1259 36 1552 648 1347 953 252 995 1672 1553 1308 1661 552 1127 840 1058 255 145 437 1152 1540 566 428 1261 1340 238 793 1559 1300 1711 1453 1021 848 1448 1319 1168 202 693 439 1486 1663 1620 1370 765 1342 1769 919 1063 1412 988 540 1520 1928 803 1063 1789 21 628 471 1038 1615 562 1087 1665 693 1194 1167 1670 1675 933 1528 115 1336 148 1793 1754 1522 827 813 1290 1174 479 1355 1646 1246 772 1454 1615 1425 1640 1713 911 1730 395 1288 319 1859 1990 1966 1927 2001 1019 18 1314 351 1599 1470 208 246 633 791 726 1621 559 1891 858 1303 208 6 490 1496 1313 1112 794 200 824 1488 1332 339 591 1250 1242 855 765 1354 1491 941 1256 1588 109 444 1661 1728 888 907 845 282 1851 248 161 1472 957 1524 1719 1334 75 147 1603 1345 1050 1988 112 1764 281 268 1412 1868 931 1836 135 341 1024 679 133 528 718 1513 779 1199 1359 1204 149 554 1051 775 1007 1341 940 1094 634 203 877 1071 1275 1733 1420 1347 1113 1141 193 985 1639 187 1479 512 1171 247 1351 1113 939 1713 119 905 1136 82 1225 728 1397 160 1187 410 1239 1536 428 918 363 1119 200 1824 43 1595 1103 1637 269 611 1681 669 1597 34 1019 1811 1019 1952 1493 491 137 636 624 1240 985 991 1926 943 1793 585 229 1004 1089 1254 640 1780 1206 49 37 1113 471 1787 140 1942 1709 383 890 177 1796 1894 937 1091 185 1894 243 1367 103 605 1458 231 626 892 316 1846 1733 1300 495 1708 1088 1465 1473 1822 1813 1933 1624 198 730 1313 1749 322 696 1342 1971 307 91 1582 42 428 928 128 277 1625 1266 408 1102 1605 58 999 206 1419 1968 1147 702 1359 1634 1665 433 611 57 990 123 18 370 316 35 1263 334 158 1129 1233 683 371 1711 552 622 1369 362 116 1073 193 401 1935 841 1002 584 1045 536 970 1574 565 1193 878 1579 581 1938 942 1003 1967 1890 79 761 1354 1215 127 1455 1684 1462 1057 974 944 893 1837 1237 426 264 1766 1904 1714 1187 1873 853 1653 188 1349 1122 1759 1246 1501 615 678 1019 586 451 784 15 970 1883 1997 1760 1420 1121 1902 1359 520 192 20 1223 974 1908 715 486 1987 541 1148 1619 1110 1541 507 191 989 804 1358 1316 1494 889 1446 855 1415 814 1290 882 1522 1127 1404 1519 826 759 42 488 1486 1073 1924 536 1962 359 758 69 15 1247 684 670 519 902 1858 795 683 1536 356 1750 809 1253 1778 411 720 773 23 1478 375 1026 57 1624 543 921 1139 1033 539 454 1787 566 438 317 157 631 1912 1777 990 600 1836 1731 1654 454 843 1203 864 503 1988 1884 36 218 447 512 673 167 1744 552 506 749 520 1300 112 1531 1795 1341 131 882 1700 16 942 599 1240 455 1849 1083 1816 171 1306 236 319 867 825 745 1640 635 1698 1860 727 841 1067 778 1918 189 1218 288 231 36 880 766 1555 1748 1808 74 993 1961 966 1341 1787 1687 852 1621 1087 654 544 8 1053 1929 968 1087 1781 1356 1340 324 1772 1272 646 1132 1382 1758 848 1125 345 337 699 1911 1515 1650 528 1347 1080 1838 1278 22 1573 926 1077 1860 1099 303 1359\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 152,
        "task_id": 559,
        "test_case_id": 41,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "241\n1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1\n",
        "output": "1 117 14 72 26 114 74 73 183 208 117 121 52 4 214 68 19 8 52 119 161 184 214 96 195 165 208 132 153 199 137 73 135 17 7 139 215 33 41 44 191 166 176 187 124 237 33 151 194 21 204 73 84 6 33 41 79 148 23 56 17 41 150 121 105 166 103 201 50 128 141 23 60 113 194 212 218 99 197 200 73 107 96 67 83 33 1 27 168 107 19 206 63 36 225 203 176 141 76 156 5 189 53 178 129 111 210 108 172 46 134 118 233 203 107 35 72 23 41 186 10 196 187 107 184 15 134 166 160 142 87 40 114 143 133 104 51 14 88 13 201 181 72 179 153 61 145 191 173 195 138 72 128 156 105 61 200 54 93 178 159 197 108 91 198 65 42 117 41 226 10 165 237 204 145 222 112 91 152 53 228 103 165 130 126 50 141 93 210 93 140 140 170 83 103 90 142 67 171 198 43 207 238 105 105 127 98 190 122 207 196 94 113 26 100 217 186 44 97 29 123 225 135 232 72 61 125 63 230 74 123 203 112 82 2 54 84 189 222 147 90\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 153,
        "task_id": 559,
        "test_case_id": 42,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
        "input": "1109\n0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0\n",
        "output": "0 429 532 710 77 16 402 285 286 374 665 696 812 229 605 652 983 112 198 139 740 836 437 1010 1079 341 939 263 319 594 719 537 101 923 808 538 1047 482 163 844 1033 104 569 983 761 648 215 883 96 941 862 862 788 836 558 991 579 383 586 15 85 260 912 316 315 462 646 675 535 474 459 453 503 1046 860 530 697 627 533 943 803 696 390 431 36 435 322 70 928 391 536 412 1091 1050 688 33 634 222 893 448 316 1103 874 628 830 1033 663 522 470 180 356 987 416 399 427 141 615 895 899 576 622 359 374 537 777 788 475 838 832 71 221 225 354 1084 617 992 958 1023 844 993 1088 233 329 423 128 491 86 955 633 539 484 544 1079 15 740 926 1097 974 87 586 170 482 686 206 960 1102 868 896 374 575 90 619 592 529 935 422 57 1078 952 5 875 287 160 857 299 419 442 419 932 495 984 642 194 750 877 442 1001 873 882 71 94 277 332 37 457 699 995 1054 833 1042 104 1045 535 678 309 62 992 203 434 475 153 1049 995 3 741 617 672 377 756 350 954 146 932 414 645 91 593 219 1014 1011 782 698 356 1005 996 338 922 519 996 142 961 826 637 668 70 432 330 599 920 624 861 1093 864 970 541 689 739 1016 795 237 134 338 621 112 43 345 147 1089 969 970 817 541 394 378 207 818 649 653 342 194 892 95 1085 479 841 871 406 158 1027 225 272 877 438 636 258 549 1062 592 613 423 193 974 832 366 321 366 755 878 151 621 534 995 196 322 562 150 639 1062 573 637 349 1101 831 352 545 283 523 1041 676 28 629 119 1081 827 1021 682 476 6 946 503 65 622 598 494 245 193 639 997 479 499 547 918 964 608 606 582 72 470 894 600 893 24 421 460 293 756 647 181 1033 750 157 941 703 859 780 770 681 813 870 962 591 559 456 886 795 218 1104 228 1026 18 921 469 280 534 130 273 932 1042 29 1021 1000 126 878 385 760 264 75 145 370 1064 94 824 480 807 624 1036 682 1017 136 947 71 26 508 125 1082 719 716 674 926 671 542 38 940 156 117 75 155 667 86 83 45 888 819 897 58 944 934 199 423 718 816 884 686 806 35 216 626 1060 560 651 468 784 428 346 1057 897 418 1031 141 1031 330 619 412 1071 295 834 184 32 803 830 726 541 64 719 440 212 498 772 888 385 322 1096 419 736 471 430 606 428 624 958 346 88 192 173 827 277 1097 530 968 503 90 337 545 333 785 868 747 1082 753 88 1094 395 910 1009 305 984 606 529 747 26 433 358 628 658 979 420 224 352 192 415 945 1023 35 427 9 495 555 867 658 224 82 907 609 875 670 28 113 1081 168 454 332 596 1031 226 186 891 1078 963 420 393 733 747 857 375 515 514 1097 681 912 475 666 619 583 482 876 53 2 671 294 149 477 589 287 32 908 1106 883 721 947 614 470 162 851 367 507 134 304 136 305 1092 473 111 785 584 789 807 639 367 595 539 428 463 696 492 771 1076 728 383 298 798 452 1044 504 4 242 1050 188 513 451 984 1039 908 174 115 382 346 678 553 318 262 865 245 860 651 826 306 675 533 593 577 33 813 492 415 39 672 825 401 455 911 429 286 981 262 156 319 277 208 97 867 922 942 257 21 418 2 366 416 461 857 38 518 282 1022 114 105 804 42 1071 733 866 257 770 608 527 259 499 477 253 322 942 83 524 936 913 734 4 952 702 707 1045 874 1099 81 401 477 521 841 107 853 425 671 140 342 279 760 732 416 846 908 1087 1025 828 578 1050 902 100 743 201 1108 256 571 889 540 534 995 669 720 941 629 152 656 972 364 1104 54 258 889 724 574 471 251 360 764 50 1048 147 845 267 380 1045 247 1049 341 929 470 35 398 231 447 740 752 410 708 253 150 662 368 449 487 493 221 7 381 64 799 662 1041 96 318 1067 543 1041 101 6 59 548 1072 797 861 183 30 572 685 601 444 581 1062 838 510 636 793 437 234 56 384 26 281 587 995 966 1107 332 922 271 217 768 354 360 1082 511 213 690 212 866 52 689 1093 248 993 895 1102 381 186 124 923 362 985 215 971 418 690 281 677 1024 755 1025 935 82 856 336 499 366 778 492 320 409 1021 827 620 356 633 555 352 47 621 964 842 674 704 631 538 44 819 295 899 876 485 746 826 217 138 845 358 582 194 878 358 321 547 760 786 630 917 452 30 970 8 70 1096 474 1002 231 398 104 108 836 442 626 494 658 1046 890 111 228 826 36 72 1073 329 731 570 401 619 610 856 371 27 360 860 765 3 1008 1074 343 479 768 534 503 361 35 686 572 222 958 375 721 1026 545 592 532 785 975 586 346 963 1009 179 626 329 656 687 581 888 837 902 1099 452 846 635 131 40 423 718 662 381 292 488 225 139 501 376 1056 308 107 654 955 347 665 952 1029 252 58 409 683 1087 937 641 124 314 1036 968 942 935 672 301 842 812 525 884 57 208 478 788 1043 894 72 1080 957 568 193 491 116 898 1011 632 257 118 569 455 31 880 3 270 904 599 479 1082 574 272 354 815 574 202 875 1007 926 832 326 566 57 916 444 438 90 473 912 890 1041 736 598 912 227 47 267 421 447 568 782\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 154,
        "task_id": 559,
        "test_case_id": 43,
        "question": "Given are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n - For each i (0 \\leq i \\leq p-1), b_i is an integer such that 0 \\leq b_i \\leq p-1.\n - For each i (0 \\leq i \\leq p-1), f(i) \\equiv a_i \\pmod p.\n\n-----Constraints-----\n - 2 \\leq p \\leq 2999\n - p is a prime number.\n - 0 \\leq a_i \\leq 1\n\n-----Input-----\nInput is given from Standard Input in the following format:\np\na_0 a_1 \\ldots a_{p-1}\n\n-----Output-----\nPrint b_0, b_1, \\ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.\nIt can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.\n\n-----Sample Input-----\n2\n1 0\n\n-----Sample Output-----\n1 1\n\nf(x) = x + 1 satisfies the conditions, as follows:\n - f(0) = 0 + 1 = 1 \\equiv 1 \\pmod 2\n - f(1) = 1 + 1 = 2 \\equiv 0 \\pmod 2",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\n# k,i -> i^k\\npower = np.ones((P,P),dtype = np.int64)\\nfor k in range(1,P):\\n    power[k] = power[k-1] * np.arange(P,dtype=np.int64) % P\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor i,a in enumerate(A):\\n    if a == 1:\\n        f[0] += 1\\n        f -= power[:,i][::-1]\\nf %= P\\n\\nf %= P\\nprint((*f))\\n\\n\", \"import numpy as np\\n\\np = int(input())\\naaa = list(map(int, input().split()))\\n\\nbins = [1]\\nfor i in range(1, p):\\n    bins.append(bins[-1] * (p - i) * pow(i, p - 2, p) % p)\\nbins = np.array(bins, dtype=np.int32)\\n\\npows_base = -np.arange(p, dtype=np.int32)\\npows = np.zeros((p, p), dtype=np.int32)\\npows[:, p - 1] = 1\\nfor i in range(p - 2, -1, -1):\\n    pows[:, i] = pows[:, i + 1] * pows_base % p\\n\\ncoefs = np.zeros(p, dtype=np.int32)\\n\\nfor i, a in enumerate(aaa):\\n    if a == 0:\\n        continue\\n\\n    coefs[0] += 1\\n    coefs = (coefs - bins * pows[i]) % p\\n\\nprint((*coefs))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * -i % p\\n    R[-1] = (R[-1] + len(I)) % p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"p = int(input())\\nb_list = [0 for _ in range(p-1)]\\na_list = list(map(int,input().split()))\\ndef frac(n):\\n    if a_list[n] == 1:\\n        t = 1\\n        for j in range(p-1):\\n            b_list[j] -= t\\n            t = (t*n)%p\\nif a_list[0] == 1:\\n    b_list[0] -= 1\\nfor i in range(p-1):\\n    frac(i+1)\\nb_list.reverse()\\nprint(a_list[0],end = ' ')\\nfor j in b_list:\\n    print(j % p,end = ' ')\\n\", \"# -*- coding: utf-8 -*-\\nfrom sys import stdin\\nimport numpy as np\\n# import sys\\n# sys.setrecursionlimit(10**4)\\n# import time\\n\\ndef _li(): return list(map(int, stdin.readline().split()))\\ndef _li_(): return list([int(x)-1 for x in stdin.readline().split()])\\ndef _lf(): return list(map(float, stdin.readline().split()))\\ndef _ls(): return stdin.readline().split()\\ndef _i(): return int(stdin.readline())\\ndef _f(): return float(stdin.readline())\\ndef _s(): return stdin.readline()[:-1]\\n\\n\\np = _i()\\na_list = np.array(_li())\\n\\nfactorial_invs = {0: 1, 1: 1}\\nfor i in range(2, p):\\n    factorial_invs[i] = (factorial_invs[i-1] * pow(i, p-2, p)) % p\\nnp_fact_invs = np.tile(np.array(list(factorial_invs.values()))\\n                       .reshape(1, -1), (p, 1))\\n\\npow_table = np.ones((p, p), dtype=int)\\npow_table[1, :] = np.arange(p)\\nfor i in range(2, p):\\n    pow_table[i] = (pow_table[i-1] * pow_table[1]) % p\\npow_table = pow_table.T\\n\\nfact_pminus1 = pow(factorial_invs[p-1], p-2, p)\\n\\ncoefs = np.zeros(p, dtype=int)\\n# for i, a in enumerate(a_list):\\n#     if a == 1:\\n#         for k in range(1, p):\\n#             coefs[k] = coefs[k] - (-1)**(k % 2) * pow(i, p-1-k, p)\\\\\\n#                     * fact_pminus1\\\\\\n#                     * factorial_invs[k]\\\\\\n#                     * factorial_invs[p-1-k]\\n#             coefs[k] %= p\\n\\ncoefs[0] = a_list[0]\\nsign_array = np.tile(((-1) ** (np.arange(1, p) % 2)).reshape(1, -1), (p, 1))\\ncoefs[1:] = - ((((sign_array[a_list == 1, :]\\n                  * pow_table[a_list == 1, :-1][:, ::-1]\\n                  * fact_pminus1) % p\\n                 * np_fact_invs[a_list == 1, 1:]) % p\\n                * np_fact_invs[a_list == 1, :-1][:, ::-1]\\n                ) % p).sum(axis=0)\\ncoefs %= p\\n\\nprint((*coefs))\\n\", \"import sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10 ** 7)\\n\\nimport numpy as np\\nfrom numpy.fft import rfft, irfft\\nimport itertools\\n\\nP = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfft_len = 6144\\ndef fft_convolve(A,B):\\n    C = irfft(rfft(A,fft_len) * rfft(B,fft_len))\\n    C = (C + .5).astype(np.int64)\\n    C[:P] += C[P:P+P]\\n    return C[:P] % P\\n  \\none = np.array([1], dtype=np.int64)\\narr = [np.array([(-x)%P,1],dtype=np.int64) for x in range(P)]\\nL = [one] + list(itertools.accumulate(arr[:-1],lambda a,b: np.convolve(a,b) % P))\\nR = ([one] + list(itertools.accumulate(arr[1:][::-1],lambda a,b: np.convolve(a,b) % P)))[::-1]\\nX = [fft_convolve(A,B) % P for A,B in zip(L,R)]\\n\\nf = np.zeros(P,dtype=np.int64)\\nfor a,x in zip(A,X):\\n    if a == 1:\\n        f -= x\\n\\nf %= P\\nprint((*f))\\n\", \"def solve():\\n    p = int(input())\\n    *A, = map(int, input().split())\\n\\n    L = p-1\\n    fact = [1]*(L+1)\\n    rfact = [1]*(L+1)\\n    r = 1\\n    for i in range(1, L+1):\\n        fact[i] = r = r * i % p\\n    rfact[L] = r = pow(r, p-2, p)\\n    for i in range(L, 0, -1):\\n        rfact[i-1] = r = r * i % p\\n    V = [(-fact[p-1] * rfact[k] * rfact[p-1-k]) % p for k in range(p)]\\n\\n    B = [-i for i in range(p)]\\n    R = [0]*p\\n    I = [i for i, a in enumerate(A) if a]\\n    C = [a for a in A]\\n\\n    for k in range(p):\\n        r = 0\\n        R[k] = V[k] * sum(C) % p\\n\\n        for i in I:\\n            C[i] = C[i] * B[i] % p\\n    R[-1] += len(I)\\n    for k in range(p):\\n        R[k] %= p\\n    R.reverse()\\n    print(*R)\\nsolve()\", \"import os\\nimport sys\\n\\nimport numpy as np\\n\\nif os.getenv(\\\"LOCAL\\\"):\\n    sys.stdin = open(\\\"_in.txt\\\", \\\"r\\\")\\n\\nsys.setrecursionlimit(10 ** 9)\\nINF = float(\\\"inf\\\")\\nIINF = 10 ** 18\\n\\n\\n# MOD = 10 ** 9 + 7\\n\\n\\n# MOD = 998244353\\n\\n\\ndef get_factorials(max, mod=None):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max!\\n    :param int max:\\n    :param int mod:\\n    :return:\\n    \\\"\\\"\\\"\\n    ret = [1]\\n    n = 1\\n    if mod:\\n        for i in range(1, max + 1):\\n            n *= i\\n            n %= mod\\n            ret.append(n)\\n    else:\\n        for i in range(1, max + 1):\\n            n *= i\\n            ret.append(n)\\n    return ret\\n\\n\\ndef mod_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u9006\\u5143\\u306e\\u30ea\\u30b9\\u30c8 0 \\u304b\\u3089 max \\u307e\\u3067\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    invs = [1] * (max + 1)\\n    for x in range(2, max + 1):\\n        invs[x] = (-(mod // x) * invs[mod % x]) % mod\\n    return invs\\n\\n\\ndef factorial_invs(max, mod):\\n    \\\"\\\"\\\"\\n    \\u968e\\u4e57 0!, 1!, 2!, ..., max! \\u306e\\u9006\\u5143\\n    :param int max:\\n    :param int mod:\\n    \\\"\\\"\\\"\\n    ret = []\\n    r = 1\\n    for inv in mod_invs(max, mod):\\n        r = r * inv % mod\\n        ret.append(r)\\n    return ret\\n\\n\\nclass Combination:\\n    def __init__(self, max, mod):\\n        \\\"\\\"\\\"\\n        :param int max:\\n        :param int mod: 3 \\u4ee5\\u4e0a\\u306e\\u7d20\\u6570\\u3067\\u3042\\u308b\\u3053\\u3068\\n        \\\"\\\"\\\"\\n        self._factorials = get_factorials(max, mod)\\n        self._finvs = factorial_invs(max, mod)\\n        self._mod = mod\\n\\n    def ncr(self, n, r):\\n        \\\"\\\"\\\"\\n        :param int n:\\n        :param int r:\\n        :rtype: int\\n        \\\"\\\"\\\"\\n        if n < r:\\n            return 0\\n        return (\\n                self._factorials[n]\\n                * self._finvs[r]\\n                % self._mod\\n                * self._finvs[n - r]\\n                % self._mod\\n        )\\n\\n\\nP = int(sys.stdin.readline())\\nA = list(map(int, sys.stdin.readline().split()))\\n\\n\\n# A = np.array(A, dtype=int)\\n# vpow = np.vectorize(lambda a, b: pow(a, b, P))\\n# mat = []\\n# for i in range(P):\\n#     mat.append(vpow(i, np.arange(P)))\\n# print(np.array(mat).sum(axis=1) % P)\\n# print(np.array(mat).sum(axis=0) % P)\\n# mat = np.hstack((mat, [[a] for a in A]))\\n#\\n# print(mat)\\n#\\n\\n\\ndef power_table():\\n    ret = np.ones((P, P), dtype=int)\\n    row = -np.arange(P, dtype=int)\\n    for i in range(1, P):\\n        ret[i] = ret[i - 1] * row % P\\n    return ret\\n\\n\\n# \\u89e3\\u8aacAC\\n# f(x) = 1\\u2212(x - j)^(P - 1) \\u306f\\u3001x == j \\u306e\\u3068\\u304d1\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u306e\\u3068\\u304d0\\n# A[j] == 1 \\u3067\\u3042\\u308b j \\u306b\\u3064\\u3044\\u3066\\u4e0a\\u8a18\\u306e\\u5f0f\\u3092\\u8db3\\u3057\\u5408\\u308f\\u305b\\u308b\\ncomb = Combination(max=P - 1, mod=P)\\nncr = np.array([comb.ncr(P - 1, i) for i in range(P)])\\n# power[i][j]: (-j)^i\\npower = power_table()\\n\\nB = np.zeros(P, dtype=int)\\nfor j, a in enumerate(A):\\n    if a == 0:\\n        continue\\n    B -= power[:, j] * ncr % P\\n    B[-1] += 1\\n    B %= P\\nprint((*B[::-1]))\\n\", \"import numpy as np\\nmod = 998244353\\n\\ndef poly_mul(f, g):\\n    # \\u53c2\\u8003: https://judge.yosupo.jp/submission/2380\\n    Lf = len(f); Lg = len(g); L = Lf + Lg - 1\\n    if Lf <= 16 or Lg <= 16:\\n        if Lf == 0 or Lg == 0:\\n            return np.zeros((0,), dtype=np.int64)\\n        return (np.convolve(f.astype(np.uint64), g.astype(np.uint64)) % mod).astype(np.int64)\\n    fft = np.fft.rfft; ifft = np.fft.irfft\\n    fft_len = 1 << L.bit_length()\\n    fl = f & (1 << 15) - 1; fh = f >> 15\\n    gl = g & (1 << 15) - 1; gh = g >> 15\\n    x = (ifft(fft(fl, fft_len) * fft(gl, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    y = (ifft(fft(fl+fh, fft_len) * fft(gl+gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    z = (ifft(fft(fh, fft_len) * fft(gh, fft_len))[:L] + 0.5).astype(np.int64) % mod\\n    return (x + ((y - x - z) << 15) + (z << 30)) % mod\\n\\ndef poly_inv(fps, n=None):\\n    assert fps[0] != 0\\n    if n is None:\\n        n = len(fps)\\n    res = np.zeros(1<<(n-1).bit_length(), dtype=np.int64)\\n    res[0] = pow(int(fps[0]), mod-2, mod)\\n    i = 1\\n    while i < n:\\n        i <<= 1\\n        res[:i] = ((res[:i]<<1) - poly_mul(poly_mul(res[:i>>1], res[:i>>1]), fps[:i])[:i]) % mod\\n    return res[:n]\\n\\ndef poly_div(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return np.zeros((0,), dtype=np.int64)\\n    n = n1 - n2 + 1\\n    res = poly_mul(fps1[-1:-n-1:-1], poly_inv(fps2[::-1], n))[n-1::-1]\\n    return res\\n\\ndef poly_mod(fps1, fps2):\\n    n1, n2 = len(fps1), len(fps2)\\n    if n1 < n2:\\n        return fps1\\n    res = fps1[:n2-1] - poly_mul(poly_div(fps1, fps2), fps2)[:n2-1]\\n    return res % mod\\n\\ndef multipoint_evaluation(fps, xs):\\n    threshold = 8\\n    n_xs = len(xs)\\n    bit = (n_xs-1).bit_length()\\n    if bit <= threshold:\\n        res = np.zeros_like(xs)\\n        xs_cumprod = np.ones_like(xs)\\n        for coef in fps:\\n            res += xs_cumprod * coef\\n            xs_cumprod *= xs\\n            xs_cumprod %= mod\\n        return res\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, k+1), dtype=fps.dtype)\\n    fpss[0, :n_xs] = -xs % mod\\n    fpss[1, :k:2] = fpss[0, :k:2] * fpss[0, 1::2] % mod\\n    fpss[1, 1::2] = (fpss[0, :k:2] + fpss[0, 1::2]) % mod\\n    for i in range(1, bit):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+step] = f[:-1]\\n    f = poly_mod(fps, f)\\n    fpss[-1, :len(f)] = f\\n    fpss[-1, len(f):] = 0\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, k, step):\\n            f = fpss[i+1, j:j+step]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss[i, j:j+half] = poly_mod(f, f1)\\n            fpss[i, j+half:j+step] = poly_mod(f, f2)\\n    xs = (-fpss[0, :k] % mod).reshape(-1, 1<<threshold)\\n    xs_cumprod = np.ones_like(xs)\\n    res = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        res += fpss[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    return res.reshape(-1)[:n_xs] % mod\\n\\ndef poly_differential(fps):\\n    return fps[1:] * np.arange(1, len(fps)) % mod\\n\\ndef lagrange_interpolation(X, Y, mod):\\n    # old\\n    n = len(X)\\n    g = [0]*(n+1)\\n    g[0] = 1\\n    for i, x in enumerate(X):\\n        for j in range(i, -1, -1):\\n            g[j+1] += g[j] * (-x) % mod\\n    res = [0]*n\\n    for x, y in zip(X, Y):\\n        f = g[:]\\n        denom = 0\\n        v = 1\\n        pow_x = [1]  # x \\u306e idx \\u4e57\\n        for _ in range(n-1):\\n            v = v * x % mod\\n            pow_x.append(v)\\n        pow_x.reverse()  # n-1 \\u4e57 ~ 0 \\u4e57\\n        for i, po in enumerate(pow_x):\\n            f_i = f[i]\\n            f[i+1] += f_i * x % mod  # f = g / (x - x_i) \\u3092\\u7d44\\u7acb\\u9664\\u6cd5\\u3067\\u6c42\\u3081\\u308b\\n            denom = (denom + f_i * po) % mod\\n        denom_inv = pow(denom, mod-2, mod)\\n        for i, f_i in enumerate(f[:n]):\\n            res[i] += (f_i * y * denom_inv)# % mod  # mod \\u304c\\u5927\\u304d\\u3044\\u3068 64bit \\u306b\\u53ce\\u307e\\u3089\\u306a\\u304f\\u306a\\u308b\\u306e\\u3067\\u3072\\u3068\\u3064\\u305a\\u3064 mod \\u53d6\\u3063\\u305f\\u65b9\\u304c\\u3044\\u3044\\u304b\\uff1f\\n    return [v % mod for v in res]\\n\\ndef polynomial_interpolation(xs, ys):\\n    # \\u53c2\\u8003: https://rsk0315.hatenablog.com/entry/2020/04/05/203210\\n    assert len(xs) == len(ys)\\n    threshold = 8\\n    as_strided = np.lib.stride_tricks.as_strided\\n    n = len(xs)\\n    if n==1:\\n        return ys.copy()\\n    bit = (n-1).bit_length()\\n    if bit <= threshold:\\n        res = lagrange_interpolation(xs.tolist(), ys.tolist(), mod)\\n        return np.array(res[::-1], dtype=np.int64)\\n    k = 1<<bit\\n    fpss = np.zeros((bit+1, n+1), dtype=np.int64)\\n    fpss[0, :n] = -xs % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss[i+1, j:n] = fpss[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            f = poly_mul(f1, f2)\\n            fpss[i+1, j:j+len(f)-1] = f[:-1]\\n    fpss2 = np.zeros((bit+1, k+1), dtype=np.int64)\\n    fpss2[bit, :n] = poly_differential(f)\\n    for i in range(bit-1, threshold-1, -1):\\n        step = 2<<i\\n        half = step>>1\\n        for j in range(0, n, step):\\n            if j+half >= n:\\n                fpss2[i, j:n] = fpss2[i+1, j:n]\\n                continue\\n            f = fpss2[i+1, j:min(j+step, n)]\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:min(j+step, n)+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i, j:j+half] = poly_mod(f, f1)\\n            fpss2[i, j+half:min(j+step, n)] = poly_mod(f, f2)\\n    xs = as_strided(xs, (k>>threshold, 1<<threshold), (8<<threshold, 8))\\n    xs_cumprod = np.ones_like(xs)\\n    f = np.zeros_like(xs)\\n    for i in range(1<<threshold):\\n        f += fpss2[threshold, i:k:1<<threshold, None] * xs_cumprod % mod\\n        xs_cumprod *= xs\\n        xs_cumprod %= mod\\n    f = f.ravel()\\n    for j in range(n):\\n        fpss2[0, j] = ys[j] * pow(int(f[j]), mod-2, mod) % mod\\n    for i in range(bit):\\n        step = 2 << i\\n        half = step >> 1\\n        for j in range(0, k, step):\\n            if j+half >= n:\\n                fpss2[i+1, j:n] = fpss2[i, j:n]\\n                continue\\n            f1 = fpss[i, j:j+half+1].copy()\\n            f2 = fpss[i, j+half:j+step+1].copy()\\n            f1[-1] = f2[-1] = 1\\n            fpss2[i+1, j:min(j+step, n)] = (\\n                poly_mul(fpss2[i, j:j+half], f2)\\n                + poly_mul(fpss2[i, j+half:min(j+step, n)], f1)\\n            ) % mod\\n    return fpss2[bit, :n]\\n\\nmod = int(input())\\nA = np.array(input().split(), dtype=np.int64)\\nX = np.arange(mod, dtype=np.int64)\\nAns = polynomial_interpolation(X, A)\\nprint((\\\" \\\".join(map(str, Ans.tolist()))))\\n\"]",
        "difficulty": "interview",
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        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc137/tasks/abc137_f"
    },
    {
        "id": 155,
        "task_id": 753,
        "test_case_id": 1,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "1 1 3 2\n",
        "output": "1/3\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 156,
        "task_id": 753,
        "test_case_id": 2,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "4 3 2 2\n",
        "output": "1/4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 157,
        "task_id": 753,
        "test_case_id": 3,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "3 4 2 3\n",
        "output": "1/9\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 158,
        "task_id": 753,
        "test_case_id": 4,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "4 4 5 5\n",
        "output": "0/1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 159,
        "task_id": 753,
        "test_case_id": 5,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "1 1 1 1\n",
        "output": "0/1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 160,
        "task_id": 753,
        "test_case_id": 6,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "1000 1000 1000 1000\n",
        "output": "0/1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 161,
        "task_id": 753,
        "test_case_id": 7,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "125 992 14 25\n",
        "output": "10763/13888\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 162,
        "task_id": 753,
        "test_case_id": 8,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "999 998 997 996\n",
        "output": "1/497503\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 163,
        "task_id": 753,
        "test_case_id": 9,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "984 286 976 284\n",
        "output": "10/8733\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 164,
        "task_id": 753,
        "test_case_id": 10,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "999 1000 1000 999\n",
        "output": "1999/1000000\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 165,
        "task_id": 753,
        "test_case_id": 11,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "999 1000 998 999\n",
        "output": "1/998001\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 166,
        "task_id": 753,
        "test_case_id": 12,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "1 1000 1000 1\n",
        "output": "999999/1000000\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 167,
        "task_id": 753,
        "test_case_id": 13,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "1 999 1000 1\n",
        "output": "998999/999000\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 168,
        "task_id": 753,
        "test_case_id": 14,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "50 80 6 3\n",
        "output": "11/16\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 169,
        "task_id": 753,
        "test_case_id": 15,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "114 891 20 3\n",
        "output": "971/990\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 170,
        "task_id": 753,
        "test_case_id": 16,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "10 13 75 57\n",
        "output": "27/65\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 171,
        "task_id": 753,
        "test_case_id": 17,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "21 35 34 51\n",
        "output": "1/10\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 172,
        "task_id": 753,
        "test_case_id": 18,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "41 95 82 30\n",
        "output": "16/19\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 173,
        "task_id": 753,
        "test_case_id": 19,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "123 150 82 60\n",
        "output": "2/5\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 174,
        "task_id": 753,
        "test_case_id": 20,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "100 175 164 82\n",
        "output": "5/7\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 175,
        "task_id": 753,
        "test_case_id": 21,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "101 202 37 72\n",
        "output": "1/37\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 176,
        "task_id": 753,
        "test_case_id": 22,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "103 305 34 61\n",
        "output": "67/170\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 177,
        "task_id": 753,
        "test_case_id": 23,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "100 131 70 77\n",
        "output": "21/131\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 178,
        "task_id": 753,
        "test_case_id": 24,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "193 246 82 95\n",
        "output": "1837/20172\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 179,
        "task_id": 753,
        "test_case_id": 25,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "188 199 121 123\n",
        "output": "955/24079\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 180,
        "task_id": 753,
        "test_case_id": 26,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "289 361 162 198\n",
        "output": "70/3249\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 181,
        "task_id": 753,
        "test_case_id": 27,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "294 356 178 185\n",
        "output": "4489/31684\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 182,
        "task_id": 753,
        "test_case_id": 28,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "201 335 268 402\n",
        "output": "1/10\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 183,
        "task_id": 753,
        "test_case_id": 29,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "202 404 404 505\n",
        "output": "3/8\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 184,
        "task_id": 753,
        "test_case_id": 30,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "206 412 309 515\n",
        "output": "1/6\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 185,
        "task_id": 753,
        "test_case_id": 31,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "803 949 657 730\n",
        "output": "7/117\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 186,
        "task_id": 753,
        "test_case_id": 32,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "804 938 871 938\n",
        "output": "1/13\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 187,
        "task_id": 753,
        "test_case_id": 33,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "826 944 826 885\n",
        "output": "1/16\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 188,
        "task_id": 753,
        "test_case_id": 34,
        "question": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.\n\nCalculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p / q.\n\n\n-----Input-----\n\nA single line contains four space-separated integers a, b, c, d (1 ≤ a, b, c, d ≤ 1000).\n\n\n-----Output-----\n\nPrint the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.\n\n\n-----Examples-----\nInput\n1 1 3 2\n\nOutput\n1/3\n\nInput\n4 3 2 2\n\nOutput\n1/4\n\n\n\n-----Note-----\n\nSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: [Image]\n\nSample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: [Image]",
        "solutions": "[\"from fractions import Fraction,gcd\\n\\na,b,c,d = [int(x) for x in input().split()]\\n\\nif a*d > b*c:\\n    num = a*d-b*c\\n    denom = a*d\\nelse:\\n    num = b*c-a*d\\n    denom = b*c\\ndiv = gcd(num,denom)\\nprint('%d/%d'%(num//div,denom//div))\\n\", \"from fractions import gcd\\na,b,c,d = list(map(int, input().split()))\\nax, bx, cx, dx = a,b,c,d\\n\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans1 = (negru, monitor)\\n\\n\\na,b,c,d = bx, ax, dx, cx\\na,b,c,d = a*d, b*d, c*b, d*b\\n\\nmonitor = a*b\\nfilm = c*d\\nnegru = monitor - film\\n\\nmonitor, negru = monitor//gcd(monitor, negru), negru//gcd(monitor, negru)\\nans2 = (negru, monitor)\\n\\n\\n\\n\\nif ans1[1] == 0 or ans1[0] / ans1[1] < 0:\\n    sol = ans2\\nelif ans2[1] == 0 or ans2[0] / ans2[1] < 0:\\n    sol = ans1\\nelse:\\n    if ans1[0] / ans1[1] < ans2[0] / ans2[1]: sol = ans1\\n    else: sol = ans2\\n\\nprint('%i/%i' % sol)\\n    \\n\\n\", \"import fractions\\n\\ndef solve(a, b, c, d):\\n    if a * d == b * c:\\n        return \\\"0/1\\\"\\n    elif a / c > b / d:\\n        return str(fractions.Fraction(a * d - c * b, a * d))\\n    else:\\n        return str(fractions.Fraction(c * b - a * d, c * b))\\n\\ndef test():\\n    assert solve(1, 1, 3, 2) == \\\"1/3\\\"\\n    assert solve(4, 3, 2, 2) == \\\"1/4\\\"\\n    assert solve(1, 1, 1, 1) == \\\"0/1\\\"\\n    print(\\\"test passes\\\")\\n\\n##test()\\na, b, c, d = tuple(map(int, input().split()))\\nprint(solve(a, b, c, d))\\n    \\n\", \"from fractions import Fraction\\n\\ndef __starting_point():\\n    inp = input()\\n    arr = inp.split(\\\" \\\")\\n    a = Fraction(int(arr[0]),1)\\n    b = Fraction(int(arr[1]),1)\\n    c = Fraction(int(arr[2]),1)\\n    d = Fraction(int(arr[3]),1)\\n\\n\\n    if d*a == c*b:\\n        ans=Fraction(0,1)\\n    elif d*a<c*b:\\n        ans = (b-(d*(a/c)))/b\\n    else:\\n        ans = (a-(c*(b/d)))/a\\n    \\n    print(ans.numerator,end='')\\n    print('/',end='')\\n    print(ans.denominator)\\n\\n__starting_point()\", \"a, b, c, d = list(map(int, input().split()))\\n\\n\\ndef largest_div(n, m):\\n    while m > 0:\\n        rest = n % m\\n        n = m\\n        m = rest\\n    return n\\n\\nif a/b == c/d:\\n    print(\\\"0/1\\\")\\nelse:\\n    if a/b > c/d:  # full height\\n        f_new_width = c * b\\n        f_upper = d * a - f_new_width\\n        f_lower = d * a\\n    else:  # full width\\n        f_new_height = d * a\\n        f_upper = c * b - f_new_height\\n        f_lower = c * b\\n\\n\\n    div = largest_div(f_upper, f_lower)\\n    print(\\\"/\\\".join((str(int(f_upper/div)), str(int(f_lower/div)))))\\n\", \"3\\n\\nimport sys\\nfrom fractions import Fraction\\n\\na, b, c, d = list(map(int, sys.stdin.readline().strip().split()))\\nd2 = Fraction(d*a, c)\\nans = None\\nif d2 <= Fraction(b):\\n    # fits left-to-right\\n    ans = (Fraction(b) - d2) / Fraction(b)\\nelse:\\n    # fits top-to-bottom\\n    c2 = Fraction(c*b, d)\\n    ans = (Fraction(a) - c2) / Fraction(a)\\n\\nif ans.denominator == 1:\\n    print(\\\"%d/1\\\" % ans.numerator)\\nelse:\\n    print(ans)\\n\", \"from math import *\\ndef GCD(a, b):\\n\\twhile (b):\\n\\t\\ta %= b\\n\\t\\ta, b = b, a\\n\\treturn a\\na, b, c, d = map(int, input().split())\\nC, D = min(a*d,b*c), max(a*d,b*c)\\nC = D - C\\nG = GCD(C, D)\\nC = C // G\\nD = D // G\\nprint (str(C) + \\\"/\\\" + str(D))\", \"from fractions import Fraction\\nfrom decimal import Decimal\\na, b, c, d = list(map(int, input().split()))\\nans = max(Fraction((a * d - b * c)/ (a * d)).limit_denominator(), Fraction((b * c - a * d) / (b * c)).limit_denominator())\\nif ans == 0:\\n    ans = '0/1'\\nprint(ans)\\n\", \"from fractions import gcd\\n\\n\\ndef socr(a, b):\\n    tmp = gcd(a, b)\\n    return a // tmp, b // tmp\\n\\na, b, c, d = list(map(int, input().split()))\\n\\nans = socr(a * d - b * c, a * d)\\na, b = b, a\\nc, d = d, c\\nans = socr(a * d - b * c, a * d) if ans[0] < 0 or ans[1] < 0 else ans\\nprint(str(int(ans[0])) + '/' + str(int(ans[1])))\\n\", \"from fractions import gcd,Fraction,Decimal\\na,b,c,d=map(int,input().split())\\n\\n##c->a\\n##d->b\\nif(a/b<c/d):\\n    N=(b*c)-(a*d)\\n    D=b*c\\nelse:\\n    N=(a*d)-(b*c)\\n    D=a*d\\n\\nx=gcd(N,D)\\n\\nprint(N//x,end=\\\"/\\\")\\nprint(D//x)\\n\\n\\n\", \"import sys\\n\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\n\\nclass Fraction:\\n    def __init__(self, p = 0, q = 1, reduced = True):\\n        if type(p) == int:\\n            self.p = p\\n            if type(q) == int:\\n                self.q = q\\n        elif type(p) == Fraction:\\n            self.p = p.p\\n            self.q = p.q\\n        else:\\n            i = p.find(' ')\\n            if i == -1:\\n                i = p.find('/')\\n            if i == -1:\\n                self.p = int(p)\\n                self.q = 1\\n            else:\\n                self.p = int(p[:i])\\n                self.q = int(p[i + 1:])\\n        if reduced:\\n            self.reduce()\\n\\n    def reduce(self):\\n        g = gcd(self.p, self.q)\\n        self.p //= g\\n        self.q //= g\\n\\n    def __str__(self):\\n        if self.q == 1:\\n            return(str(self.p))\\n        else:\\n            return(str(self.p) + '/' + str(self.q))\\n\\n    def __lt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p < other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q < self.q * other.p\\n\\n    def __le__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p <= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q <= self.q * other.p\\n\\n    def __gt__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p > other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q > self.q * other.p\\n\\n    def __ge__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p >= other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q >= self.q * other.p\\n\\n    def __eq__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p == other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q == self.q * other.p\\n\\n    def __ne__(self, other):\\n        self.reduce()\\n        if type(other) == float or type(other) == int:\\n            return self.p != other * self.q\\n        else:\\n            other.reduce()\\n            return self.p * other.q != self.q * other.p\\n\\n    def __mul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __rmul__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p * other, self.q)\\n        elif type(other) == float:\\n            return self.p * other / self.q\\n        else:\\n            return Fraction(self.p * other.p, self.q * other.q)\\n\\n    def __imul__(self, other):\\n        self = self * other\\n        return self\\n\\n    def __truediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p, self.q * other)\\n        elif type(other) == float:\\n            return self.p / self.q / other\\n        else:\\n            return Fraction(self.p * other.q, self.q * other.p)\\n\\n    def __rtruediv__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other, self.p)\\n        elif type(other) == float:\\n            return other * self.q / self.p\\n        else:\\n            return Fraction(self.q * other.p, self.p * other.q)\\n\\n    def __itruediv__(self, other):\\n        self = self / other\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == int:\\n            if other >= 0:\\n                return Fraction(self.p ** other, self.q ** other, False)\\n            else:\\n                return Fraction(self.q ** (-other), self.p ** (-other), False)\\n        elif type(other) == float:\\n            return (self.p / self.q) ** other\\n        else:\\n            return (self.p / self.q) ** (other.p / other.q)\\n\\n    def __rpow__(self, other):\\n        if type(other) == int or type(other) == float:\\n            return other ** (self.p / self.q)\\n        else:\\n            return (other.p / other.q) ** (self.p / self.q)\\n\\n    def __ipow__(self, other):\\n        self = self ** other\\n        return self\\n\\n    def __add__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __radd__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p + self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q + other\\n        else:\\n            return Fraction(self.p * other.q + self.q * other. p, self.q * other.q)\\n\\n    def __iadd__(self, other):\\n        self.reduce()\\n        self = self + other\\n        return self\\n\\n    def __sub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.p - self.q * other, self.q)\\n        elif type(other) == float:\\n            return self.p / self.q - other\\n        else:\\n            return Fraction(self.p * other.q - self.q * other. p, self.q * other.q)\\n\\n    def __rsub__(self, other):\\n        self.reduce()\\n        if type(other) == int:\\n            return Fraction(self.q * other - self.p, self.q)\\n        elif type(other) == float:\\n            return other - self.p / self.q\\n        else:\\n            return Fraction(self.q * other. p - self.p * other.q, self.q * other.q)\\n\\n    def __pos__(self):\\n        return Fraction(+self.p, +self.q)\\n\\n    def __neg__(self):\\n        return Fraction(-self.p, self.q)\\n\\n    def __abs__(self):\\n        if self.p < 0:\\n            return -self\\n        else:\\n            return self\\n\\n    def __int__(self):\\n        return self.p // self.q\\n\\n    def __float__(self):\\n        return self.p / self.q\\n\\n    def __round__(self, digits = 0):\\n        return round(float(self), digits)\\n\\na, b, c, d = list(map(int, input().split()))\\nproduct = a * c\\nB1 = b * c\\nB2 = a * d\\nif B1 > B2:\\n    B1, B2 = B2, B1\\nans = Fraction(B2 - B1, B2)\\nans.reduce()\\nif ans != 0:\\n    print(abs(ans))\\nelse:\\n    print(\\\"0/1\\\")\\n\", \"import sys\\nfrom fractions import gcd\\nmy_file = sys.stdin\\n#my_file = open(\\\"input.txt\\\", \\\"r\\\")\\nline = [int(i) for i in my_file.readline().split()]\\na, b, c, d = line[0], line[1], line[2], line[3]\\nif a/b < c/d:\\n    N = (b*c) - (a*d)\\n    D = b*c\\nelse:\\n    N = (a*d)-(b*c)\\n    D = a*d\\n\\ndec = gcd(N,D)\\n\\nprint(N//dec, end=\\\"/\\\")\\nprint(D//dec)\", \"def gcd(a, b):\\n    while a % b != 0:\\n        a, b = b, a % b\\n    return b\\n\\nl = input().split(' ')\\na, b, c, d = int(l[0]), int(l[1]), int(l[2]), int(l[3])\\nif a * d > b * c:\\n    p = a * d - b * c\\n    q = a * d\\nelse:\\n    p = b * c - a * d\\n    q = b * c\\ne = gcd(p, q)\\np //= e\\nq //= e\\nprint(str(p) + \\\"/\\\" + str(q))\\n\", \"def gcd(a,b):\\n    while a!=b:\\n        if a>b:\\n            a=a-b\\n        else :\\n            b=b-a\\n    print(m//a,'/',n//a,sep='')\\na,b,c,d=map(int,input().split())\\nm=1\\nn=1\\n\\nif a==b:\\n    if c==d :\\n        print(0,'/',1,sep='')\\n    else :\\n        if c>d:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)\\nelse:\\n    if c/d ==a/b:\\n        print(0,'/',1)\\n    else :\\n        if c/d>a/b:\\n            m=b*c-a*d\\n            n=c*b\\n            gcd(m,n)\\n        else :\\n            m=a*d-c*b\\n            n=a*d           \\n            gcd(m,n)        \\n            \\n        \\n                 \\n\", \"def gcd(a, b):\\n    if(a % b == 0):\\n        return b\\n    return gcd(b, a%b)\\n\\na, b, c, d = list(map(int, input().split()))\\n\\na *= c * d\\nb *= c * d\\n\\nif a / c * d <= b:\\n    a = b - a / c * d\\n    g = gcd(a, b)\\n    print(str(int(a / g)) + '/' + str(int(b / g)))\\n\\nelse:\\n    b = a - b / d * c\\n    g = gcd(a, b)\\n    print(str(int(b / g)) + '/' + str(int(a / g)))\\n\", \"import fractions\\n\\na, b, c, d = list(map(int, input().split()))\\np = max(a * d, b * c) - min(a * d, b * c)\\nq = max(a * d, b * c)\\nx = fractions.gcd(p, q)\\nprint(str(p // x) + '/' + str(q // x))\\n\", \"from fractions import Fraction\\nwhile(1):\\n    try:\\n        a,b,c,d=list(map(int,input().split()))\\n        if a/b<c/d:\\n            ratio=0\\n        elif a/b==c/d:\\n            ratio=-1\\n        else:\\n            ratio=1\\n        if ratio==0:\\n            # ans=(bc-ad)/bc\\n            f=Fraction(b*c-a*d,b*c) \\n            print(\\\"%s\\\"%(f))            \\n        elif ratio==1:\\n             # ans=(ad-bc)/ad\\n            f=Fraction(a*d-b*c,a*d)\\n            print(\\\"%s\\\"%(f))\\n        else:\\n            print(\\\"0/1\\\")\\n    except EOFError:\\n        break\\n        \\n        \\n\", \"def gcd(a,b):\\n    if(a%b==0):return b;\\n    return gcd(b,a%b);\\ndef solve(a,b,p,q):\\n    c=a*p/gcd(a,p);\\n    b1=b*c/a;\\n    q1=q*c/p;\\n    if(b1>=q1):\\n        if(b1==q1):\\n            print(\\\"0/1\\\");\\n        else:\\n            d=gcd(b1-q1,b1);\\n            print(str(int((b1-q1)/d))+\\\"/\\\"+str(int(b1/d)));\\n        return True;\\n    return False;\\ndef __starting_point():\\n    a,b,p,q=map(int,input().split());\\n    if(not solve(a,b,p,q)):\\n        solve(b,a,q,p);\\n__starting_point()\", \"#!/usr/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\n# Author: Vitaly Pavlenko\\n\\nimport random\\nfrom fractions import gcd\\n\\n\\ndef average(x):\\n    return sum(x) / len(x)\\n\\n\\ndef shuffled(a):\\n    a = list(a)\\n    random.shuffle(a)\\n    return a\\n\\n\\ndef read_ints():\\n    return [int(i) for i in input().split()]\\n\\n\\ndef decrease(a):\\n    return [i - 1 for i in a]\\n\\n\\n\\n\\ndef main():\\n    # nonlocal input\\n    # nonlocal print\\n\\n    # fin = open('input.txt', 'r')\\n    # input = lambda: fin.readline().strip()\\n    # fout = open('output.txt', 'w')\\n    # _print = print\\n    # print = lambda *args, **kwargs: _print(*args, file=fout, **kwargs)\\n\\n    a, b, c, d = read_ints()\\n\\n    if a / b < c / d:\\n        a, b, c, d = b, a, d, c\\n\\n    p, q = a * d - c * b, b * d\\n    s, t = p, a * d\\n    print(s // gcd(s, t), t // gcd(s, t), sep='/')\\n\\n    # fout.close()\\n\\n\\ndef __starting_point():\\n    # import doctest\\n    # doctest.testmod()\\n    main()\\n__starting_point()\", \"from fractions import gcd\\n\\ndef Irreducible_Fraction(A,B):\\n    ''' Returns list of two integers representing the nominator and denominator of the Irreducible version of A/B '''\\n    x=gcd(A,B)\\n    return [A//x,B//x]\\n        \\n\\n\\n\\na,b,c,d=map(int,input().split())\\n\\n#Movie Frame Ratio:\\nF=a/b\\n\\n#Screen Ratio:\\nS=c/d\\n\\n\\n\\n#There are three case:\\n(a/b < c/d)\\n(a/b == c/d)\\n(a/b > c/d)\\n\\n\\n#Case 1:\\n#Frame's ratio is larger than screen ratio (c/d > a/b)\\n#This means that if both the screen and the movie had the same vertical length,\\n#The movie's horizontal length will be bigger which is not desired !\\n#So in this case, we will stretch the movie until it is the same horizontal length as the screen,( c -> a )\\n#And the movie's vertical length would be smaller than the screen's vertical length.( d < b )\\n#Stretching factor = a/c\\nif(a/b <c/d):\\n    stretching_factor=a/c\\n    #To avoid decimals which may result into an error while computing the fraction\\n    #We will multiply both the the new area and te screen area by c\\n    New_horizontal=a\\n    New_vertical=a*d #The multiplied c apears in ommiting the division by c in the stretching factor\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*c) #The multiplied c appears\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\\n\\n#Case 2:\\n#Frame's ratio is the same as the screen ratio (c/d == a/b)\\n#This means that we can stretch the movie till it is the same horizontal length as the screen,\\n#And the vertical length of the movie would be the same as the vertical length of the screen\\n#So The empty area will always be ZERO !\\n\\n\\nelif(a/b == c/d):\\n    print(\\\"0/1\\\")\\n\\n\\n#Case 3:\\n#Opposite to Case 1\\n#Frame's ratio is smaller than screen ratio (c/d > a/b)\\n#This means that the stretching process will end when the vertical length is the same for the screen and the frame\\n#While the horizontal length of the screen is bigger\\n#Stretching facto = b/d\\nelse:\\n    stretching_factor=b/d\\n    #To_avoid decimals, the same as case 1 was done !\\n    New_vertical=b\\n    New_horizontal=(b)*c\\n    New_Movie_Area=int(New_horizontal*New_vertical)\\n    Screen_Area=int(a*b*d)\\n    Empty_Area=Screen_Area-New_Movie_Area\\n    desired_ratio=Irreducible_Fraction(Empty_Area,Screen_Area)\\n    nominator=desired_ratio[0]\\n    denominator=desired_ratio[1]\\n    print(nominator,end=\\\"/\\\")\\n    print(denominator)\\n\", \"from fractions import Fraction\\n\\na, b, c, d = map(int, input().split())\\n\\nif a / c <= b / d:\\n  res = Fraction(b * c - a * d, b * c)\\nelse:\\n  res = Fraction(a * d - b * c, a * d)\\n\\nprint(\\\"{0}/{1}\\\".format(res.numerator, res.denominator))\", \"def check(t):\\n    if x==int(x):return True\\n    else:return False\\n\\ndef gcd(x,y):\\n    if x%y==0 :return y\\n    else: return gcd(y,x%y)\\na,b,c,d=list(map(int,input().split()))\\na*=max(c,d)\\nb*=max(c,d)\\nr=c/d\\nif a/b<r:\\n   x=b*c-a*d\\n   b=b*c\\n  \\n   \\n\\n   u=gcd(x,b)\\n   p=str(int(x/u))+'/'+str(int(b/u))\\n   print(p)\\n\\nelse:\\n    x=a*d-c*b\\n    a=a*d\\n    \\n\\n    u=gcd(x,a)\\n    p=str(int(x/u))+'/'+str(int(a/u))\\n    print(p)\\n\", \"def gcd(x, y):\\n    while x!=0:\\n        x,y = y%x,x\\n    return y\\n\\ndef main():\\n    a,b,c,d = [int(item) for item in input().split()]\\n    k1 = float(a)/float(b)\\n    k2 = float(c)/float(d)\\n    p = 0\\n    q = 1\\n    g = 0\\n\\n    if k1>k2:\\n        q = a*d\\n        p = q-b*c\\n        g = gcd(p,q)\\n    elif k1<k2:\\n        q = b*c\\n        p = q - a*d\\n        g = gcd(p, q)\\n\\n    if g>1:\\n        p = int(p / g)\\n        q = int(q / g)\\n\\n    print('{}/{}'.format(p, q))\\n\\nmain()\\n\", \"def gcd(a, b):\\n    c = a % b\\n    return gcd(b, c) if c else b\\n\\na, b, c, d = map(int, input().split())\\nif a * d < b * c: a, b, c, d = b, a, d, c\\np = a * d - b * c\\nq = d * a\\nt = gcd(p, q)\\n\\nprint(str(p // t) + '/' + str(q // t))\", \"from sys import stdin\\nfrom fractions import Fraction\\n\\n(a,b,c,d) = map(int, input().split());\\n\\ncd = Fraction(c, d)\\nab = Fraction(a, b)\\nf1 = Fraction(1, 1)\\n\\nif cd < ab:\\n\\tprint(f1 - Fraction(c * b, a * d))\\nelif cd > ab:\\n\\tprint(f1 - Fraction(a * d, c * b))\\nelse:\\n\\tprint(\\\"0/1\\\")\"]",
        "difficulty": "interview",
        "input": "603 938 804 871\n",
        "output": "17/56\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/337/B"
    },
    {
        "id": 189,
        "task_id": 1088,
        "test_case_id": 1,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "3 13\n3 2 7\n4 8 9\n1 6 5\n",
        "output": "12\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 190,
        "task_id": 1088,
        "test_case_id": 2,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "10 165\n82 94 21 65 28 22 61 80 81 79\n93 35 59 85 96 1 78 72 43 5\n12 15 97 49 69 53 18 73 6 58\n60 14 23 19 44 99 64 17 29 67\n24 39 56 92 88 7 48 75 36 91\n74 16 26 10 40 63 45 76 86 3\n9 66 42 84 38 51 25 2 33 41\n87 54 57 62 47 31 68 11 83 8\n46 27 55 70 52 98 20 77 89 34\n32 71 30 50 90 4 37 95 13 100\n",
        "output": "348179577\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 191,
        "task_id": 1088,
        "test_case_id": 3,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "1 1\n1\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 192,
        "task_id": 1088,
        "test_case_id": 4,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "1 2\n1\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 193,
        "task_id": 1088,
        "test_case_id": 5,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "44 3432\n1 45 89 133 177 221 265 155 353 397 441 485 529 573 617 661 705 749 793 837 881 925 969 159 1057 1101 1145 1189 1233 1277 1703 1365 1409 1453 1497 1541 1585 1629 1673 1717 1761 1805 1849 1893\n2 46 90 134 178 222 359 310 354 398 1880 486 530 574 618 662 706 750 794 838 882 926 970 1014 1058 1102 1146 12 567 1278 1322 495 1410 1815 1498 1542 1586 1630 1674 1718 1762 1806 1850 1894\n3 47 91 135 179 223 267 311 355 1053 443 487 531 575 1369 663 707 751 795 839 883 927 1632 1015 1059 1103 1147 1191 1235 1279 1323 1367 1411 1455 1499 1543 1587 1631 1787 1719 1763 1807 1851 1895\n937 48 1274 136 180 224 268 312 356 400 545 488 532 546 620 664 708 752 796 840 884 928 972 1016 1060 1104 1148 1854 1236 1280 913 1346 1412 1456 1500 1544 1588 971 1676 1720 1764 1808 1852 1896\n5 49 93 137 181 225 269 313 357 401 445 489 533 787 621 665 709 11 797 841 885 929 973 1017 1061 1105 873 1193 1237 1281 1325 619 1413 1457 1501 1553 1589 1633 1677 1721 1765 1809 1853 1897\n6 50 94 138 182 226 270 314 358 402 446 490 534 578 622 666 710 754 798 842 886 1184 974 1018 1062 1106 1150 1194 1238 1282 1326 1370 1414 1458 1502 1546 1590 1634 1678 1722 1766 1810 1192 1898\n7 51 95 139 183 227 271 315 266 403 447 491 535 579 623 667 1538 755 799 843 887 931 975 1019 1063 1107 1151 1195 500 1337 1327 1371 1117 1459 1503 1547 1591 1635 1679 1723 1767 1811 1855 1899\n8 52 96 140 184 228 272 386 360 404 448 492 536 580 624 668 712 756 800 844 888 932 976 1020 1064 1108 1152 1196 1240 1284 1328 1372 1416 1460 1504 1548 1592 1636 1680 1724 1768 1526 1856 1900\n915 53 97 141 185 229 273 317 361 405 449 493 537 581 625 669 713 757 801 845 889 1514 977 1021 1065 1109 1315 1197 1241 1285 1329 1373 1876 1461 1505 1549 1593 1637 1681 1725 1769 1813 208 1901\n10 54 98 142 186 230 696 318 362 171 450 494 538 582 626 670 714 758 802 846 1331 934 978 1022 1066 1110 1154 1198 1242 1791 1330 1374 1418 1462 828 1550 1594 1638 1682 1726 1770 1814 1858 1902\n74 55 99 143 1224 231 275 412 363 407 451 1366 539 583 627 671 715 759 803 847 891 935 979 858 1133 1111 1155 1199 1243 1287 890 1375 1419 1463 1507 1551 1595 1639 1683 672 1771 1454 1859 1903\n1190 56 100 144 1756 232 276 320 364 408 452 496 540 584 628 1727 716 760 804 848 892 936 980 1024 1068 1112 1156 1200 1244 1288 1332 1143 1420 1464 1508 1552 1596 1640 1684 1728 1772 1816 1860 1904\n13 57 101 145 189 233 277 321 365 409 453 1610 541 585 629 867 717 761 805 686 893 4 1729 1025 1069 1113 1157 1201 1245 1289 1333 1377 1421 1465 1509 1545 1597 1357 1685 981 1773 1817 1861 1905\n14 58 102 146 190 234 278 322 366 410 454 498 542 586 630 674 718 1622 806 906 894 938 753 1026 1070 1114 1158 1360 1246 1290 1334 1378 1422 1466 1510 1554 1598 1183 1686 1730 1774 1818 1862 1906\n15 59 103 147 191 235 279 323 367 411 455 499 543 587 631 675 719 763 872 851 895 939 983 1027 1071 1115 1159 1203 1247 1291 1335 1379 1423 1467 1511 1555 1599 1643 1687 1731 1775 1260 1863 1078\n16 60 104 148 192 236 280 324 368 319 456 1239 544 1691 632 676 720 764 808 852 896 940 984 1028 1072 1116 1564 1204 1248 1292 1336 1380 1424 1468 1512 1556 692 1644 1688 1732 1776 1820 1864 1908\n17 61 105 149 193 237 281 325 369 413 457 501 444 589 633 677 721 765 809 853 897 941 985 1029 1073 1415 1161 1205 1249 1293 1283 1381 1425 1469 1513 1557 1601 1645 1689 959 1777 1821 1865 1909\n18 62 106 150 194 238 282 326 370 414 458 502 576 590 634 678 722 766 810 854 898 942 986 1030 1074 1118 1162 1206 1250 1294 1338 158 1426 1470 1890 1558 1602 1646 1690 1734 1778 1822 917 1910\n19 63 107 1214 195 239 283 327 371 415 459 503 547 591 635 679 723 767 811 855 899 943 987 1031 1075 1119 1163 1207 1251 1295 1339 1383 1427 1471 1515 1559 1603 1647 588 1735 786 1823 1867 1911\n20 64 108 152 196 240 284 328 372 416 460 504 548 592 636 680 724 1878 812 856 900 944 988 1032 1076 1120 1164 1208 1252 1296 1340 1384 1428 1472 608 1160 1604 1345 1692 1736 1780 1824 1868 1912\n21 65 109 153 197 241 285 329 373 417 461 505 549 593 637 681 725 769 813 857 901 945 989 1033 1077 1121 1165 1209 733 1297 1341 1385 1429 1473 1517 1561 1605 1649 1693 1737 1399 1825 1869 1913\n22 66 1883 154 198 242 286 330 374 418 1430 506 550 594 638 682 726 770 814 1023 902 946 990 1034 1907 1122 1166 1210 1254 1298 1342 1386 462 1474 1518 1562 1606 1650 1694 1738 1782 1826 1870 1914\n23 67 111 309 199 243 287 331 375 419 463 507 551 595 639 683 727 771 815 859 903 947 991 1035 1079 1123 1167 1211 1255 1299 1343 1387 1431 1475 1519 1563 1607 1651 1695 1739 1783 1827 1871 1915\n24 68 112 156 200 244 288 332 376 420 464 508 552 655 640 562 728 772 816 860 904 948 992 1036 1080 1124 1168 1212 1256 1300 1344 1388 1432 1476 1520 1560 1608 1652 1696 1740 1784 1828 1872 1916\n25 69 113 157 201 245 289 333 377 421 465 509 553 597 641 685 729 773 817 780 905 949 993 1037 1081 1125 1169 1213 1257 1301 1648 1389 1433 1477 1521 1565 933 1653 1697 1741 1785 1829 1873 1917\n26 70 114 1382 202 246 290 334 378 422 466 510 554 598 642 849 730 774 818 862 850 950 994 1038 1082 1126 1170 151 1258 1302 1368 1390 1434 1478 1522 1566 497 1654 1698 1742 1786 1830 1874 1918\n27 71 115 1013 203 247 291 335 379 423 467 511 555 599 643 687 731 775 819 863 907 951 995 1039 1083 1127 1171 1215 1259 1303 1347 1391 1262 1479 1523 1567 1611 1655 1699 1743 1675 1831 1875 1919\n1187 72 116 160 204 248 292 336 380 424 1051 512 556 600 644 688 211 776 820 864 908 952 996 1040 1393 1128 1172 1216 1819 1304 1348 1392 1436 1480 1524 1568 702 1656 1700 1744 1788 1832 1417 1920\n29 73 117 161 205 249 293 337 381 425 469 513 557 601 645 689 1253 777 162 865 909 953 997 1041 1085 1129 1173 1217 1261 1305 1349 1084 1437 1481 1525 1569 1613 1657 1701 1745 1789 1833 1877 1921\n30 982 118 821 206 250 294 338 382 426 470 514 558 602 646 690 734 778 822 866 910 954 998 1042 1086 1130 1174 1218 1435 1306 1350 1394 1438 1482 1812 1570 1614 1658 1702 1746 1790 1834 768 1922\n31 75 119 163 207 251 295 339 383 427 471 515 559 603 647 691 735 779 823 673 711 955 999 1043 1087 1131 1175 1219 1263 1307 1351 1395 1439 1483 1527 1571 1615 1659 1321 1747 1286 1835 1879 1923\n32 76 120 164 1857 252 296 340 384 428 472 516 560 604 648 1600 736 861 824 868 912 956 1000 1044 1088 1132 1176 1220 1264 1308 1352 1396 1440 1484 1528 1572 1616 1660 1704 1748 1792 1836 442 1924\n33 77 121 165 209 253 297 341 385 429 473 517 561 605 649 693 737 781 825 869 1324 957 1001 1045 1089 1067 1177 1221 1265 1309 1353 1397 1441 1485 1529 1573 1617 1661 1705 1749 1793 656 1881 1925\n34 78 122 166 210 254 298 342 316 430 474 518 684 606 650 694 738 782 826 870 914 958 1002 1046 1090 1134 1178 1222 1266 1310 1354 1398 1442 1486 1530 1574 1618 1662 1706 1750 1794 1838 1882 1926\n35 79 123 167 732 255 299 343 387 431 475 519 563 607 651 695 739 783 827 871 9 1733 1003 1047 1091 1135 1179 1223 1267 1311 1355 1781 1443 1487 1531 1575 1619 1663 1707 1751 1576 1839 110 1927\n36 80 124 168 212 256 300 344 388 432 476 520 564 1516 1231 274 740 784 1506 807 916 960 1004 1048 1092 1136 1180 187 1268 1312 1356 1400 1444 1488 1532 1795 1620 1664 1708 1752 1796 1840 1884 1928\n37 81 125 169 213 257 301 1445 389 433 477 521 565 609 653 697 741 785 829 1149 1866 961 1005 1049 1093 1137 1181 1225 1269 1313 1641 1401 345 1489 1533 1577 1621 1665 1709 1753 1797 1841 1885 1929\n38 82 126 170 214 258 302 346 390 434 478 522 566 610 654 698 742 1779 830 874 918 962 1006 1050 1094 1138 1182 1226 1270 1314 1358 1402 1446 1490 1534 1578 762 1666 1710 1754 911 1842 1886 1930\n39 83 127 406 215 259 303 347 391 1447 479 523 1234 611 596 699 743 577 831 875 919 963 1007 468 1095 1139 1642 1227 1271 1153 1359 1403 435 1491 1535 1579 1623 1667 1711 1755 1799 1843 1887 1931\n40 84 128 172 216 260 304 348 392 436 480 524 568 612 1837 700 744 788 832 876 920 964 1008 1052 1096 1140 930 1228 1272 1316 1202 1404 1448 1492 1536 1580 1624 1668 1712 188 1800 1844 1888 1932\n41 85 129 173 217 261 305 349 393 437 481 525 569 613 657 701 745 789 833 877 921 965 1009 399 1097 1141 1185 1229 1273 1317 1361 1405 1449 1493 1537 1581 1625 1669 1713 1757 1801 1845 1889 1933\n42 86 130 174 218 394 306 350 262 438 482 526 570 614 658 1612 746 790 834 878 922 966 1010 1054 1098 1142 1186 1230 92 1318 1362 1406 1450 1494 1798 1582 1626 1670 1714 1758 1802 1846 1609 1934\n43 87 131 175 219 263 307 351 395 439 483 527 571 615 659 703 747 791 835 879 923 967 1011 1055 1099 1376 28 652 1275 1319 1363 1407 1451 1495 1539 1583 1848 1671 1715 1759 1803 1847 1891 1935\n44 88 132 176 220 264 308 352 396 440 484 528 572 616 660 704 748 792 836 880 924 968 1012 1056 1760 1144 1188 1232 1276 1320 1364 1408 1452 1496 1540 1584 1628 1672 1716 1100 1804 1627 1892 1936\n",
        "output": "376967120\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 194,
        "task_id": 1088,
        "test_case_id": 6,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "45 3643\n1 46 91 136 181 226 271 575 361 406 451 1902 541 586 631 676 721 92 811 856 901 946 991 36 1081 1126 1651 1216 1261 1306 1351 1396 1441 1486 1531 1576 1621 1666 1711 1756 1801 1846 1891 1936 1981\n2 47 766 137 182 227 272 317 362 407 452 497 542 587 632 677 722 767 812 857 902 947 992 1037 1082 1127 1172 1217 604 882 1352 1397 1442 1487 711 1577 1622 1667 1712 1757 1802 1847 1892 1937 1982\n950 48 93 138 183 228 273 318 363 408 453 498 543 619 633 678 723 768 813 858 903 948 993 1038 1083 1128 1173 1218 1263 1308 1353 1398 1443 1406 1533 1578 1623 1668 1713 1758 1803 1315 1893 1938 595\n4 49 94 139 184 229 274 319 364 409 454 499 544 589 634 679 724 769 814 859 904 949 994 1039 1084 1129 1174 1219 1264 1309 1354 1399 1444 1489 1534 1579 1624 1669 1714 1639 1804 1849 1894 1716 1984\n5 50 1124 140 185 230 275 320 365 410 135 500 545 590 1784 680 725 547 815 860 905 3 995 1040 1085 1130 1175 1220 1265 1310 1355 1400 1445 1490 1535 1580 1625 1670 1715 1760 1805 1850 1895 1940 1985\n6 51 96 141 186 231 276 321 366 411 456 501 546 591 771 1184 726 636 816 861 906 951 996 1041 1086 1131 1176 1221 1266 1683 1356 1401 1446 1491 1065 1581 1626 1671 1939 1761 1806 1851 1896 19 1986\n7 52 1977 142 187 232 277 322 367 412 457 502 770 592 637 682 727 772 817 862 907 952 997 1042 1087 1132 1177 1222 1267 1312 131 1402 1447 1492 1537 1582 1627 180 1717 1762 1807 1524 1897 1942 1987\n8 53 98 143 188 233 278 323 368 413 458 503 548 593 638 1200 728 773 818 2009 908 953 998 1043 1088 1133 1178 1223 1268 1313 1358 1403 1448 1493 1538 1583 1628 1673 1275 1763 1808 1853 1898 9 1988\n1943 54 99 144 189 234 279 324 1859 414 459 504 549 594 1514 684 729 774 819 864 909 954 999 1044 1089 1134 1179 1224 1269 1314 1359 1404 1449 1494 1539 1584 1629 1674 1719 1764 1809 1854 1899 1944 1989\n10 55 100 145 190 235 689 325 370 415 460 1160 550 1983 640 685 730 775 820 865 910 955 1000 1045 1090 1135 1180 1225 1270 1848 1360 1405 1450 1495 1540 1585 1630 1675 1720 1765 1810 1855 1900 1945 1990\n11 56 101 146 191 236 281 326 371 1047 588 506 551 596 641 686 731 776 821 866 97 956 2020 1046 1091 1136 1181 1226 1271 1316 1361 1488 1451 1496 1541 1586 1631 1676 1721 1682 1811 1856 1901 1946 1991\n12 57 102 147 192 1385 282 327 200 417 462 507 552 597 168 687 732 777 822 867 912 957 1002 416 1092 1137 1182 1227 1272 1317 1362 1407 1452 1206 1542 1587 1632 1677 1722 1767 762 1857 496 1947 1992\n13 58 853 148 193 238 283 328 373 825 463 508 553 598 643 688 733 778 823 868 913 958 1003 1048 1093 1138 1183 1228 1273 1318 1363 1408 1453 1498 626 1588 1633 1678 838 1768 1813 1858 1903 1948 1993\n14 59 104 153 194 239 284 329 374 419 464 509 554 599 644 280 734 779 824 869 914 959 1004 1049 1094 1139 681 1229 393 1319 1364 1912 1454 1499 1544 1589 1634 1679 1724 900 1814 369 1904 1949 1994\n15 60 105 150 195 240 285 330 375 420 465 510 555 600 645 690 735 780 418 870 915 960 1005 1050 1095 1140 1185 1230 1718 1320 1365 1410 1455 1500 1545 1590 1635 1680 1725 1770 1815 1860 1905 1950 1995\n16 61 106 151 196 241 286 331 450 421 968 511 556 601 646 691 736 781 826 871 916 961 1006 1051 524 1141 1186 1231 1276 1321 925 1411 1456 1501 1546 1591 1636 1681 1726 1771 1816 1861 1906 1951 1996\n17 62 107 152 197 242 287 332 377 422 467 512 557 602 647 692 737 1515 827 872 917 962 1007 1052 1097 1142 1187 1232 1277 1322 1367 1412 1457 1502 1547 1592 1637 1766 1727 1772 1817 1862 2011 1952 1997\n18 63 108 149 198 243 288 333 378 423 468 513 558 603 648 693 738 783 828 2006 918 963 1008 1053 1098 1143 1188 1438 1236 1323 1563 1413 1458 1503 1548 1593 1638 1311 1728 1773 1818 1863 1908 1953 1998\n1941 64 109 154 199 244 289 334 379 424 469 514 559 1262 649 694 739 784 829 874 919 964 1009 1054 1099 1144 1189 1234 1279 1324 1369 1414 1459 1504 1795 1024 1759 1684 1729 1774 1819 1864 1909 1954 1999\n20 65 110 155 372 245 290 335 380 425 470 515 560 605 650 695 740 785 830 875 920 965 1010 1055 1100 1145 1190 1235 1280 1325 1370 1415 1460 1505 1550 1595 1640 1685 1730 1775 1820 1865 1910 1955 2000\n21 66 111 156 201 246 291 177 381 426 471 516 561 606 651 696 741 786 831 876 921 966 1011 1056 1001 1146 1191 1278 1281 1326 1371 1416 1461 1506 1551 1596 1641 1686 1731 1745 1821 1866 1911 1956 2001\n22 67 112 157 202 247 292 1870 382 427 472 517 562 607 652 697 742 787 832 877 922 967 1012 1057 1102 1147 1192 1237 1282 1327 1372 1417 1462 1507 1552 1597 1642 1687 1732 1777 1822 1867 1409 523 2002\n23 68 159 158 203 248 293 338 383 428 473 518 563 608 653 1433 743 1555 833 878 1701 466 1013 1058 1103 1148 1193 1238 1283 1328 1373 1418 1463 1508 1553 1598 1643 1688 1733 1778 1823 1868 1913 1958 2003\n24 69 114 113 204 249 294 339 384 429 474 519 564 609 654 699 744 789 834 879 924 969 1014 1059 1104 1149 1194 1239 1284 1329 1374 1419 712 1509 1554 1599 1644 1689 1734 1779 1824 1869 1914 1959 2004\n25 70 115 160 205 250 295 340 385 430 475 520 565 610 655 700 745 790 835 880 1366 970 1015 1060 1105 1150 1195 1240 1285 1330 1375 1420 1465 1510 788 1600 1645 1690 1735 1780 1825 337 1915 1960 2005\n26 71 116 161 206 251 296 1917 386 431 476 521 566 611 656 701 746 791 836 881 926 971 1016 1061 1106 1151 1477 1241 1877 1331 1376 1782 1466 1078 1556 1601 1646 1691 1736 1781 1826 1871 1916 1961 873\n27 72 117 162 207 252 297 342 387 432 477 522 567 747 657 702 612 792 837 1066 927 972 1017 1062 1107 1152 1197 1242 1287 482 1377 1422 1467 1512 1557 1602 1647 1692 1737 1421 1827 1872 341 706 2007\n28 73 118 163 208 253 298 343 388 433 478 1957 568 613 658 703 748 793 1723 883 928 973 1018 1063 2008 1153 1198 1243 1288 1333 1378 1423 1468 1513 1558 1603 1648 1693 1738 1783 1828 1873 1918 1963 1108\n29 74 119 164 209 254 299 344 389 434 479 1096 569 614 659 704 749 794 839 884 929 974 1019 1064 1109 1154 1199 1244 1289 1334 1379 1424 1469 639 1559 1604 1649 1694 1739 635 1829 1874 1919 1964 863\n30 75 120 165 210 255 300 345 390 435 710 525 570 615 660 705 750 795 840 885 930 975 1020 1536 1110 1155 683 1245 1565 1335 1380 1425 1470 782 1560 1605 1650 1695 1740 1785 1830 1875 1920 1965 2010\n31 76 121 166 211 256 301 346 391 436 481 526 571 616 661 1962 751 796 841 260 931 976 1021 1307 1111 1156 1201 1246 1291 1336 1381 1426 1471 1516 1561 1606 1171 1696 1741 1786 1831 1876 1921 1966 1907\n32 77 122 167 212 257 302 347 392 437 1332 527 572 617 662 707 752 797 842 887 932 977 1022 1067 1112 1157 1202 1247 1292 1337 1382 1427 1472 1517 1562 1607 1652 1697 1742 1787 1832 1286 1922 1967 2012\n33 78 807 642 213 258 303 348 1274 438 483 528 573 618 663 708 495 798 843 888 933 978 1023 1068 1113 1158 1203 1248 1293 1338 1383 1428 1473 1518 1368 1608 1653 1698 1743 1788 1833 1878 1923 1968 2013\n34 79 124 169 214 259 304 349 394 439 484 529 574 461 664 709 754 799 844 889 934 979 1594 1069 1114 1159 1204 1249 1294 1339 1384 1429 1474 42 1564 1609 1654 1699 1744 1789 1834 1879 1924 1969 2014\n35 1341 125 170 215 886 305 350 395 440 485 530 316 620 665 480 755 800 1790 890 935 980 1025 1070 1115 505 1205 1250 1295 1340 237 1430 1475 1520 1290 1610 1655 1700 1776 845 1835 1880 1925 1970 2015\n1036 81 126 171 216 261 306 351 396 441 486 531 576 621 666 1532 756 801 846 891 936 981 1026 1071 1116 1161 1497 1251 1296 1209 1386 1431 1476 1521 1566 1611 1656 923 1746 1791 1836 1881 1926 1971 2016\n37 82 127 172 217 262 307 352 397 442 487 532 577 622 667 1464 757 802 847 892 937 982 1027 1072 1117 1162 1207 1252 1297 1342 1387 1432 1196 1522 1567 1612 1657 1702 1747 1792 1837 1882 1927 1972 2017\n38 83 128 173 314 263 308 1074 398 443 488 533 578 623 668 713 758 803 848 893 938 983 1028 1073 1118 178 1208 1253 1298 1343 1388 698 1478 1523 1568 1613 1658 1703 1748 1793 1838 1883 1928 1973 2018\n39 84 129 174 219 264 1031 354 399 444 489 534 579 624 669 714 759 804 849 894 939 1076 1029 353 1119 1164 80 1254 1299 1344 1389 1434 1479 1852 1569 1614 1659 1704 1749 1794 1839 1884 1929 1974 2019\n40 85 130 175 220 265 310 355 400 445 490 535 580 625 670 715 760 805 850 895 940 985 1030 1075 1120 1165 1210 1255 1300 1345 1390 1435 1480 1525 1570 1615 1660 1705 1750 1549 1840 1885 1930 1975 1101\n41 86 1357 176 221 266 311 356 401 446 491 536 581 1543 671 716 761 806 851 896 941 986 309 984 1121 1166 1211 1256 1301 1346 1391 1436 1481 1526 1571 1616 1661 1706 1751 1796 1841 1886 1931 1976 2021\n1519 87 132 336 222 267 312 357 402 447 492 537 582 627 672 717 1812 123 852 897 942 987 1032 1077 1122 1167 1212 1257 1302 1347 1392 1437 1482 1527 1572 1617 1662 1707 1752 1797 1842 1887 1932 911 2022\n43 88 133 1163 223 268 313 358 403 448 493 538 583 628 673 718 763 808 103 898 943 988 1033 1511 1123 1168 1213 1258 1303 1348 1393 1233 1483 1528 1573 1618 1663 1708 1753 1798 1843 1888 1933 1978 2023\n44 89 134 179 224 269 218 359 404 449 494 539 584 629 674 719 764 809 854 899 944 989 1034 1079 95 1169 1214 1259 1304 1349 1394 1439 1484 1529 1574 1619 1664 1709 1754 1799 1844 1889 1934 1979 2024\n45 90 455 1672 225 270 315 360 405 376 753 540 585 630 675 720 765 810 855 1769 945 990 1035 1080 1125 1170 1215 1260 1305 1350 1395 1440 1485 1530 1575 1620 1665 1710 1755 1800 1845 1890 1935 1980 2025\n",
        "output": "958442747\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 195,
        "task_id": 1088,
        "test_case_id": 7,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "47 3015\n1 48 95 142 189 236 283 330 377 424 1846 518 565 612 659 706 753 758 1802 894 941 988 1035 1082 1129 1176 1223 1270 1317 1364 1411 1458 1505 1552 1599 1646 1693 1740 1787 1834 1319 1928 1975 2022 2069 1947 2163\n237 49 96 143 190 2 284 331 378 425 472 519 566 613 660 564 754 801 848 895 942 989 1036 1083 1130 1177 1224 1271 1318 1365 1412 1459 1506 1553 1600 1647 1694 1741 1788 1835 1882 1929 1976 2023 2070 2117 2164\n3 50 97 144 358 238 623 597 379 426 473 5 567 614 900 708 755 802 849 896 943 990 1037 1084 1131 1178 1225 1272 1881 1366 1413 1067 1507 1554 1601 1722 1695 1742 1789 1836 1883 1930 1977 1545 2071 2118 2165\n4 51 98 145 192 239 286 333 380 427 474 521 568 615 662 709 756 1355 850 897 944 991 1038 1564 1737 1179 1226 313 1320 1367 995 1461 1508 1555 1602 1649 1696 1884 1790 1837 1743 1931 1978 2025 2072 2119 2166\n520 52 99 146 193 240 287 334 2007 428 475 522 569 616 663 710 757 804 851 898 945 1773 1039 1086 1133 1180 1227 890 1321 1368 1415 1462 1509 1556 1603 1650 1697 1744 1791 1838 1885 1932 1979 2026 2073 2120 2167\n6 53 2173 147 194 241 288 335 382 429 2115 523 570 617 664 711 800 805 852 899 946 993 1040 1087 1134 1181 1228 1275 1322 1778 1416 1463 1510 1557 1604 1651 1698 1745 1792 1839 1886 1933 1980 2027 2074 2121 64\n7 54 101 148 195 2170 289 1474 383 779 477 524 571 618 665 712 759 1094 853 661 947 292 1041 1088 1135 1182 1229 562 1323 1370 1417 1464 1511 1558 1605 1652 1699 1746 1793 1840 1887 1934 1981 2092 2075 2122 2169\n8 55 102 149 196 243 290 337 384 431 478 525 572 619 666 713 760 807 854 901 948 1414 1042 1089 1136 1183 1230 1277 1324 1371 1418 1465 1512 1559 1606 1653 1700 1769 1794 1841 1888 1935 1982 2029 2076 1305 242\n9 56 933 150 197 244 291 338 385 432 479 526 573 620 667 714 761 808 855 902 949 996 1043 1090 1137 1184 1231 1278 1325 1372 1419 1466 1513 1560 1607 1654 1701 1748 1795 1842 1901 1936 1983 2030 2077 2124 2171\n10 732 104 151 198 245 1708 339 386 433 480 527 574 621 668 1420 762 809 856 903 950 997 1044 1091 1138 1185 1232 1830 1326 1373 715 1467 1514 1049 1608 1655 1702 1749 1796 1843 1890 1937 1984 2031 2078 2125 2172\n11 58 105 152 199 246 293 340 387 434 481 528 575 622 669 716 763 810 857 904 951 998 1045 1092 1139 1186 1233 1280 1327 1374 1421 1468 1515 1562 1609 1656 1703 1750 1797 1844 1891 1938 1985 2032 2079 2126 100\n12 59 106 153 200 247 294 341 388 435 482 529 576 285 670 717 764 1689 858 905 952 999 1046 1093 1140 1187 1234 1281 1328 1375 1422 1469 1516 1563 1610 1657 1704 1751 1798 1845 1892 1939 1986 2033 2080 2127 1668\n13 60 107 154 201 248 295 342 389 608 559 530 577 624 671 718 765 812 859 906 953 1000 1047 806 1634 1188 1235 1282 1329 1376 1423 1470 1517 1085 1611 1658 1705 1752 1799 471 1893 1940 1987 2034 2081 2128 2175\n14 33 108 155 202 249 296 343 390 437 484 531 578 353 672 719 766 813 860 907 954 1001 1048 1095 1142 1189 1236 1283 1330 1377 1424 1471 1518 1565 1612 1659 1706 1753 1800 1847 1894 1941 1988 2035 2082 2129 2176\n15 62 109 156 203 250 297 344 391 438 485 532 579 2107 673 720 767 814 861 908 955 1002 1561 1096 1143 1190 1237 1284 1331 1378 1425 1472 1519 1566 1613 1660 1707 1754 1801 1848 1895 1942 1989 2036 2083 2130 402\n16 1686 110 157 204 251 298 345 392 439 486 533 580 627 674 1206 768 815 862 909 956 1003 1050 1097 2108 1191 1238 1285 1332 1379 1426 1473 1520 1567 1614 1661 994 1755 847 1849 1896 1943 1990 2037 2084 2131 2178\n17 2168 111 158 205 252 299 346 393 440 487 534 581 628 675 722 769 816 863 910 1339 1004 1051 1098 1145 1192 1239 1286 1333 1380 1427 336 1521 1568 1615 1662 1709 1756 1803 1850 1897 1944 1991 2038 2085 2132 2179\n18 65 112 502 206 253 300 347 394 441 488 535 582 629 557 723 770 817 864 911 958 1005 1052 1099 1259 1193 1240 789 1334 1381 259 1475 1522 1569 1616 1663 1710 1757 1804 1851 1898 1945 1992 2039 2086 2133 2180\n19 66 113 160 207 254 301 117 395 442 489 536 583 630 677 724 771 818 865 912 959 1006 1053 1100 1147 1194 1241 1288 1335 1382 1429 1476 1523 1570 1617 1664 1711 1758 1805 1852 1899 1946 213 2040 2087 2134 2181\n20 67 1199 161 208 255 302 349 396 443 490 537 584 631 678 725 772 819 866 913 960 1007 1054 1101 1497 1195 1242 1289 1336 1383 1430 1477 1524 1571 1618 1665 1712 1759 1806 1487 1900 2116 1994 2041 2088 2135 2182\n21 68 115 162 209 256 303 350 397 444 491 538 585 632 679 726 773 820 867 914 961 1008 1055 89 1070 1196 1243 1290 1337 1384 1018 1478 1525 1572 1619 1666 1713 1760 1807 1854 1889 1948 1995 2042 2089 1342 2183\n22 69 116 163 210 257 304 351 398 445 492 539 586 633 680 727 774 821 868 915 962 1009 1056 1103 1150 1197 1244 1291 1338 1385 1432 1479 1526 1573 1620 1667 741 1761 1808 1855 1902 1949 1996 2043 2090 2137 2184\n2192 70 348 164 211 258 305 352 399 446 493 838 587 634 681 728 775 822 869 1021 1868 1010 1057 1104 1151 1198 1245 1292 957 1386 1433 1480 1527 1574 1621 2174 1715 1762 1809 1856 1903 1950 1997 2044 2091 2138 2185\n24 71 992 165 212 1428 306 1221 400 447 494 541 588 635 682 729 776 823 870 917 964 1011 1058 1105 1152 114 1246 1293 1340 1387 1434 1481 1528 1575 1622 1669 1716 1763 1810 1857 1904 1951 1998 2045 2028 2139 1210\n25 72 119 166 1993 260 307 354 401 448 495 542 589 636 683 730 777 824 871 918 965 1012 1059 1106 1153 1200 1247 1294 1341 1388 1435 1482 1529 1576 1623 1670 1717 1764 1811 1858 1905 1952 459 2046 2093 2140 2187\n26 73 120 167 214 261 308 355 2177 1031 496 543 590 637 684 546 778 825 872 919 966 1013 1060 1107 1154 1201 1729 1295 2136 1389 1436 1483 1530 1577 1624 1671 1718 1765 1812 1859 1906 1953 2000 2047 2094 2141 2188\n27 74 121 168 215 262 702 356 403 450 497 544 591 638 685 57 430 826 873 920 967 1014 1061 1108 1155 1202 1249 1296 1343 1390 1437 1484 1531 1578 1625 1672 1719 1766 1813 1860 1907 1954 2001 2048 2095 2142 2189\n28 75 122 169 216 263 2105 357 404 451 498 545 592 639 686 733 780 827 874 921 968 1015 1062 1109 1156 1203 1250 1297 1344 1391 1438 1485 1532 1579 1626 1673 316 1767 1814 2015 1908 1955 2002 2049 2096 2143 2190\n29 76 123 170 217 264 311 191 405 452 499 731 593 500 687 734 781 828 875 922 969 1016 1063 1110 1157 1204 1251 1298 1345 1392 1439 1486 1533 1580 1627 1674 1721 1768 1815 1862 1909 1956 1169 2050 2097 2144 2191\n30 77 124 171 218 265 312 359 406 453 640 547 594 641 688 735 782 829 876 923 970 1017 1064 981 1158 1205 1252 1299 1346 1393 1440 1853 1534 1581 1628 1675 1648 1747 1816 1863 1910 1957 2004 2051 2098 2145 23\n31 78 125 172 219 266 1273 360 407 454 501 548 595 642 689 736 783 830 877 924 971 1431 1065 507 1159 721 1253 1300 1347 1394 1441 1488 1535 1582 1629 1676 1723 1770 1817 1864 1911 1958 2005 2052 2099 2146 2193\n32 79 126 173 220 267 314 361 408 455 159 549 596 643 690 737 784 831 878 925 972 1019 1066 1113 1160 1207 1254 1301 1348 1395 1442 1489 1536 1583 1630 1677 1724 1771 1818 1865 1912 1959 2006 2053 2100 2147 2194\n61 80 127 174 221 268 315 362 409 456 503 550 332 644 691 738 785 832 879 926 973 1020 1460 1114 1161 1208 1255 1302 1349 1396 1443 1490 1537 1584 1631 1678 1725 1772 1256 1866 1913 1960 381 2054 2101 2148 2195\n34 81 128 175 222 269 1720 363 410 457 504 551 598 645 692 739 786 833 880 927 974 916 1068 1115 1162 1209 1819 1303 1350 1397 1444 1491 1538 1585 1632 1679 1726 118 1820 1867 1914 1961 2056 2055 2102 2149 2196\n35 82 129 176 223 270 317 364 411 458 505 552 599 646 693 740 787 932 881 928 975 1022 1069 1116 1163 2186 1257 1304 310 1398 1445 1492 1539 1586 1633 1680 1727 1774 1821 963 1915 1962 2009 2008 2103 2065 2197\n36 83 130 177 224 271 318 365 412 1999 506 553 600 647 694 1714 788 835 882 929 976 1023 1149 1117 1164 1211 1258 2123 1352 1399 1446 1493 1540 1587 1141 1681 1728 1775 1822 1869 1916 1963 2010 2057 2104 2151 2198\n37 84 131 178 225 272 319 366 413 460 1112 554 601 648 695 742 1287 836 883 930 977 1024 1071 1118 1165 1212 1146 1306 1353 1400 1447 1494 1541 1588 1635 1682 1248 1776 1823 1870 1917 1964 2011 2058 1351 2152 2199\n38 85 132 179 226 273 320 367 414 461 508 555 602 649 696 743 790 837 884 931 978 1025 1072 1119 1166 1213 1260 1307 1354 1401 1448 1495 1542 1589 1636 1683 1730 1777 1824 1871 1918 1965 2012 2059 2106 2153 2200\n39 86 133 180 227 274 321 368 415 462 509 556 603 650 697 744 791 540 885 834 979 1026 1073 1120 1167 1214 1261 1308 803 1402 1449 1496 1543 1590 1637 1684 1731 1369 1825 1872 1919 1966 2013 2060 626 2154 2201\n40 87 134 181 228 275 322 369 416 463 510 676 604 651 698 745 792 839 886 103 980 1027 1074 1121 1168 1215 1262 1309 1356 1403 1450 1148 1544 1591 1638 1685 1732 1779 1826 1873 1920 1967 2014 2061 1144 2155 2202\n41 88 135 182 229 276 323 370 417 464 511 558 605 652 699 746 793 840 887 934 1111 1028 1075 1122 2003 1216 1263 1310 1357 1404 1451 1498 2024 1592 1639 63 1733 1780 1827 1874 1921 1968 1861 2062 2109 658 2203\n42 1102 136 183 230 277 324 371 1034 465 512 1081 606 653 700 747 794 841 888 935 982 1029 1076 1123 1170 1217 1264 1311 1358 1405 1452 1499 1546 1593 1640 1687 1734 1781 1828 1875 1922 1969 2016 2063 2110 2157 2204\n43 90 137 184 231 278 325 372 281 466 513 560 607 654 701 748 795 842 889 936 983 1030 1077 1124 1171 1218 1265 1312 1359 1406 1453 1500 1547 1594 1641 1688 1735 1782 1829 1876 1923 1970 2017 2064 2111 2158 2205\n44 91 138 185 232 279 326 373 420 467 514 561 436 655 309 749 796 843 1274 937 984 449 1078 1125 1172 1219 1266 1313 1360 1407 1454 1501 1548 1595 1642 811 1736 1783 1279 1877 1924 1971 2018 2150 2112 2159 2206\n45 92 139 186 233 280 327 374 421 468 515 1276 609 656 703 750 797 844 891 938 985 1032 1079 1126 1173 1220 1267 1314 1361 1408 1455 1502 1549 1596 1643 1690 1132 1784 1831 1878 1925 1972 2019 2066 2113 2160 2207\n46 93 140 187 234 419 328 375 422 469 516 563 610 657 704 751 798 845 892 939 986 1033 1080 1127 1174 625 1268 1315 1362 1409 1456 1503 1550 1597 1644 1691 1738 1785 1832 1879 1926 1973 2020 2067 2114 2161 2208\n47 94 141 188 235 282 329 376 423 470 517 707 611 2156 705 752 799 846 893 940 987 418 483 1128 1175 1222 1269 1316 1363 1410 1457 1504 1551 1598 1645 1692 1739 1786 1833 1880 1927 1974 2021 2068 476 2162 2209\n",
        "output": "631819933\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 196,
        "task_id": 1088,
        "test_case_id": 8,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "40 2959\n1 41 81 121 537 201 241 281 321 361 401 1227 481 521 561 601 641 681 721 761 801 665 881 921 961 1001 1041 1081 1121 855 1201 1241 1281 1321 1361 1520 1441 1481 1521 1561\n2 891 82 525 162 202 242 282 322 362 402 442 482 522 562 602 642 682 722 762 802 842 994 922 962 1002 1042 1082 1122 1162 1202 1242 1282 1322 1362 1402 1442 1482 1522 1562\n1090 43 83 123 163 203 243 283 323 363 403 443 483 523 563 603 643 795 723 763 803 843 883 923 963 1003 1043 1083 1123 1163 1184 1243 1283 1323 236 1403 1443 1483 1523 1563\n4 44 84 124 394 204 244 284 324 364 404 444 484 524 564 604 644 799 724 1097 804 844 418 924 964 1068 1044 1084 1124 1164 264 1244 1284 1324 1364 1404 1444 1484 1524 1564\n5 45 85 125 165 205 245 285 325 365 405 445 485 122 565 605 645 685 725 765 805 1249 885 925 965 1005 1045 1085 1125 1165 1205 93 1285 1325 718 1405 1445 1485 1525 1565\n6 46 86 126 166 206 246 286 326 1496 406 446 486 944 566 606 646 686 936 1109 806 846 143 926 966 1006 1046 1086 188 1166 1206 39 1286 1326 1366 1406 351 1486 1526 1566\n7 47 456 127 167 207 247 287 327 367 407 447 487 527 567 607 647 687 727 767 807 847 887 927 967 1007 1047 1087 1127 1167 1207 1247 1287 1327 1367 689 1447 1487 1527 1567\n8 48 88 128 168 208 248 288 328 368 408 448 488 398 568 608 648 688 728 768 808 848 888 928 968 1008 1048 1088 1128 1168 1208 1248 1288 309 1368 1408 1448 1488 1528 1568\n9 49 89 129 169 311 249 289 329 369 409 449 489 529 569 609 649 1407 729 769 809 849 889 929 969 1009 1049 1089 1129 1169 1209 216 1092 1329 1369 1409 1449 1489 1529 1569\n10 50 90 130 1262 176 250 290 330 370 410 450 490 530 570 610 650 690 730 770 810 850 890 930 970 1010 1050 3 1130 1170 1210 31 1290 1330 1370 1410 1450 1490 1530 1154\n11 51 91 131 171 211 251 291 331 371 411 451 491 531 571 611 651 691 731 771 811 851 42 931 971 1011 1051 191 1131 1171 1211 1251 1291 387 1371 1411 1451 1491 1531 220\n12 52 92 132 172 212 252 292 332 372 412 452 492 532 572 612 652 692 732 547 812 852 892 586 972 1012 1052 1289 1132 1172 1212 1252 137 30 1372 1412 1452 1492 1532 1572\n13 53 1064 133 173 213 253 293 333 373 413 453 493 533 573 613 653 693 733 773 813 853 893 933 973 1013 1053 1093 1133 1173 1213 1253 1293 1333 1373 1413 1453 1493 1533 1573\n14 54 94 134 174 214 254 294 419 374 414 1268 494 534 574 614 654 694 734 774 814 854 894 1547 974 1014 1054 1094 1134 1174 1214 1254 1294 1334 1374 1414 180 1494 1534 1574\n15 55 95 135 175 215 255 295 335 375 415 455 495 535 575 615 655 695 735 775 32 1161 1556 935 1397 1015 1055 1095 1135 1175 1215 1255 1295 1335 1375 1415 1455 1495 1535 1575\n16 56 96 136 210 473 256 296 336 376 416 87 138 536 576 616 656 696 698 776 816 856 896 726 976 1016 1056 1096 1136 1176 1216 1256 1296 1336 1376 1515 1456 366 1536 1576\n17 57 97 1477 177 1583 257 297 340 377 417 457 497 161 577 617 657 697 737 777 817 857 897 937 977 1017 701 764 1137 1177 1217 1257 1297 1337 1377 1417 1457 1497 1537 1577\n18 58 98 496 178 218 258 298 338 378 884 458 498 440 578 618 658 736 738 778 818 858 1328 938 978 1018 1058 1098 1138 1178 1218 1258 948 1338 1378 1418 1458 1498 1538 65\n19 59 99 139 179 219 259 299 339 379 334 270 499 539 579 619 190 699 739 779 819 859 899 939 979 1019 1059 1099 1139 1179 1219 1259 1299 1339 70 1419 1459 1499 1539 1579\n20 60 100 140 1454 1571 260 300 337 380 420 460 1072 540 580 620 660 700 740 160 820 860 900 940 980 1020 1060 1100 1140 1180 1220 1260 1300 1340 1380 1420 1460 1500 1540 1580\n21 61 101 141 181 221 261 301 33 1039 421 461 501 659 581 621 661 1057 741 781 821 861 901 941 981 1021 1061 587 1141 1181 1221 1261 1301 1341 1381 1421 1461 1501 1541 1581\n22 62 102 142 182 222 262 302 1148 382 422 462 502 542 582 622 662 702 742 782 822 862 902 942 982 1022 1062 1102 1142 1182 1222 170 1302 1342 1382 1422 1462 1502 217 1582\n23 63 871 886 183 223 263 303 343 383 423 463 1275 543 583 623 663 703 743 783 823 863 903 943 983 1023 1063 1103 1143 1183 1223 1263 1303 1343 1383 1423 1463 1503 1543 1542\n24 64 104 144 184 224 1204 304 344 384 424 464 504 544 584 624 664 704 744 784 824 864 904 526 984 1024 1245 1104 1144 1203 1224 1264 1304 1344 1384 990 1464 1504 431 1584\n25 1578 105 145 185 225 265 305 345 385 538 465 505 545 585 625 841 705 745 785 825 865 905 945 985 313 1065 1105 1145 1185 1225 1265 1305 1345 1385 1425 599 1505 1545 1585\n26 66 106 146 186 226 266 815 346 386 426 466 506 546 932 275 666 706 746 786 826 866 906 946 986 1026 1066 1106 1146 1186 1226 1266 1306 1346 1386 1426 1466 1506 787 1586\n27 67 107 147 187 227 267 307 347 1331 427 467 507 772 1101 627 667 707 747 1546 827 867 907 947 987 1027 1067 1107 1147 1187 441 1267 1307 1347 1387 1427 1467 1507 934 1587\n28 68 108 148 1126 228 268 308 348 388 428 468 508 548 588 628 668 708 748 788 828 868 908 1298 988 1028 1004 1108 149 1188 1228 454 1308 1348 1388 1428 1468 1508 1548 1588\n29 69 109 277 189 229 269 898 349 389 429 469 509 549 589 629 669 709 749 789 829 869 909 949 989 1029 1069 766 1149 1189 1229 1269 1309 1349 1389 1429 1469 1509 1549 1589\n1332 1379 110 150 1197 230 459 310 350 1280 430 470 510 550 590 630 670 710 750 1550 830 870 910 950 1424 1030 1070 1110 1150 1190 1230 1270 1310 1350 1390 1430 1470 1510 790 1590\n1250 71 111 151 1091 231 271 1025 1446 391 1544 471 511 551 591 631 671 711 751 791 831 103 911 951 991 1031 1071 1111 1151 1191 1231 1271 1311 1351 1391 1431 1471 1511 1551 1591\n306 72 112 152 192 232 272 312 975 392 432 472 512 552 592 632 672 712 752 792 832 872 912 952 992 1032 500 1112 1152 1192 1232 1272 1312 1352 1392 1432 1472 1512 1552 1592\n341 73 113 153 193 233 273 209 353 393 433 845 513 553 593 633 673 713 753 793 833 873 913 953 993 1033 1073 1113 1153 1193 1233 1273 1313 1353 1393 1433 1473 1513 1553 1593\n34 74 114 154 194 234 274 314 354 164 434 474 514 554 594 634 674 342 754 794 834 874 914 954 882 1034 1074 1114 1570 1194 1234 1274 1314 1354 1394 1434 1474 381 1554 1594\n35 75 115 1276 195 235 626 315 355 395 435 475 515 1278 595 635 675 715 755 683 835 875 915 955 995 1035 1075 1115 1155 1195 1235 503 1315 1355 1395 1435 1475 1416 1555 1595\n36 1277 116 156 196 1363 276 316 356 396 436 476 516 556 596 636 676 716 756 796 836 876 916 956 996 1036 1076 1116 1156 1196 1236 155 1316 1356 1396 1436 1476 1516 895 1596\n37 77 117 157 197 237 714 317 357 397 437 477 517 557 597 637 677 717 757 797 837 877 917 957 997 1037 1077 1117 1157 541 1237 76 1317 1357 352 1437 1292 1517 1557 1597\n38 78 118 158 198 238 278 318 358 528 438 478 518 558 598 638 678 1365 758 798 838 878 918 958 998 1038 1078 1118 1158 1198 1238 555 1318 1358 1398 1438 1478 1518 1558 1598\n1246 79 119 159 199 239 279 319 359 399 439 479 519 559 1465 639 679 719 759 684 839 879 919 959 999 1514 1079 1119 1159 1199 1239 1279 1319 1359 1399 1439 1479 1519 1559 1599\n40 80 120 780 200 240 280 320 360 400 425 480 520 560 600 640 680 720 760 800 840 880 920 960 1000 1040 1080 1120 1160 1200 1240 390 1320 1360 1400 1440 1480 1401 1560 1600\n",
        "output": "504900914\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 197,
        "task_id": 1088,
        "test_case_id": 9,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "43 3578\n1 1563 87 130 173 661 259 302 345 1190 431 474 517 560 85 646 689 732 775 818 861 1359 947 990 1033 1076 1119 1162 1205 1248 1291 1334 1377 1420 1463 1506 1549 1592 1635 1678 1721 1764 1807\n2 45 88 131 174 217 260 303 346 389 432 475 235 561 1246 647 690 733 776 819 862 905 948 991 1034 1077 1120 1163 1206 1249 1292 1335 1378 1421 1464 1507 1550 1593 1636 1679 1722 1765 1808\n3 46 89 132 175 218 261 304 347 390 433 476 519 562 605 648 691 734 777 820 863 906 949 992 1035 1078 1121 1164 1207 1250 1293 1336 1379 1422 1465 1508 1551 1594 1637 1680 1723 964 154\n4 47 90 133 176 219 262 305 348 391 434 477 520 563 606 649 692 735 778 821 864 907 950 993 1036 1079 1122 1165 1208 1251 1294 1337 1380 1322 1466 1509 1552 1595 1638 1681 1724 1767 1810\n5 48 91 134 177 220 263 306 349 392 435 478 521 564 607 650 693 736 779 822 865 908 951 994 1037 1080 1123 412 1209 1252 579 1338 1381 1510 1467 1424 1553 1596 1639 1682 1725 318 1811\n6 49 92 1216 178 221 264 307 350 393 436 479 84 565 608 711 694 737 780 823 866 909 952 995 1038 1081 1124 1167 1210 1253 1296 1339 1382 1425 1468 1515 1554 1597 1640 1683 1726 1307 888\n7 50 93 136 291 222 1763 308 351 394 437 754 523 566 856 1317 695 738 781 824 867 910 953 1512 1039 1082 1125 1168 385 1254 808 1340 1383 1426 1052 996 1555 1598 1641 1684 1727 1770 1813\n8 51 94 137 180 223 266 309 352 395 438 481 524 56 610 653 696 739 782 825 868 911 954 997 1483 1083 1126 1169 584 1255 1298 1341 1384 1427 1137 1513 1613 1599 1642 354 1728 1771 1814\n9 52 95 138 181 224 267 310 353 1470 439 482 525 568 611 654 697 740 1362 826 869 912 955 998 1041 1084 1127 1170 1213 1256 1299 1342 1385 1428 1471 1514 1557 1600 1643 1686 1729 1772 1815\n10 53 96 139 182 225 268 311 1685 397 440 483 526 569 612 655 698 741 784 827 1556 913 956 999 1042 1085 1128 1171 443 1257 1300 1343 1802 1429 1472 1511 1558 1601 1644 1687 1730 1773 1816\n11 54 97 140 183 226 269 1631 355 398 441 484 527 570 613 656 699 742 785 828 871 914 215 1000 1043 1086 1129 1172 547 1258 1301 1344 1387 1430 1473 1516 1559 588 1645 1688 1731 1774 1817\n12 55 98 141 184 227 270 313 356 399 442 485 528 571 614 657 700 743 786 829 103 915 958 1348 1044 1087 1130 1173 135 1259 1302 1345 1388 1431 1474 1517 1560 1603 1646 1689 1732 1775 1818\n13 567 99 142 185 228 271 314 357 400 1214 486 529 514 192 658 701 1697 787 830 873 916 959 1002 1045 1088 1131 1174 1217 1260 1303 1346 1389 1432 1475 1518 1561 1604 1647 1690 1733 1776 1819\n1221 57 100 143 186 229 272 315 358 401 444 487 530 573 616 659 702 745 788 831 874 917 960 1003 1046 1089 1132 1175 232 1261 1304 1347 513 1433 1476 1519 1562 1605 1648 1691 1734 1777 1820\n15 58 101 144 187 230 273 316 359 402 445 488 531 574 617 660 703 746 789 832 875 918 961 1004 1047 1090 1133 1176 1219 1262 1305 1001 1391 1434 1477 1520 339 1606 1649 1692 1735 1778 1821\n16 59 102 145 188 231 200 843 360 403 446 489 532 575 618 216 704 1199 790 833 1193 919 962 1005 1048 1091 1134 1177 1220 1263 1306 1349 1392 1435 1478 1521 1564 1607 1650 1693 1736 1779 1587\n17 60 872 146 189 280 275 1768 361 404 447 490 533 576 619 662 705 748 791 834 877 920 963 1006 1049 1092 1135 1178 124 1264 1769 1350 1393 1436 1479 1522 1565 1608 1651 1694 1737 1780 1823\n18 61 104 147 190 233 276 319 362 405 939 491 534 1582 620 663 706 749 792 835 878 921 1766 1007 1050 1093 1622 1179 1222 1265 1308 1351 1394 1437 1480 1523 1566 1609 1652 1695 1738 1781 1824\n19 62 63 148 191 234 277 472 363 406 449 492 535 578 621 664 1634 750 793 836 879 922 965 1008 1051 1094 396 1180 1223 1266 1309 1352 1028 1438 1481 1524 1567 1610 1653 1696 1739 1782 1825\n20 105 106 149 615 518 278 321 364 407 450 493 536 1295 622 665 708 751 794 837 880 923 966 1009 1469 1095 1138 1181 1224 1267 1310 1353 1396 1439 1482 1525 1568 1611 1654 744 1740 1783 1826\n715 64 107 150 193 883 279 322 365 408 451 494 537 580 623 666 709 752 384 838 557 924 967 1010 1053 1096 1139 1182 1225 1268 1311 1354 1397 1440 1040 1526 1569 1612 1655 1698 1741 1784 1827\n22 65 108 151 1583 237 1218 323 366 409 452 495 897 581 624 667 710 1105 796 839 882 925 968 1011 1054 1097 1140 1183 1226 1269 1312 1355 1398 941 1484 1527 1570 870 1656 1537 1742 1785 1828\n23 66 109 152 195 238 281 324 367 410 453 496 539 603 625 668 651 1197 797 840 236 926 969 1012 1055 1098 1141 1184 1227 1270 1313 1356 1399 1442 1485 1528 1571 1614 1657 1700 1743 1786 1829\n24 67 110 153 196 683 1204 325 368 411 454 497 540 583 626 669 712 755 798 841 884 927 970 1013 1056 1099 1142 1185 1228 1271 1314 1357 1400 1443 1486 1529 1572 1615 1658 1701 1744 1787 1830\n25 68 111 1809 197 240 283 326 369 1166 1331 498 541 1212 627 670 713 756 799 842 885 928 971 1014 1057 1100 1143 1186 1229 1272 1315 1358 1401 1444 1624 1530 1573 1616 1659 1702 1745 1788 1831\n26 69 112 155 198 241 284 327 370 413 1663 499 1413 673 628 671 714 757 800 317 886 274 972 1015 1058 1101 1144 1187 1230 1273 1316 904 1402 1445 1488 1531 1574 1617 1660 1703 1746 1789 1832\n27 70 113 156 199 242 285 328 371 414 457 500 543 586 629 672 21 758 801 844 887 930 973 1016 1059 1102 1145 1188 1231 1274 652 1360 1403 1446 1489 1532 1575 1075 1661 1704 1747 1790 1833\n28 71 114 157 929 243 286 329 372 415 458 501 544 587 630 585 716 759 802 845 1812 931 974 1017 1060 1103 1146 1189 1232 1275 1318 1361 1404 1447 1490 1533 1576 1619 1662 1705 1748 1791 1834\n29 686 115 158 201 244 287 330 373 416 459 502 545 1602 1589 674 717 760 803 846 889 932 975 1018 1061 1104 1147 388 1233 1276 1319 783 1405 1448 1491 1534 1577 1620 986 1112 1749 1792 1835\n30 73 116 159 202 245 288 331 374 417 460 503 546 589 632 675 718 761 804 900 890 933 976 1019 1062 753 1148 1191 1234 1277 1320 1363 1406 1449 1492 1535 1578 1621 1664 1707 1750 469 1836\n31 74 117 160 203 246 289 1793 375 418 461 504 1215 590 633 676 719 762 805 848 891 934 977 1020 1063 1106 1149 1192 1235 1278 1321 1364 1407 1450 1493 1536 1579 1136 1665 1708 1751 1794 1837\n32 75 118 161 204 247 290 333 376 419 462 505 548 591 634 677 720 763 1674 849 892 935 978 1021 1064 1107 1150 876 1236 1279 1423 1365 1408 1451 725 1699 1580 1623 1666 1709 1752 1795 1838\n33 76 119 162 205 248 179 334 377 420 463 506 549 592 635 678 721 764 1074 850 893 936 979 1022 1065 1108 1151 1194 1237 1280 1323 1366 1409 1452 1495 1538 1581 1487 1667 1710 1753 1796 1839\n34 77 120 163 206 249 292 335 378 421 464 507 550 593 636 679 722 765 1297 851 894 937 980 1023 1066 1109 1152 1195 1238 1281 1324 1367 1410 1453 1496 1539 577 1625 1668 1711 1754 1797 1840\n35 78 121 164 207 250 293 336 379 422 465 508 551 594 1670 680 723 766 809 852 895 938 981 1024 1067 1110 1153 1196 1239 1282 1325 682 1411 1454 1497 1540 194 1626 1669 1712 1591 1798 1841\n36 79 122 165 208 251 294 337 380 423 466 509 552 595 638 681 724 767 810 853 896 448 982 1025 1068 1111 1154 480 1240 1283 1326 1369 1412 1455 1498 1541 1584 1627 637 1713 1756 1799 1842\n37 80 123 166 209 252 295 338 381 424 467 510 553 596 639 1368 1494 768 811 854 538 940 983 1026 1069 1706 1155 1198 1241 1284 1327 1370 542 1456 1499 1542 1585 1628 1671 1714 1757 1800 1843\n38 81 14 167 210 253 296 44 382 425 468 511 554 597 640 239 726 769 812 855 898 1441 984 1027 1070 1113 1156 747 1242 1285 1328 1371 1414 1457 1500 1543 1586 1629 1672 1715 1758 1801 1844\n39 82 125 168 211 254 297 340 383 426 332 512 555 598 641 684 727 770 813 609 899 942 985 1395 1071 1114 1157 1200 1243 1286 1329 1372 1415 1458 1501 1544 1822 1630 1673 1716 1759 1386 1845\n40 83 126 169 212 255 298 341 795 427 470 1390 556 599 642 685 728 771 814 857 847 943 456 1029 1072 1115 1158 1201 1244 1287 1330 1373 1416 1459 1502 1545 1588 312 806 1717 1760 1803 1846\n41 522 127 170 213 256 299 342 1211 428 471 572 881 600 643 72 729 772 815 858 901 944 987 1030 1073 1116 1159 1202 1245 1288 455 1374 1417 1460 1503 1546 631 1632 1675 1718 1761 1804 1847\n42 582 128 171 214 257 300 343 386 429 320 515 558 601 644 687 730 773 816 859 902 945 988 1031 807 1117 1160 1203 604 1289 1332 1375 1418 1461 1504 1547 1590 1633 1676 1719 1762 1805 1848\n43 86 129 172 957 258 301 344 387 430 473 516 559 602 645 688 731 774 817 860 903 946 989 1032 1618 1118 1161 282 1247 1290 1333 1376 1419 1462 1505 1548 1755 707 1677 1720 265 1806 1849\n",
        "output": "827660031\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 198,
        "task_id": 1088,
        "test_case_id": 10,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "49 4643\n1 50 99 148 197 246 295 344 393 442 491 540 589 638 687 736 785 834 883 932 981 1030 1079 1128 1177 1226 1275 1324 1373 1422 1471 1520 1569 1618 1667 1716 1765 1814 1863 1912 1961 2010 2059 2108 2157 2185 2255 2304 2353\n2 51 742 149 198 247 296 345 394 443 1148 541 590 639 688 737 786 835 1431 933 982 1031 1080 1129 1178 1227 1276 1325 1374 1423 1472 1521 1570 1619 1668 1717 1766 1815 1864 1913 1962 2011 2060 1028 2158 2207 2256 2305 2354\n3 52 101 150 199 248 297 346 395 444 493 542 591 640 689 738 787 836 885 934 983 1032 1081 1130 1179 1228 1277 1326 1375 1424 767 1522 1571 1620 1669 1718 1767 1816 1865 1914 1963 2012 2061 2110 2159 2208 2257 1341 2355\n4 53 102 151 200 249 298 347 396 445 494 543 592 641 690 739 788 837 886 935 984 1033 1082 1131 1180 1229 1278 1327 1376 1425 1474 1523 1572 1621 1670 1719 1768 1817 1866 1915 1964 2013 2062 2111 2160 2209 2258 2307 2356\n5 54 1536 152 2369 250 299 348 397 446 495 544 762 642 691 740 789 838 887 936 985 1034 1083 1132 1181 1230 1279 1328 1377 1426 1475 1691 1573 1622 1671 1720 1769 1818 1867 1916 1965 2014 1888 2112 2161 1904 2259 2308 1852\n6 1005 104 153 202 251 300 349 398 447 496 545 594 643 692 741 790 839 1380 937 986 1035 1084 1133 1182 1231 1280 2327 1378 1427 1476 1733 1574 1623 1672 2289 1770 1819 1868 1917 1966 2015 2064 2113 2162 2211 2260 2309 137\n7 56 105 154 203 252 301 350 399 448 497 546 595 644 693 2206 791 840 889 938 987 1036 1085 1134 1183 1232 1281 1330 1379 1428 1477 1526 1575 1624 1673 1722 1771 1820 2302 1918 1967 2016 2065 2114 2163 2212 2261 2310 2359\n8 57 106 155 204 1463 302 351 400 449 498 547 596 645 694 743 792 841 890 939 988 1037 1086 1135 1184 1233 1282 1331 888 1429 1478 1527 1576 1625 1674 2115 1772 1821 1870 1919 1968 2017 2066 1723 2164 2213 2262 2311 2360\n1104 58 107 39 205 254 303 352 401 450 776 548 597 646 695 744 793 842 891 940 989 1038 1087 1136 1185 1234 1283 1332 1381 1430 1479 1528 1577 1626 1675 1724 1773 1822 1871 652 1969 2018 2067 2116 667 2214 2263 2312 2361\n10 2196 108 157 206 255 304 292 854 451 500 549 598 647 696 745 794 843 892 941 990 1039 1088 1137 1186 1235 1284 1586 1382 884 1480 1529 1578 1627 1676 1725 1774 1823 1872 1921 1970 2019 2068 2117 2166 2215 2264 2313 2362\n11 60 109 158 207 256 305 354 403 452 501 550 599 648 697 746 795 844 893 942 991 1040 1089 1138 1187 1236 1285 1124 1383 1432 1481 1530 1579 1628 1677 1726 1775 1824 1873 1922 1971 2020 672 2118 2167 2216 2265 2314 2363\n12 61 110 159 208 257 306 355 404 453 502 551 600 649 698 747 796 845 1310 943 992 1041 1090 1139 1188 1237 1286 1335 1384 233 1482 1531 1580 1629 1678 1727 1776 1825 1874 1923 1972 2021 2070 2119 2168 2217 2266 2315 2364\n13 62 111 160 209 258 307 356 405 454 503 552 601 650 2287 748 797 846 895 944 993 1042 1091 1140 1189 1238 1287 1336 1385 1434 1483 1532 1581 1630 1679 1728 1470 1826 1875 1924 1973 2022 2071 2120 2169 2218 2267 2316 2365\n14 63 112 161 210 259 308 357 406 455 504 553 602 651 700 749 798 847 896 945 994 1043 1092 1141 1190 1239 1288 1337 1386 1435 266 180 1582 1631 1680 1729 1778 1827 1876 1925 1974 2023 2072 2121 2170 2219 2268 2317 2366\n15 64 113 162 211 260 309 358 126 456 505 554 603 1920 701 666 799 848 897 946 995 1044 1093 1142 1544 1240 1289 1338 1387 1436 1485 1534 1583 1632 1681 1730 509 1828 1877 1926 1975 2024 2073 2122 2171 2220 2269 2318 2367\n16 65 114 163 212 261 310 359 408 457 506 555 604 653 702 751 800 849 898 947 996 1045 1094 1143 874 1241 1290 1339 1388 1437 1486 1535 1584 1633 1682 1731 1780 1829 1878 1927 1976 2025 2074 2123 2172 2221 2270 860 2368\n17 66 115 164 213 262 311 360 409 458 507 556 605 654 703 752 801 624 899 948 997 1046 1095 1144 1193 1242 1291 1340 1389 1438 1487 103 1585 1634 1683 1732 1781 1830 729 1928 1977 2026 2075 2124 2173 2222 2271 2320 201\n18 67 116 165 214 263 312 361 410 459 508 1394 606 655 704 753 802 851 900 949 998 1047 1096 1145 1194 1243 1292 2306 1390 1439 1488 1537 1333 1635 1684 1525 1782 1831 1880 1929 1978 2027 2076 2125 2174 2223 2272 2321 2370\n19 68 117 166 215 264 313 362 411 460 1779 558 959 656 705 754 803 852 901 950 999 1048 1097 1146 1195 1244 1293 1342 1391 1440 1489 1538 1587 1636 1685 1734 1783 1352 1881 1930 1979 2028 2077 2126 2175 2224 2273 2322 2371\n20 69 118 167 216 265 314 363 412 461 510 559 608 657 706 755 804 853 902 951 1000 1049 1098 1147 1196 1245 1294 1163 1392 1441 1490 1539 1588 1637 1686 2286 1784 1833 1882 1931 1980 2029 2078 2127 2176 2225 2274 2323 2372\n21 70 119 168 217 1484 315 364 413 2143 511 560 609 658 707 756 805 402 903 952 1001 1050 1099 492 1197 1246 1295 1344 1393 1442 1491 1540 1589 1638 1687 1736 1785 1834 1883 1932 1981 2030 2079 2128 2177 2226 2275 1748 2373\n22 2192 120 169 218 267 316 365 2089 463 512 561 610 659 708 757 806 855 904 953 1002 1051 1100 1149 1198 1247 565 1345 557 1443 1492 1541 1590 1639 1688 1708 1786 1835 817 1933 1982 2031 2080 2129 570 2227 2276 2325 2374\n23 72 121 170 219 268 317 366 415 464 513 562 611 660 709 758 807 856 905 954 2348 1052 1101 1315 1199 1248 1297 1346 1395 1444 1493 1542 1591 1640 1689 1738 1787 367 1885 1934 1983 2032 2081 2130 2179 2228 2277 2326 2375\n24 73 122 171 220 269 318 1836 416 465 1984 563 612 661 710 629 808 857 423 955 1004 1053 1102 1151 1200 1249 1298 1347 1396 1445 1494 1543 1592 1641 1690 1739 1788 1837 1886 1935 514 2033 2082 2131 2180 2229 2278 1329 2376\n876 74 123 172 221 270 319 368 417 466 515 564 613 662 711 760 809 858 907 1259 55 1054 1103 1986 1201 1250 1299 1348 1397 1446 1495 1191 1593 1642 1524 1740 1789 1838 1887 1936 1985 1600 2083 2132 2181 2230 2279 2328 2377\n26 75 124 173 222 271 320 369 418 467 516 1296 614 663 712 761 810 859 908 957 1006 1055 9 1153 1202 1120 1300 1349 1398 1447 1496 1545 1594 1643 1692 1741 1790 1839 2063 1937 1152 2035 2084 2133 2182 2231 2280 2329 2378\n27 76 125 174 223 272 321 370 419 468 517 566 615 664 713 593 811 2319 909 958 1007 1056 1105 1154 1203 1252 1301 1350 1399 1448 1497 1546 1595 1644 1693 1742 1791 1840 1889 1938 1750 2036 2085 681 2183 2232 2281 2330 528\n28 77 407 175 224 273 322 371 420 1165 518 567 616 665 714 763 812 861 910 607 1008 1057 1106 1155 1204 1253 1302 1351 1400 1449 1498 1547 1596 1645 1694 1743 2145 1841 1890 1939 1988 2037 2086 2135 2184 2233 2282 2331 2380\n29 78 127 176 225 274 323 372 421 470 519 568 617 750 715 764 813 862 911 960 1009 1058 1107 1156 1205 1254 1303 1832 1401 1450 1499 1548 1597 1646 1695 1744 1793 1842 1891 1940 1989 2038 2087 2136 100 2234 2283 2332 2381\n30 79 128 177 226 275 324 373 422 471 520 569 618 2165 716 765 814 863 912 961 1010 1059 1108 1157 1206 1255 1304 1353 1402 1451 1500 1549 1598 1647 1696 1745 1794 1843 1892 1941 1990 2039 2088 2137 2186 2235 2284 2333 2382\n31 80 1758 178 227 276 325 374 906 472 1067 2178 619 668 717 766 815 864 2249 962 1011 1060 1109 1158 1207 1256 1305 1354 1403 1452 1501 1550 1599 1648 1697 1746 1795 1844 1893 621 1991 2040 414 2138 2187 2236 2285 2334 2383\n32 81 130 179 228 277 326 375 424 473 522 571 620 669 718 1473 816 865 914 963 1012 1061 1110 1159 1208 1257 1306 1355 1404 1453 1502 2253 2034 1649 1698 1747 1796 1845 1894 1943 1992 2041 2090 2139 2188 2237 1735 2335 1018\n33 82 131 1533 229 278 327 376 425 474 523 572 1942 670 719 2294 1884 866 915 964 1013 1062 1111 1160 1209 1258 1307 1356 1405 1454 1503 1552 1601 1650 1699 2324 1797 1846 1895 1944 1993 2042 2091 2140 2189 2238 699 2336 2385\n34 83 132 181 230 279 328 377 426 475 524 573 622 671 720 769 818 867 916 965 1014 1063 1112 1161 1210 956 1308 1357 1406 1455 1504 1553 1602 1651 1700 1749 1798 1847 1896 1945 1994 2043 2092 2141 2190 2239 2288 2337 2386\n35 84 133 182 231 280 329 378 427 476 525 574 623 2069 721 770 819 1020 917 966 1015 1064 1113 1162 1211 1260 1309 1358 1407 1456 1505 1554 1603 1652 1420 1987 1799 1848 1897 1946 1995 2044 2093 2142 2191 2240 1721 2338 2387\n36 85 134 183 232 281 330 379 428 477 526 575 1854 673 722 771 820 869 918 967 1016 536 1114 1343 1212 1261 894 392 1408 1457 1363 1555 1604 1653 1702 1751 1800 1849 1898 1947 1996 2045 2094 462 71 2241 2290 2339 2388\n37 86 135 184 1563 282 331 380 429 478 527 576 625 674 723 772 821 870 919 968 1017 1066 1115 1164 1213 1262 1311 1360 1409 1953 1507 1556 1605 1654 1703 1752 1801 1850 1899 1948 1997 2046 2095 2144 2193 2242 2291 2340 2389\n38 87 136 185 234 283 332 381 430 479 2379 577 626 675 724 773 822 871 920 969 2384 521 1116 469 1214 1263 1312 1361 1410 1459 1508 1557 1606 1655 1704 1753 1802 1851 1900 1949 1998 2047 2096 1792 2194 2243 2292 2341 2390\n156 88 2358 186 235 284 333 382 431 480 529 578 627 676 725 774 823 872 921 970 1019 1068 1117 1166 1215 1264 1313 1362 1411 1460 1509 1558 1607 1656 1705 1754 1803 2357 1901 1950 1999 2048 2097 2146 2195 2244 2293 2342 2391\n40 89 138 187 236 285 334 383 432 481 530 95 628 677 726 775 824 873 922 971 868 1069 1118 1167 1216 1265 1314 1506 1412 1461 1510 1559 1608 1657 1706 1755 1804 1853 1902 1951 2000 2049 2098 2147 59 2245 768 2343 2392\n41 90 139 188 237 286 335 384 433 482 531 580 759 678 727 499 825 1192 923 972 1021 1070 1119 1168 1217 1266 1150 1364 1413 1462 1511 1560 1609 1658 1707 1756 1805 850 1903 1952 2001 2050 2099 2148 2197 2246 2295 2344 2393\n42 91 140 189 238 287 336 385 434 483 532 581 630 679 728 777 826 875 924 973 1022 1071 1251 1169 1218 1267 1316 1365 1414 253 1512 1561 1610 1659 1737 1757 1806 1855 2210 1458 2002 2051 2100 2149 2198 2247 2296 2345 2394\n43 49 141 190 913 288 337 386 435 484 533 582 631 680 1879 778 827 1469 925 974 1023 1072 1121 1170 1219 1268 1317 1366 1415 1464 1513 1562 1611 1660 1709 129 1807 1856 1905 1954 2003 534 2101 2150 2199 2248 2297 2346 2395\n44 93 142 191 240 289 1433 387 436 485 2052 583 632 2134 730 779 828 877 926 975 1024 1073 1122 1171 1220 1269 1318 1367 1416 1465 1514 338 1612 1661 1710 1759 1808 1857 1906 1955 2004 2053 2102 2151 2200 239 2298 2347 2396\n45 94 143 192 241 290 339 388 437 486 535 584 538 682 731 780 829 878 927 976 1025 1074 1123 1172 1221 1270 1319 1368 1417 1466 1515 1564 1613 1662 1711 1760 1809 1858 1907 1956 2005 2054 2103 2152 2201 2250 2299 1003 2397\n46 579 144 193 242 291 340 389 438 487 1065 585 634 683 732 781 830 879 928 977 1026 1075 1334 1173 1222 1271 1320 1369 1418 1467 1516 1565 1614 1663 1712 1761 1810 1859 1908 1957 2006 2055 2104 2153 2202 2251 2300 2349 2398\n47 96 145 194 243 353 341 390 439 488 537 586 635 684 733 782 831 880 929 978 1027 1076 1125 1174 1223 1272 1321 1370 1419 1468 1517 1566 1615 1664 1713 1762 1811 1860 1909 1958 2007 2056 2105 2154 2203 2252 2301 2350 2399\n48 97 146 195 244 293 342 391 440 489 633 587 636 685 734 783 832 881 930 979 2109 1077 1126 1175 1224 1273 1322 1371 1701 25 1518 1567 1616 1665 1714 1763 1812 1861 1910 1959 2008 2057 2106 2155 2204 1551 1869 2351 2400\n92 98 147 196 245 294 343 1359 441 490 539 588 637 686 735 784 833 882 931 980 1029 1078 1127 1176 1225 1274 1323 1372 1421 1777 1519 1568 1617 1666 1715 1764 1813 1862 1911 1960 2009 2058 2107 2156 2205 2254 2303 2352 2401\n",
        "output": "540447840\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 199,
        "task_id": 1088,
        "test_case_id": 11,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "45 3598\n1166 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 804 23 24 25 26 1127 28 29 30 31 32 33 236 35 36 37 38 39 40 41 42 43 44 45\n46 1718 48 49 50 51 52 53 423 55 393 57 58 59 60 61 62 63 97 65 66 67 68 69 70 71 72 73 74 1124 76 77 78 79 80 81 82 147 84 85 86 87 88 89 1112\n91 92 93 94 95 96 64 98 99 100 101 102 103 104 105 106 1556 108 109 110 111 112 113 114 115 116 1983 118 119 1451 121 122 123 124 204 126 127 128 129 345 131 132 133 134 135\n136 288 138 139 140 141 142 143 1141 145 146 83 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180\n181 182 183 292 185 186 187 188 189 190 191 192 193 194 195 196 197 1800 199 200 1378 202 203 125 205 206 207 208 209 210 211 212 213 214 215 216 217 919 219 220 221 222 223 224 225\n671 227 228 229 230 231 1816 233 234 235 34 237 238 239 240 241 242 243 244 245 1858 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 1089 268 269 270\n271 272 273 969 275 1392 277 278 279 280 281 282 283 284 285 286 287 137 289 290 291 184 293 753 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 868 315\n316 317 318 319 320 321 322 323 1381 325 326 327 328 329 330 331 332 333 334 1683 336 337 338 1777 340 341 342 343 344 130 346 347 348 349 350 351 352 353 1051 355 356 357 1658 359 360\n361 362 363 364 365 366 367 368 369 370 1267 372 373 374 375 376 377 378 379 1848 381 382 383 384 1609 386 387 388 389 390 391 392 56 394 395 396 397 398 399 400 401 458 403 404 405\n406 407 408 409 410 1275 412 413 414 415 416 417 418 419 420 421 422 54 424 425 426 427 428 429 681 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450\n451 452 453 454 455 456 457 402 459 460 461 462 463 464 465 1985 467 468 469 470 471 472 473 474 1842 476 477 478 479 480 481 482 483 484 485 635 487 488 489 490 491 492 493 494 495\n496 497 498 499 500 1146 502 1954 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540\n758 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 934 558 559 883 561 562 1122 564 565 1376 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 775\n586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 1072 611 612 613 614 615 2025 617 618 619 620 621 622 623 624 625 626 627 628 629 630\n1990 632 633 634 486 636 637 638 639 640 641 642 643 644 645 1877 647 648 649 1970 651 652 1860 232 999 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 226 672 673 674 675\n676 677 678 679 680 430 682 683 747 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720\n721 722 723 724 725 726 727 1571 729 730 899 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 684 748 749 750 751 752 294 754 755 756 757 541 759 760 761 762 763 764 765\n766 767 768 769 770 771 772 773 774 585 776 777 778 779 780 781 1656 783 784 785 786 787 788 789 790 791 1414 793 794 795 796 797 798 799 800 801 802 803 22 805 806 807 808 809 810\n1071 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 1880 828 829 830 831 929 833 951 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855\n856 857 858 859 860 861 862 863 864 865 866 867 314 869 870 871 872 873 874 875 876 877 878 879 880 881 882 560 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 731 900\n901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 218 920 921 922 1475 924 925 926 927 928 1490 930 931 1317 933 557 935 936 937 938 939 1279 941 942 943 1583 945\n946 947 948 949 950 834 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 274 970 971 972 973 974 1154 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990\n991 992 993 994 995 996 997 998 655 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035\n1036 1037 1038 1039 1040 1041 1082 1043 1044 1045 1046 1047 1048 1049 1050 354 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 811 610 1073 1074 1075 1076 1077 1078 1079 1644\n1081 1042 1083 1084 1085 1086 1087 1088 267 1090 1091 1092 1093 1726 1095 1096 1097 1098 1099 1100 1101 1972 1103 1104 1105 1106 1107 1108 1109 1110 1111 90 1113 1114 1115 1116 1117 1118 1119 1120 1121 563 1123 75 1125\n1126 1174 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 144 1142 1143 1144 1145 501 1147 1148 1149 1150 1151 1152 1153 975 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1495 1167 1168 1169 1170\n1171 1172 1173 27 1175 117 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1624 1215\n1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260\n1261 1262 1263 1264 1265 1266 371 1268 1269 1270 1271 1272 1273 1274 1635 1276 1277 1278 940 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305\n1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 932 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1526 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1989 1344 1345 1346 1347 1348 1349 1350\n1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 566 1377 201 1379 1380 324 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 276 1393 1394 1395\n1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 792 1415 1416 1432 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1417 1433 1434 1435 1436 1437 1533 1439 1440\n1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 120 1452 1453 1878 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 923 1476 1477 1478 1479 1480 1481 1482 1483 1814 1485\n1486 1487 1488 1489 832 1491 1492 1214 1494 1875 1496 1497 1498 1499 1500 1501 1969 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1330 1527 1528 1529 1530\n1531 1532 1438 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1701 1548 1549 1550 1551 1552 1553 1554 1555 107 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 728 1724 1573 1574 1575\n1576 1577 1578 1579 1580 1581 1582 944 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1613 1607 1608 385 1610 1611 1612 1606 1614 1615 1616 1617 1618 1619 1620\n1621 1622 1623 1493 1625 1626 654 1628 1629 1630 1631 1632 1633 1634 411 1636 1637 1638 1639 1640 1641 1642 1643 1080 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 782 1657 358 1659 1660 1661 1662 1663 1664 1665\n1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 335 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1547 1702 1703 1704 1705 1706 1707 1708 1709 1710\n1711 1712 1713 1714 1715 1716 1717 47 1719 1720 1721 1722 1723 1572 1725 1094 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755\n1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 339 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 198\n1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1484 1815 1627 1817 1818 1819 1820 1821 1822 1823 475 1825 1826 1996 1828 1829 1830 1831 2012 1833 1834 1835 1836 1837 1838 1839 1840 1841 1824 1843 1844 1845\n1846 1847 380 1849 1850 1851 1852 1853 1854 1855 1856 1857 246 1859 653 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1 1876 646 1454 1879 827 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890\n1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935\n1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 503 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1502 650 1971 1102 1973 1974 1975 1976 1977 1978 1979 1980\n1981 1982 1176 1984 466 1986 1987 1988 1343 631 1991 1992 1993 1994 1995 1827 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 1832 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 616\n",
        "output": "991610752\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 200,
        "task_id": 1088,
        "test_case_id": 12,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "44 955\n144 1303 830 309 793 387 1559 935 90 691 1002 44 584 1560 162 554 1265 865 1514 894 880 1638 1127 1277 409 1802 1317 134 883 1070 1715 617 1683 28 969 237 666 1428 1353 1650 952 667 1243 829\n1274 154 587 412 1555 933 1100 884 1085 212 107 1768 1191 391 1245 290 101 1176 1921 635 799 882 312 369 1237 1528 1168 1471 1417 568 277 1117 1350 1862 889 33 781 1478 1532 1121 891 43 591 150\n523 12 639 1195 774 998 634 1775 981 1906 993 1241 179 1899 977 1791 537 973 1316 1742 731 1744 1753 355 1457 1527 194 1022 321 724 1882 1823 484 1125 251 404 284 735 1110 215 285 1804 360 893\n695 441 1233 42 662 1609 1028 1248 1115 672 593 923 198 435 1806 1779 494 1723 722 809 1758 453 1413 1480 479 1219 1596 1163 1847 1431 1908 1704 962 660 906 1734 901 24 131 651 900 1263 1375 424\n1180 1185 433 1571 1597 115 636 1752 756 926 1323 350 542 1287 826 747 157 1049 121 1819 552 7 1209 26 632 47 1475 219 699 1572 1467 1853 1751 1531 141 1144 1534 847 1701 676 501 1184 1386 1709\n375 1590 1159 607 1035 1536 598 1114 1646 78 700 1762 6 903 140 169 1642 1079 1737 831 196 260 754 1874 535 246 561 1813 627 188 1162 1736 791 1546 357 372 944 1858 1382 226 1365 1207 540 1684\n1679 1004 844 327 1591 855 469 1019 1474 1380 265 1338 1501 1505 864 1355 1383 473 961 1484 1746 653 93 863 1298 1045 701 1147 269 573 904 16 1681 1188 1777 1645 1171 146 1861 834 319 848 256 1031\n1278 1778 822 1498 1416 474 536 937 374 1448 611 1137 129 1612 497 1169 482 1920 1010 49 899 172 1898 139 1637 395 427 1320 518 1831 942 775 1691 1705 509 989 1930 1181 1150 373 434 126 1859 534\n291 1661 941 644 1577 446 324 1788 11 1754 1671 207 486 1694 1291 1558 1104 1836 838 1432 550 1351 1294 41 1504 1821 310 1932 1840 1774 65 1223 601 1565 718 943 960 210 29 1061 1502 751 1673 455\n873 98 738 800 368 429 1575 787 1379 235 1437 1801 1487 1352 1608 283 758 868 1138 595 1833 316 1488 1809 1541 1726 305 1069 1897 295 1062 1900 189 749 533 81 258 1231 1666 1870 1268 1615 934 1708\n1214 1295 37 1039 1780 1290 685 1912 1221 649 1660 330 1091 1491 382 1602 1203 571 850 367 1875 1877 1629 1805 1644 1879 763 227 959 271 442 1516 1246 1567 916 1343 161 1411 1523 1594 1426 1927 967 1665\n1814 1360 417 245 938 789 1415 1154 1933 280 1787 643 1023 853 580 1674 36 402 9 776 448 612 239 723 1254 20 1894 1302 1330 268 366 466 1672 879 168 1080 1519 386 1453 1890 1903 204 415 1084\n698 287 1830 128 34 1578 1345 1835 679 1916 657 1706 785 307 1455 558 1053 326 1081 1020 1579 1286 777 671 600 610 557 1394 1335 1247 201 240 1729 877 688 4 1048 1197 1776 529 1280 414 436 1904\n1119 658 1917 1434 1388 628 1668 1598 1201 1798 202 1340 806 431 1253 1490 48 1721 1756 1283 1266 209 1123 1509 949 1389 481 1911 620 1105 821 1771 267 583 197 876 661 1230 1562 301 1816 881 569 1628\n1346 1361 843 1907 1160 1014 965 1526 1088 160 1341 1766 407 1825 1376 1595 1860 465 1793 1189 910 278 1402 195 217 1038 1556 762 425 684 1695 264 1133 1324 633 1599 983 87 136 951 421 1496 223 1773\n1477 866 1936 1914 132 946 689 905 294 1826 1739 720 1669 55 422 325 1676 67 994 439 1446 596 704 592 1633 443 978 1135 1405 1143 338 1884 203 1194 166 1057 1710 279 1005 530 462 178 675 1494\n396 84 922 769 1606 1003 1393 655 717 1630 1033 560 1401 674 1318 1132 958 1682 117 1542 1187 792 1164 306 538 1686 1868 89 772 1292 222 1146 606 1157 1099 783 1134 1935 133 885 191 737 713 392\n1624 10 1664 1068 504 1220 682 1492 1451 1300 1497 995 1438 1149 920 1112 1118 302 1851 1385 524 625 857 1354 1054 574 390 819 648 1232 1092 1712 413 786 710 80 1109 394 1399 992 328 1398 1733 1152\n1312 1925 135 456 1257 64 631 450 748 1215 272 788 1098 389 1073 199 940 1636 948 1439 1750 1769 1347 947 1357 1728 1029 300 477 930 1427 1106 114 1918 654 21 1568 1743 1680 1419 996 1618 1120 1408\n1533 892 673 925 276 1849 566 861 1410 138 681 1866 1464 519 1126 693 827 331 576 468 1210 1510 1792 680 228 1634 1619 221 971 1270 1740 1267 323 130 803 797 526 1607 1529 999 976 909 1550 919\n1850 426 1447 380 1725 706 1928 503 823 379 1552 1319 1625 629 1301 1007 1052 1018 913 1107 1573 1076 3 1377 8 1359 506 779 1520 346 575 1730 1212 683 184 30 1337 712 249 1358 1145 1659 232 1009\n1414 1539 183 74 490 498 615 1030 1032 1817 1050 567 1026 400 1503 812 902 1313 361 250 233 1373 1811 1136 499 428 1588 957 1166 344 1483 1592 1864 1923 371 220 1570 1834 32 1307 955 362 1902 1086\n770 1065 1827 411 491 1348 1799 849 1090 224 334 175 572 23 1310 1242 810 1060 707 563 816 766 318 553 320 714 1315 1584 860 1306 1880 956 1922 263 335 1688 512 1071 597 485 96 1663 1199 236\n1271 637 1764 1547 1178 1384 1735 1051 1381 890 1252 480 686 1551 1611 1249 1696 1244 492 14 846 728 1658 1797 1236 1820 505 740 646 1387 430 1829 1876 912 76 1151 1587 1407 730 370 103 1604 757 243\n281 1886 982 458 1289 927 985 1067 867 99 156 1934 577 393 298 669 489 252 1580 1692 715 742 1583 778 1824 1422 1749 1153 297 247 677 185 837 964 1025 687 5 790 694 755 205 1128 317 1059\n975 1702 541 840 585 1863 697 460 1216 895 1424 1037 1714 565 1445 1016 1077 531 408 180 1885 1213 914 616 1931 640 349 1175 1311 148 1366 122 1784 1196 359 896 1910 244 1082 1905 364 1545 1613 1697\n641 911 887 385 696 966 842 716 650 1852 609 1508 659 578 1179 348 403 109 1296 1653 1891 1 73 1856 1913 39 1759 1374 1690 1569 299 1443 293 1812 833 1507 1021 1790 638 1421 1390 66 1844 1755\n1476 970 1841 273 626 1640 516 721 410 1781 1096 22 1364 376 100 1440 159 832 111 652 437 527 496 1342 692 1218 119 59 1056 1512 45 1459 1713 921 112 1193 190 495 1929 1202 642 602 1349 51\n193 1616 1327 1915 991 1632 1403 1173 507 1378 1367 1309 487 1842 1418 1657 1305 1425 1700 1662 556 513 794 488 70 767 238 814 1205 329 1789 343 17 773 1284 1006 1796 31 444 514 734 1563 1258 1540\n171 986 1362 1482 1156 795 771 1626 915 862 859 1883 1489 870 177 1703 708 841 60 1204 1486 145 1623 1042 405 476 739 1001 725 668 1260 1593 1344 1677 1299 1024 665 242 1693 1101 470 917 142 1761\n82 968 1027 69 116 475 1462 1297 158 1518 1012 440 782 398 1078 137 1177 711 61 1442 229 1075 1763 1322 807 1506 918 528 1535 1732 705 835 174 1087 124 401 336 40 939 1008 1158 472 50 796\n1372 15 91 151 1089 1586 418 92 1783 288 423 954 332 1461 878 726 1222 1867 1807 1857 1561 703 282 399 517 1256 353 1140 1072 1275 1013 1698 79 352 886 1810 945 1748 1765 1566 1822 1108 1499 165\n104 805 1466 1517 1865 200 1217 1576 727 471 1094 1800 1848 341 454 1878 459 356 852 230 351 1251 18 1495 936 333 308 1444 1452 225 292 1240 1803 1250 1063 1141 1757 1895 874 1363 1581 1667 1627 858\n1392 57 1872 1281 780 52 974 811 68 544 1782 741 824 1326 35 1017 1525 1832 820 71 377 1129 493 1614 304 963 759 1406 511 1605 381 543 798 1400 1172 416 1011 1308 729 1058 702 1167 248 2\n153 46 1454 1333 1336 120 1116 170 599 406 987 1731 311 979 363 765 953 1479 1095 1537 1888 950 1678 1404 88 1896 551 155 1610 1543 1148 53 463 173 559 1282 1339 1155 1142 1601 1675 502 656 1064\n110 1513 1815 856 586 1718 1621 143 419 1649 1544 1420 980 1234 1689 105 678 663 613 1892 1869 818 274 624 931 548 898 1044 27 1720 1738 500 510 1845 733 690 752 825 289 744 1699 1652 216 303\n1548 95 594 1846 1582 1412 1727 347 1328 451 342 1463 123 1574 582 1549 1837 1647 645 1631 1500 1639 1711 447 745 1314 1655 1456 147 1554 1648 1429 1371 1873 102 1074 339 1767 1192 152 1622 621 1641 1685\n464 1707 630 753 1225 768 13 19 192 546 1409 254 1794 167 1170 1670 1190 1854 77 438 590 457 647 1893 1465 211 1481 1055 928 1839 1524 1620 802 1717 214 383 1600 261 1261 1103 1716 420 365 1041\n125 186 461 1262 1468 1818 25 270 1901 1046 181 164 113 828 1808 149 1334 206 1111 257 1238 340 286 72 525 118 515 1182 314 1485 213 1273 813 1034 231 1097 1887 1530 1433 54 579 275 1760 1473\n1770 1635 736 1589 521 1391 589 452 1909 997 1093 127 605 86 296 1396 1747 432 815 907 872 56 588 845 266 564 1047 255 1843 555 1919 1557 63 1722 604 478 746 522 322 38 808 603 804 1325\n581 1368 58 1724 1436 1397 1113 1228 259 1538 1924 1200 1122 1643 924 1522 1279 1926 1174 570 988 1423 106 929 888 719 187 75 1369 614 218 176 1493 449 1211 1131 908 1521 1654 1460 1329 743 1276 163\n875 854 761 836 1651 1161 1124 932 388 253 182 108 618 1321 1206 1795 467 1745 1511 670 1272 315 709 1889 1066 760 817 1472 1255 549 1036 1515 1285 1786 354 1224 94 539 1332 1198 1227 532 750 97\n1395 1741 1356 337 1331 234 801 1772 520 1785 562 1288 345 897 384 1469 1719 445 1687 1304 622 871 1226 623 839 1293 1139 990 1871 869 784 1435 1102 1259 545 262 483 1235 972 547 83 764 1564 1015\n62 664 1553 851 1165 1828 1229 397 1239 508 1430 1264 1458 732 1043 984 1585 241 1208 1881 1449 313 1130 619 85 1441 1083 1450 1656 1617 1603 608 1855 1470 208 1838 1040 1183 1000 1269 1186 378 1370 358\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 201,
        "task_id": 1088,
        "test_case_id": 13,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "45 1684\n493 1928 712 565 33 1129 1026 1184 1558 960 1979 82 1761 1415 992 802 1666 750 1518 1537 534 1399 512 1634 334 932 1330 1015 69 1082 683 1830 90 1891 655 1865 345 37 585 738 1623 131 1211 67 1470\n755 378 1948 1102 290 918 423 1127 1757 1166 956 1833 617 987 1507 1183 1413 1975 1153 206 1386 1411 143 1004 674 900 1800 885 1973 360 994 1391 386 1140 1834 426 105 431 1593 1152 269 248 1324 478 800\n477 46 191 1941 1091 784 522 1597 364 1248 907 1019 948 467 281 1903 464 102 228 1106 1613 1383 1804 927 291 882 1516 589 1557 369 1061 249 1863 1556 2019 1021 1465 1370 427 1603 251 945 1611 1404 1092\n130 236 162 1548 1555 1449 1047 1454 408 1261 1008 1612 1808 1569 1060 1011 149 98 1213 586 1596 1422 860 275 1135 1665 721 701 1103 1219 616 886 1050 1546 392 125 208 820 1815 1005 41 380 646 50 1474\n1751 1776 940 292 2009 1579 746 324 1295 1912 219 1057 1534 1744 1197 1733 1938 1729 761 302 1559 1073 1578 596 452 19 75 573 1469 1343 883 39 152 1920 1409 451 465 2008 1712 982 489 78 716 1310 1628\n322 422 218 594 1306 1009 106 1743 1581 1749 1517 1366 892 1031 1526 287 2010 1639 1503 1996 470 146 869 1466 1468 1251 1997 1212 1364 754 1489 705 1625 667 1490 804 1888 60 520 842 704 1105 751 1037 1139\n958 332 1651 1150 2024 498 743 1531 1158 1186 1631 1801 566 1297 1535 1416 1328 1121 268 702 342 65 66 529 576 123 1592 1877 1794 1266 1922 337 912 1245 1176 1275 595 1290 1289 1349 773 70 747 499 1522\n1737 810 100 1783 980 556 545 492 814 557 664 1887 1688 803 835 1471 307 1962 230 1904 1196 772 966 878 1347 414 246 1885 1154 1986 341 569 145 737 1494 375 409 95 1870 1643 1969 1250 822 314 864\n1308 1204 1898 1758 730 849 1851 1392 1028 135 1089 1829 54 1584 1957 1819 1305 1732 638 543 494 874 1821 1536 154 1571 1296 1902 284 1700 354 1372 1760 944 1071 1010 1560 1239 1215 1840 258 1763 615 1045 651\n4 1726 1916 273 879 1658 693 1511 1065 505 247 1203 934 59 502 1988 1809 335 1663 1482 776 1836 214 1378 635 732 53 1983 1151 618 393 1304 665 1327 1498 582 572 1034 525 574 910 677 85 460 194\n1453 418 717 479 142 942 14 120 601 1818 2022 1168 1756 199 1018 2000 1698 558 1530 1260 919 1446 1711 1109 1001 1044 555 644 706 519 939 1202 62 1125 1495 760 1457 1365 301 1172 511 1995 186 2015 241\n177 1715 227 88 1259 51 18 1775 1481 144 1478 768 604 1766 97 1977 113 112 1382 1843 1860 1693 1360 1463 1844 801 759 1048 172 1087 1363 250 643 193 1774 1694 1441 629 906 930 1218 863 1164 289 1346\n1225 1058 173 1376 1207 107 1189 686 1734 1374 1249 916 1352 1953 714 811 1042 432 694 27 781 1241 192 1713 831 1242 1265 265 1689 377 973 1602 850 296 1832 852 1966 657 531 813 509 440 1253 1848 614\n843 775 1325 264 744 1243 649 1635 1691 103 1739 925 1397 748 1208 1544 740 931 1894 1273 1946 1934 58 1479 126 447 267 1074 577 13 503 1520 1955 788 48 1566 416 1419 1540 119 1277 972 349 159 1586\n304 306 679 429 164 1062 752 1313 943 727 1116 315 56 1945 997 1210 662 785 1811 348 1108 507 1487 1157 501 1395 1083 1394 79 104 741 923 1282 1276 1464 1590 266 1023 40 1052 1336 469 1096 1389 180\n385 571 430 1104 1655 1638 283 1600 49 1359 1447 1767 483 1113 1400 680 581 968 77 1989 1855 443 1338 1842 1538 1786 1908 647 137 1708 1990 1238 389 1279 2001 1226 317 1805 865 255 1206 1810 111 1038 1750\n1182 1445 1673 1233 1434 1551 1402 209 1769 1063 1644 171 1431 202 1572 1456 1130 1090 1448 1880 351 1680 1033 830 796 486 1768 999 1601 1772 1792 1641 30 949 757 583 723 838 1337 938 1247 1795 148 446 1527\n762 1345 1506 221 370 21 1199 668 1425 816 1745 1812 873 141 547 1424 237 8 1136 1647 101 711 708 666 24 1027 1614 343 1935 1695 890 259 411 134 310 277 975 1401 671 608 406 1654 544 211 155\n226 1869 454 83 1943 542 672 1533 535 1706 687 203 1461 1793 1619 1173 1779 952 300 851 2006 1652 1100 1072 1357 121 234 457 1947 71 1111 839 356 875 435 232 1267 1657 827 1707 2 758 792 1493 1263\n1300 403 2023 34 837 175 818 383 868 1679 1541 1231 789 1752 17 1230 1669 795 609 1000 1118 424 696 74 1879 1356 400 163 915 591 1442 207 546 876 902 1972 1965 151 139 1568 824 1358 1396 1913 872\n1155 487 1188 415 633 854 1788 1561 1287 197 1574 1806 1974 362 829 606 1281 1799 1175 1982 1451 261 1719 1588 1156 1086 1915 1867 1591 458 1344 2005 1773 1640 384 1268 1299 333 116 318 894 1283 539 560 1228\n832 331 1107 753 373 1991 434 305 1097 1896 592 35 299 150 223 562 128 1780 2007 568 303 690 1291 1067 1839 1927 1085 584 1585 1098 109 361 756 347 745 168 225 1428 421 1703 1861 1452 1307 319 1414\n224 1143 76 1049 959 1615 475 1079 187 710 528 871 1637 359 1671 1476 1077 697 911 61 1649 1458 1738 971 229 288 1429 1040 1221 480 1949 895 484 1642 1685 642 1003 669 1137 1244 1500 1274 1417 1717 240\n1926 1905 1278 933 950 1420 532 1617 779 404 1798 495 2018 889 490 198 195 459 1070 220 1961 1046 625 623 445 327 941 1897 734 395 438 1740 1145 1254 1901 857 1762 1444 114 1952 1236 1521 1577 1787 1030\n720 461 1674 1981 215 185 978 1348 1598 1857 367 1069 645 138 836 1440 353 844 970 1724 1246 63 947 1754 593 1288 286 722 1856 1407 2013 1746 549 1161 28 1524 648 1144 1126 1595 1661 1149 1573 1393 365\n825 640 99 887 791 16 954 1385 1539 1725 1616 998 1850 661 1159 481 244 419 1771 1565 1610 799 366 1594 1162 1893 1170 977 1670 1459 1361 417 924 807 845 368 1958 636 2016 1179 1187 1828 986 767 122\n969 1418 790 1438 597 1626 1321 23 1881 165 1280 22 1293 1873 1080 1532 579 183 1853 846 1194 817 1849 441 1502 1742 496 1410 188 94 598 967 1994 1827 764 1333 896 1604 239 691 1925 898 1132 1930 1355\n2017 1492 624 1110 1606 1716 182 1636 1980 1064 1101 174 1473 1167 1131 1286 631 257 735 782 1322 10 1782 515 1675 1093 965 488 554 391 1727 1545 1180 57 1439 770 321 1648 991 156 405 688 11 1781 1627\n1163 184 1041 552 1718 453 26 449 1133 1807 81 1480 1978 1303 158 55 1270 1684 1002 612 698 632 397 1017 1342 178 260 603 731 1954 9 1937 798 739 1705 840 1217 166 1813 1702 1720 1570 1123 1910 282\n1353 1443 450 200 797 312 1789 905 1956 909 1890 25 1177 1933 787 853 1704 1770 957 1820 2021 1054 841 513 1006 1951 1859 1271 1741 1633 2003 508 1043 1301 929 285 990 1240 1075 1875 917 684 1824 806 995\n1380 1864 1350 564 1630 44 1055 920 778 1998 897 352 870 627 382 550 541 858 1039 786 1939 242 1882 725 1255 466 1318 278 1523 855 1081 1339 87 1575 599 1472 473 68 736 1375 1012 96 914 1791 379\n129 861 1907 1122 298 1237 1993 1232 1059 235 1976 1128 676 160 338 1605 622 1426 1660 769 551 530 1529 1160 1178 463 1475 523 1272 1329 1387 1007 1433 962 1722 833 719 108 821 1936 1302 147 1835 407 1117\n1099 637 1552 118 29 953 444 1112 179 176 1509 1235 279 190 297 561 1852 1403 996 1730 1312 1256 1677 774 1659 1971 1284 1264 1664 1095 983 1796 1223 904 724 1899 1992 401 1549 233 1646 1147 425 1858 1224\n1709 1608 1872 1373 1200 1999 1285 675 652 340 700 613 1940 961 437 402 766 350 913 847 1624 399 1501 1892 1697 578 1759 276 7 1777 420 1528 329 1035 293 1814 1919 1214 253 124 412 527 660 433 692\n628 682 935 1486 709 1036 974 908 20 167 439 985 1714 742 1587 1845 1320 157 733 619 626 1398 504 52 1862 1335 1681 189 1785 1621 1294 1258 132 212 1505 1367 355 699 1368 115 1710 1906 1462 703 1668\n1512 1229 47 1874 1676 1960 979 1323 963 1114 1013 1911 1298 1923 1014 537 270 1257 1120 1629 937 1390 1525 1883 880 2002 1029 1068 812 363 559 308 204 1316 252 1076 1932 181 984 610 32 976 1650 689 91\n1510 1388 1450 1871 1884 1181 590 1696 1964 6 1632 410 1020 1192 1984 1165 1550 1056 271 161 575 428 553 600 621 84 64 793 2011 1317 521 540 1216 1146 1022 1645 1185 567 387 1477 1119 1620 1421 1687 1053\n605 1735 1803 1485 1683 1319 563 1817 587 516 922 1134 1124 196 780 1437 2004 238 2014 1963 1822 413 862 15 1315 371 169 1917 170 1483 726 1868 1580 1141 374 881 921 1436 639 1753 1678 1914 1895 472 1607\n888 309 1985 396 510 946 231 1589 381 650 524 1334 1656 1499 1311 1309 514 1115 805 1377 388 311 1371 1362 1563 765 1866 1547 482 1351 256 538 1341 1227 658 5 866 80 328 263 471 1504 1024 707 1918\n1622 45 1088 1987 1721 1921 1340 323 1542 1562 245 1220 1784 1653 1846 92 1816 1778 390 1190 673 216 1543 663 1748 217 394 455 1384 1876 783 713 1823 1583 749 1942 1728 476 254 117 656 899 670 140 1825\n1195 153 1094 1554 1455 607 1405 681 1931 926 1929 548 1369 678 93 1078 1423 1513 485 136 794 1886 1582 1292 1567 1667 1381 89 1790 110 213 1765 1198 988 1496 1924 1430 1699 715 1515 1314 989 272 1736 316\n274 1460 928 1326 1169 1174 357 1171 86 346 1066 1682 1427 763 133 2025 1332 1252 1970 1701 611 1968 1084 468 2012 243 201 1618 620 1889 1142 1854 1690 73 500 1406 330 1191 641 867 848 1209 1148 442 1609\n43 1138 262 1838 1686 398 1692 326 728 320 859 526 462 1672 1747 718 517 1797 210 1491 1755 280 1234 981 659 295 1831 828 1841 1 325 1331 1051 834 358 72 294 808 1847 951 1016 506 936 1909 1269\n1802 436 1435 1408 891 1205 580 893 344 1222 654 1025 36 533 12 809 570 518 955 1379 877 42 823 695 491 1467 1576 1950 339 1354 588 456 1553 1484 376 1032 1900 1837 771 993 630 336 1564 634 685\n1262 1731 1201 903 1432 1959 602 2020 1764 729 448 826 31 127 1967 1599 1878 1519 1488 497 222 38 819 1514 1723 964 1412 205 1193 815 1508 901 1944 777 1662 372 3 856 1826 884 474 536 1497 653 313\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 202,
        "task_id": 1088,
        "test_case_id": 14,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "47 224\n1634 643 1719 818 680 2038 512 1996 224 1198 1630 2044 2201 105 1591 409 1005 1090 564 404 41 798 1820 902 246 581 1155 459 1183 650 152 1789 1210 1616 1244 2150 888 950 1781 1974 573 214 1737 494 1716 1034 282\n1446 2165 1224 561 1761 393 1246 2175 1115 860 967 2176 1008 243 1907 610 1641 164 1137 1480 294 1711 679 912 618 851 2196 651 1703 849 772 171 2082 979 361 1225 324 768 1028 1431 217 419 1515 1420 80 698 1397\n263 585 134 1456 1813 1718 1844 91 437 1805 971 397 836 182 316 1875 1311 887 1153 2178 1556 82 1646 819 2097 501 985 1714 845 1483 1324 1626 1838 773 1696 660 169 746 495 1910 1776 1413 1380 1538 1063 1954 1921\n1629 916 747 46 1133 1668 1970 1081 1643 2029 1189 52 2050 1143 1023 1177 2156 737 2130 1527 2024 1376 1890 1993 125 1827 567 148 755 2144 1320 1247 1021 947 1439 1533 1185 2060 1611 1563 2143 556 2117 1821 1825 514 1078\n13 469 1302 544 546 1564 2 1355 560 135 1615 1592 2122 1086 44 1790 1288 1118 1540 647 583 191 1016 1606 591 1169 1279 1614 1924 1188 1899 493 446 206 2056 1959 2067 1176 728 1203 2192 145 1009 1506 326 563 49\n306 692 2043 1839 211 1988 1511 555 1301 1386 801 1269 666 1628 1127 557 177 1272 1908 966 1889 891 759 1050 1546 597 1340 2168 1635 1911 917 76 1731 257 1581 1414 1193 1139 1576 1587 1253 11 1557 733 1673 1371 1824\n1891 1534 421 1383 543 497 943 165 2031 1561 1025 1112 1435 517 318 1967 839 1251 385 466 360 1857 1920 1892 1812 1274 1571 1772 1785 716 883 1319 1960 590 216 185 92 1287 1617 209 1298 1768 730 1348 473 85 90\n1323 377 104 1763 25 890 1579 321 372 2055 1334 802 1116 1645 1876 722 731 1429 1779 319 2014 488 1314 2187 1559 2057 1100 1461 342 198 1365 233 2158 304 1555 2145 280 2209 638 538 1011 272 1895 1754 334 2180 1929\n1810 1931 440 878 1586 146 1726 506 181 954 972 1122 2016 483 547 674 1569 608 791 1075 852 1900 260 172 154 1217 6 1467 1685 17 1981 1514 328 21 139 853 317 2185 410 1015 1756 1775 1270 1307 384 1604 719\n344 1471 675 1426 701 588 1411 981 1142 1452 161 279 2006 670 283 284 1943 253 1277 1638 66 1004 23 1773 416 1585 939 639 1166 1728 1759 1327 1003 231 1216 1432 1162 2126 1478 241 1746 775 487 2063 19 1885 2179\n2000 389 515 702 1443 376 1268 753 961 1832 1735 771 325 1475 522 788 1697 613 962 649 744 1294 1905 1914 2129 1624 228 2190 470 2087 402 2164 1336 255 2064 1865 1436 694 413 704 1030 1091 444 841 1856 1702 1956\n1517 1060 287 657 4 1014 766 1742 1597 1400 990 1357 1151 1688 1052 178 15 1267 2134 909 1472 531 1705 449 1318 894 338 1208 1123 516 1687 876 907 14 417 375 190 1523 829 2102 2069 906 782 199 400 2079 662\n176 1957 1407 428 1072 123 435 767 599 1945 368 661 1926 826 1808 1767 2167 611 448 1765 925 1535 1882 1051 1852 1919 763 1184 467 129 436 1999 1444 690 2058 641 412 2162 1415 2198 1608 101 1778 291 685 832 1866\n256 1979 530 1181 434 1070 713 572 809 2077 1345 225 158 1447 1978 1498 1958 309 828 1238 785 1450 697 1295 783 119 2132 130 1255 1369 1553 875 336 348 1598 550 987 489 1973 1104 837 2109 1333 356 682 2089 472\n1276 1855 551 975 1965 847 1119 1374 518 2034 997 1631 411 1105 197 222 1987 886 1171 1066 1489 290 877 524 1223 2085 1422 1055 219 1590 447 1020 252 903 1218 693 1199 762 1074 741 2197 1734 1262 774 1412 2068 1482\n34 311 98 58 549 47 1110 460 24 1342 1252 1793 2136 998 2008 1398 568 1499 709 1896 310 1966 223 1352 337 735 646 1758 633 22 420 373 1507 533 1522 552 1108 734 1990 492 2015 350 2166 1708 838 1449 142\n2146 1680 1437 1200 73 931 587 1667 1457 1077 1394 151 1306 1338 1061 1951 340 1912 817 1458 1501 1621 1596 490 59 1934 273 1164 201 1095 2076 271 905 355 1125 671 1092 479 656 1666 383 215 955 1290 1904 1328 1939\n677 1997 242 1361 1019 945 1678 627 1350 478 1816 919 824 1500 1395 232 2173 1550 1637 1289 250 227 1684 2041 288 1975 1455 1239 1141 978 16 1053 1713 565 298 1543 2071 1518 1463 1273 174 1601 570 1286 441 166 2090\n631 398 1421 208 1428 1120 156 2200 78 433 1811 2011 270 244 630 1068 180 2009 1679 1241 1351 1329 1046 1316 1212 602 2119 203 779 239 1036 359 1304 464 237 1521 1237 1317 521 1303 315 1822 1930 112 1000 932 1541\n445 97 1082 1962 1278 910 729 1418 1454 1565 109 1961 486 958 1894 439 846 1764 2138 424 959 1488 137 703 1526 1331 1205 1723 2118 1819 880 1466 749 1677 293 1174 1566 430 1058 122 251 870 554 1880 539 1408 2115\n1774 2018 1226 144 27 833 1041 589 2083 1806 928 196 769 307 1275 363 37 347 121 175 1258 1312 548 1047 781 1029 295 1983 322 1950 545 757 70 895 644 247 2124 117 1690 1512 1544 451 1098 1915 868 463 1285\n1425 732 2194 1932 99 1305 668 102 423 2046 1349 2137 2195 1479 455 339 443 1417 1663 184 1743 616 1147 1516 1040 715 62 1192 465 1893 941 562 725 896 537 1308 579 1644 628 2174 1724 664 1969 1797 508 989 814\n996 71 1897 471 691 673 2032 1335 1751 2051 408 1261 960 1401 1190 944 1670 234 329 625 108 830 1144 1510 1602 2022 2140 1002 1042 87 1434 806 1588 793 2131 553 1396 699 815 723 857 604 1470 1531 1595 1399 1795\n1928 289 1017 2142 162 308 84 1007 452 136 2141 1368 1551 764 1736 687 1704 1519 1700 2025 75 1752 1027 1158 578 207 1989 269 1146 1656 1898 805 751 1676 1111 1099 12 1321 930 963 1622 923 374 720 2208 816 1356\n1944 911 1682 1152 1549 118 2048 1831 354 2033 784 366 403 2101 1381 758 1672 889 456 74 1339 396 1291 898 1532 1233 1710 1689 1129 248 1554 1069 380 1530 540 1651 1609 1379 873 1080 453 221 812 2078 637 1536 40\n2052 2177 2062 2108 1012 1883 1083 1310 1618 313 2091 1202 609 213 1491 511 1073 147 2045 1640 1998 593 140 1486 672 382 406 1165 1332 333 349 688 523 1213 1424 45 1744 1389 1642 1977 1102 1612 391 35 1658 106 756\n957 606 1913 378 1284 1178 2075 1220 1232 5 1094 38 1520 2133 874 1529 1879 519 1909 1256 1613 54 684 2013 1121 1493 750 865 1297 1010 1610 212 415 36 1662 869 381 1659 1619 2036 897 1366 810 2001 8 1669 1664\n952 2135 297 1830 26 1039 1136 1600 95 1173 924 872 195 1343 2105 498 86 717 754 94 807 277 1402 278 1062 1388 623 1154 745 1473 204 457 542 426 803 988 110 596 1706 1940 2017 653 1809 927 1117 899 575\n1769 1701 57 1814 1537 1391 1804 1786 1671 2002 1552 427 1818 940 1801 1871 1330 1201 2012 1653 1747 1861 1625 526 202 1620 1766 2098 831 1089 1367 1869 1495 1829 1419 914 462 65 659 520 1720 796 1299 892 1798 30 141\n1784 881 1807 1562 705 1148 1049 500 1794 635 689 1661 1242 607 1131 1580 1570 813 89 1721 1955 1337 365 984 1992 2202 2074 577 1035 1652 1179 64 1093 1750 2088 1572 1309 918 1240 1589 405 1863 525 617 2080 1445 1594\n1211 1 1438 654 20 496 1649 992 800 1686 1575 1231 1502 68 1902 345 88 614 580 936 193 2007 760 1513 2112 1823 2154 1504 956 332 1828 1281 1935 157 81 2193 1568 1180 1370 2125 474 1044 507 1755 29 132 808\n1803 571 795 1326 2003 696 261 116 1877 1280 1648 442 10 879 1347 1266 50 510 173 150 1842 1230 1681 1984 1462 149 2155 2123 2059 1382 320 528 991 710 942 189 1363 143 665 346 885 1186 114 480 303 1037 1941\n1172 179 1263 1815 1942 1101 2096 1603 527 1878 1937 1163 1264 133 738 1840 1484 1799 1867 72 358 2182 1132 1254 367 192 323 1403 1727 1378 1464 867 1850 1135 752 2163 595 1031 1633 1593 676 712 170 820 1354 1692 804\n1725 1344 964 1693 726 1097 1459 485 1362 1584 2113 921 569 160 714 1574 934 1922 1322 1430 1780 1886 1632 268 1113 1497 1925 450 245 863 341 262 884 1149 1341 1228 632 1582 938 582 1084 605 461 1022 1300 1468 1903\n2053 1364 727 1134 1441 823 1257 1901 2028 61 1485 167 113 536 1854 2157 2092 2161 1715 1024 138 920 482 844 386 2204 1150 79 343 2093 2152 2181 681 438 1221 1487 718 1873 1709 1387 414 1730 913 387 993 983 827\n93 1654 1161 1175 2095 790 1222 1698 1995 855 1771 475 1219 1607 200 1187 811 2027 1665 2023 854 2066 292 1858 601 51 1496 259 825 194 724 937 1296 379 42 1777 2004 1835 1204 1864 1753 2199 2072 619 1392 1106 951\n566 1059 1375 2086 302 2030 1927 477 103 395 1874 995 893 1477 1528 1757 640 922 1573 1209 1946 1503 1282 1783 794 2172 1107 1214 1739 748 1293 1623 31 159 908 1492 1577 425 1986 155 1938 111 973 658 254 1168 458\n2084 124 850 1760 1026 266 1067 1733 1156 1976 969 2005 286 1130 353 1647 305 621 1836 982 776 1851 1558 77 900 314 1474 1265 69 721 2019 264 2073 1788 1440 1206 1126 1410 1994 1207 220 115 392 2186 163 535 797\n1170 33 7 603 1032 859 736 2100 968 2184 2207 1079 394 1451 2159 230 1384 882 188 1229 1525 1385 2111 1138 2160 1159 236 1076 2026 1674 574 63 476 592 1872 1991 299 678 1465 2049 946 1859 2094 1194 1103 210 848\n2099 53 153 541 1405 1448 1741 1033 986 1887 1227 131 32 2061 2070 481 2107 1968 598 229 1740 600 777 2020 965 1191 778 100 67 1043 576 265 1817 1215 502 612 226 2171 2065 351 1145 615 1906 1096 1870 558 1952\n240 1660 1849 1390 3 1490 994 2151 2081 258 1542 1346 843 1245 1160 2170 711 594 2042 1539 1627 1508 1505 1360 532 468 1406 1683 786 739 977 1404 1427 2035 218 422 296 683 534 503 1124 1071 2021 669 1933 1964 1038\n559 127 285 2104 120 168 926 1442 1971 1085 2040 1006 1707 700 1409 2103 980 586 629 1248 1985 388 1393 634 513 1292 1853 1982 864 1249 275 28 55 186 1260 645 529 1599 2106 636 2120 1800 2127 1868 1234 901 390\n1948 1358 822 2153 1826 1834 1841 835 871 48 1195 2110 1560 1547 352 1157 1802 418 1888 1847 238 2191 1243 1972 1140 1476 56 1953 765 584 235 842 915 1236 2169 1469 1548 429 622 1259 300 1848 1949 1283 1377 1087 2047\n1583 2010 399 740 1416 362 505 1045 695 432 1762 1453 1639 335 1860 128 371 2139 626 83 1353 107 1325 370 2183 1197 18 1722 1048 787 1918 1235 743 706 1545 357 1657 862 369 491 1065 1782 43 1250 620 2054 2148\n401 780 1057 1717 1088 799 1271 183 1923 1917 484 861 1732 933 2203 187 1636 274 301 1796 1947 1650 2037 1738 276 330 1837 929 499 789 2116 1770 1916 1460 2205 504 1881 1001 642 1433 2121 935 1064 1315 974 2189 1884\n1114 1792 1313 1054 1695 648 1833 327 949 267 1675 431 2039 2149 1509 1605 948 364 1128 1167 1494 742 667 792 655 1567 1018 281 1691 2188 1578 1013 1196 976 126 1712 1862 866 821 1963 904 1845 663 1694 454 858 1372\n652 60 1748 708 1423 2128 856 509 1182 1729 953 1846 407 624 1056 970 1373 1524 1936 707 1791 1843 1749 686 1699 1787 9 1980 1109 331 312 2114 840 999 761 96 834 39 1481 770 2206 249 1359 1745 2147 205 1655\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 203,
        "task_id": 1088,
        "test_case_id": 15,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "43 2929\n144 1303 830 309 793 387 1559 935 90 691 1002 43 584 1560 162 554 1265 865 1514 894 880 1638 1127 1277 409 1802 1317 134 883 1070 1715 617 1683 32 969 237 666 1428 1353 1650 952 667 1243\n829 1274 154 587 412 1555 933 1100 884 1085 212 107 1768 1191 391 1245 290 101 1176 1656 635 799 882 312 369 1237 1528 1168 1471 1417 568 277 1117 1350 897 889 34 781 1478 1532 1121 891 42\n591 150 523 64 639 1195 774 998 634 1775 981 732 993 1241 179 1229 977 1791 537 973 1316 1742 731 1744 1753 355 1457 1527 194 1022 321 724 1259 1823 484 1125 251 404 284 735 1110 215 285\n1804 360 893 695 441 1233 41 662 1609 1028 1248 1115 672 593 923 198 435 1806 1779 494 1723 722 809 1758 453 1413 1480 479 1219 1596 1163 1847 1431 984 1704 962 660 906 1734 901 22 131 651\n900 1263 1375 424 1180 1185 433 1571 1597 115 636 1752 756 926 1323 350 542 1287 826 747 157 1049 121 1819 552 10 1209 17 632 46 1475 219 699 1572 1467 1331 1751 1531 141 1144 1534 847 1701\n676 501 1184 1386 1709 375 1590 1159 607 1035 1536 598 1114 1646 78 700 1762 6 903 140 169 1642 1079 1737 831 196 260 754 1293 535 246 561 1813 627 188 1162 1736 791 1546 357 372 944 1785\n1382 226 1365 1207 540 1684 1679 1004 844 327 1591 855 469 1019 1474 1380 265 1338 1501 1505 864 1355 1383 473 961 1484 1746 653 93 863 1298 1045 701 1147 269 573 904 40 1681 1188 1777 1645 1171\n146 345 834 319 848 256 1031 1278 1778 822 1498 1416 474 536 937 374 1448 611 1137 129 1612 497 1169 482 1450 1010 11 899 172 1828 139 1637 395 427 1320 518 1831 942 775 1691 1705 509 989\n1183 1181 1150 373 434 126 562 534 291 1661 941 644 1577 446 324 1788 13 1754 1671 207 486 1694 1291 1558 1104 1836 838 1432 550 1351 1294 3 1504 1821 310 1269 1840 1774 65 1223 601 1565 718\n943 960 210 37 1061 1502 751 1673 455 873 98 738 800 368 429 1575 787 1379 235 1437 1801 1487 1352 1608 283 758 868 1138 595 1833 316 1488 1809 1541 1726 305 1069 1165 295 1062 397 189 749\n533 81 258 1231 1666 871 1268 1615 934 1708 1214 1295 19 1039 1780 1290 685 1102 1221 649 1660 330 1091 1491 382 1602 1203 571 850 367 1139 1226 1629 1805 1644 784 763 227 959 271 442 1516 1246\n1567 916 1343 161 1411 1523 1594 1426 208 967 1665 1814 1360 417 245 938 789 1415 1154 1186 280 1787 643 1023 853 580 1674 35 402 20 776 448 612 239 723 1254 18 664 1302 1330 268 366 466\n1672 879 168 1080 1519 386 1453 764 1430 204 415 1084 698 287 1830 128 33 1578 1345 1835 679 619 657 1706 785 307 1455 558 1053 326 1081 1020 1579 1286 777 671 600 610 557 1394 1335 1247 201\n240 1729 877 688 4 1048 1197 1776 529 1280 414 436 1264 1119 658 85 1434 1388 628 1668 1598 1201 1798 202 1340 806 431 1253 1490 47 1721 1756 1283 1266 209 1123 1509 949 1389 481 1208 620 1105\n821 1771 267 583 197 876 661 1230 1562 301 1816 881 569 1628 1346 1361 843 1043 1160 1014 965 1526 1088 160 1341 1766 407 1825 1376 1595 1288 465 1793 1189 910 278 1402 195 217 1038 1556 762 425\n684 1695 264 1133 1324 633 1599 983 87 136 951 421 1496 223 1773 1477 866 358 313 132 946 689 905 294 1826 1739 720 1669 54 422 325 1676 67 994 439 1446 596 704 592 1633 443 978 1135\n1405 1143 338 262 203 1194 166 1057 1710 279 1005 530 462 178 675 1494 396 84 922 769 1606 1003 1393 655 717 1630 1033 560 1401 674 1318 1132 958 1682 117 1542 1187 792 1164 306 538 1686 1304\n89 772 1292 222 1146 606 1157 1099 783 1134 1370 133 885 191 737 713 392 1624 1 1664 1068 504 1220 682 1492 1451 1300 1497 995 1438 1149 920 1112 1118 302 1356 1385 524 625 857 1354 1054 574\n390 819 648 1232 1092 1712 413 786 710 80 1109 394 1399 992 328 1398 1733 1152 1312 801 135 456 1257 63 631 450 748 1215 272 788 1098 389 1073 199 940 1636 948 1439 1750 1769 1347 947 1357\n1728 1029 300 477 930 1427 1106 114 1441 654 5 1568 1743 1680 1419 996 1618 1120 1408 1533 892 673 925 276 1849 566 861 1410 138 681 445 1464 519 1126 693 827 331 576 468 1210 1510 1792 680\n228 1634 1619 221 971 1270 1740 1267 323 130 803 797 526 1607 1529 999 976 909 1550 919 1741 426 1447 380 1725 706 1838 503 823 379 1552 1319 1625 629 1301 1007 1052 1018 913 1107 1573 1076 12\n1377 36 1359 506 779 1520 346 575 1730 1212 683 184 26 1337 712 249 1358 1145 1659 232 1009 1414 1539 183 74 490 498 615 1030 1032 1817 1050 567 1026 400 1503 812 902 1313 361 250 233 1373\n1811 1136 499 428 1588 957 1166 344 1483 1592 1469 1603 371 220 1570 1834 30 1307 955 362 508 1086 770 1065 1827 411 491 1348 1799 849 1090 224 334 175 572 29 1310 1242 810 1060 707 563 816\n766 318 553 320 714 1315 1584 860 1306 1435 956 1617 263 335 1688 512 1071 597 485 96 1663 1199 236 1271 637 1764 1547 1178 1384 1735 1051 1381 890 1252 480 686 1551 1611 1249 1696 1244 492 21\n846 728 1658 1797 1236 1820 505 740 646 1387 430 1829 990 912 76 1151 1587 1407 730 370 103 1604 757 243 281 1235 982 458 1289 927 985 1067 867 99 156 378 577 393 298 669 489 252 1580\n1692 715 742 1583 778 1824 1422 1749 1153 297 247 677 185 837 964 1025 687 24 790 694 755 205 1128 317 1059 975 1702 541 840 585 384 697 460 1216 895 1424 1037 1714 565 1445 1016 1077 531\n408 180 483 1213 914 616 1000 640 349 1175 1311 148 1366 122 1784 1196 359 896 241 244 1082 1458 364 1545 1613 1697 641 911 887 385 696 966 842 716 650 337 609 1508 659 578 1179 348 403\n109 1296 1653 1564 8 73 1772 1449 38 1759 1374 1690 1569 299 1443 293 1812 833 1507 1021 1790 638 1421 1390 66 1844 1755 1476 970 1841 273 626 1640 516 721 410 1781 1096 23 1364 376 100 1440\n159 832 111 652 437 527 496 1342 692 1218 119 14 1056 1512 44 1459 1713 921 112 1193 190 495 1040 1202 642 602 1349 50 193 1616 1327 1130 991 1632 1403 1173 507 1378 1367 1309 487 1842 1418\n1657 1305 1425 1700 1662 556 513 794 488 70 767 238 814 1205 329 1789 343 9 773 1284 1006 1796 28 444 514 734 1563 1258 1540 171 986 1362 1482 1156 795 771 1626 915 862 859 545 1489 870\n177 1703 708 841 59 1204 1486 145 1623 1042 405 476 739 1001 725 668 1260 1593 1344 1677 1299 1024 665 242 1693 1101 470 917 142 1761 82 968 1027 69 116 475 1462 1297 158 1518 1012 440 782\n398 1078 137 1177 711 60 1442 229 1075 1763 1322 807 1506 918 528 1535 1732 705 835 174 1087 124 401 336 39 939 1008 1158 472 49 796 1372 27 91 151 1089 1586 418 92 1783 288 423 954\n332 1461 878 726 1222 1687 1807 520 1561 703 282 399 517 1256 353 1140 1072 1275 1013 1698 79 352 886 1810 945 1748 1765 1566 1822 1108 1499 165 104 805 1466 1517 1719 200 1217 1576 727 471 1094\n1800 1848 341 454 869 459 356 852 230 351 1251 16 1495 936 333 308 1444 1452 225 292 1240 1803 1250 1063 1141 1757 1553 874 1363 1581 1667 1627 858 1392 56 623 1281 780 51 974 811 68 544\n1782 741 824 1326 48 1017 1525 1832 820 71 377 1129 493 1614 304 963 759 1406 511 1605 381 543 798 1400 1172 416 1011 1308 729 1058 702 1167 248 2 153 45 1454 1333 1336 120 1116 170 599\n406 987 1731 311 979 363 765 953 1479 1095 1537 547 950 1678 1404 88 851 551 155 1610 1543 1148 52 463 173 559 1282 1339 1155 1142 1601 1675 502 656 1064 110 1513 1815 856 586 1718 1621 143\n419 1649 1544 1420 980 1234 1689 105 678 663 613 1015 622 818 274 624 931 548 898 1044 25 1720 1738 500 510 1845 733 690 752 825 289 744 1699 1652 216 303 1548 95 594 1846 1582 1412 1727\n347 1328 451 342 1463 123 1574 582 1549 1837 1647 645 1631 1500 1639 1711 447 745 1314 1655 1456 147 1554 1648 1429 1371 839 102 1074 339 1767 1192 152 1622 621 1641 1685 464 1707 630 753 1225 768\n7 58 192 546 1409 254 1794 167 1170 1670 1190 234 77 438 590 457 647 61 1465 211 1481 1055 928 1839 1524 1620 802 1717 214 383 1600 261 1261 1103 1716 420 365 1041 125 186 461 1262 1468\n1818 15 270 1239 1046 181 164 113 828 1808 149 1334 206 1111 257 1238 340 286 72 525 118 515 1182 314 1485 213 1273 813 1034 231 1097 972 1530 1433 53 579 275 1760 1473 1770 1635 736 1589\n521 1391 589 452 1585 997 1093 127 605 86 296 1396 1747 432 815 907 872 55 588 845 266 564 1047 255 1843 555 1083 1557 62 1722 604 478 746 522 322 31 808 603 804 1325 581 1368 57\n1724 1436 1397 1113 1228 259 1538 608 1200 1122 1643 924 1522 1279 1470 1174 570 988 1423 106 929 888 719 187 75 1369 614 218 176 1493 449 1211 1131 908 1521 1654 1460 1329 743 1276 163 875 854\n761 836 1651 1161 1124 932 388 253 182 108 618 1321 1206 1795 467 1745 1511 670 1272 315 709 83 1066 760 817 1472 1255 549 1036 1515 1285 1786 354 1224 94 539 1332 1198 1227 532 750 97 1395\n",
        "output": "588447741\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 204,
        "task_id": 1088,
        "test_case_id": 16,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "6 61\n36 22 23 5 33 27\n12 25 1 3 24 7\n30 8 34 28 26 31\n10 32 14 13 6 9\n17 29 16 20 35 11\n21 18 4 2 15 19\n",
        "output": "518400\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 205,
        "task_id": 1088,
        "test_case_id": 17,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "24 171\n89 273 207 415 290 371 512 269 224 140 502 51 48 105 574 409 40 452 564 404 41 427 355 238\n246 303 513 459 388 99 152 7 68 250 54 126 230 251 115 390 573 214 254 494 108 64 282 312\n572 101 561 406 393 329 407 58 244 295 158 490 243 525 309 424 164 354 461 294 120 528 518 460\n530 352 32 438 268 106 171 122 423 361 88 324 128 386 193 217 419 332 121 80 552 322 263 472\n134 132 236 346 240 91 437 188 545 397 430 182 316 481 498 315 341 248 310 82 93 94 499 501\n63 47 166 149 394 79 235 480 274 74 169 300 495 533 205 111 529 18 429 229 374 67 137 350\n46 65 292 431 275 496 408 213 52 311 114 150 16 109 373 81 95 399 36 258 405 125 565 567\n148 227 29 96 548 559 571 363 351 313 369 113 278 281 556 270 379 116 514 323 13 469 542 544\n546 569 2 286 560 135 220 86 398 162 44 20 42 12 133 550 448 191 465 343 478 453 119 131\n508 5 462 493 446 206 426 28 267 37 223 327 331 145 434 179 326 563 49 306 160 107 197 211\n170 288 555 457 365 187 442 447 276 340 557 177 297 53 367 155 174 200 144 285 157 526 39 141\n266 1 76 575 257 180 362 147 271 27 527 167 11 219 153 259 500 225 333 314 421 458 543 497\n378 165 432 414 102 129 541 517 318 183 370 562 385 466 360 308 503 184 175 26 554 84 535 456\n203 57 55 534 216 185 92 420 195 209 492 69 337 256 473 85 90 348 377 104 77 25 112 450\n321 372 34 382 242 264 558 468 568 22 425 539 319 381 488 505 471 485 357 477 519 342 198 237\n233 124 304 566 221 280 78 509 538 540 272 118 353 334 72 127 507 504 440 359 202 146 159 506\n181 307 73 441 479 483 547 222 110 291 524 454 24 142 260 172 154 536 6 464 576 17 296 226\n328 21 139 156 317 521 410 232 305 349 196 366 384 83 143 344 537 30 345 467 412 45 61 422\n364 161 279 570 71 283 284 56 253 163 218 66 443 23 33 416 396 403 130 245 50 451 31 339\n231 75 320 192 194 463 241 186 204 487 392 19 3 418 173 389 515 482 491 376 201 168 138 210\n70 293 325 510 522 411 302 98 87 489 511 455 532 335 247 249 228 549 470 301 402 60 383 255\n43 265 299 391 413 38 474 136 444 35 59 395 433 358 262 287 189 4 62 100 208 380 212 9\n387 277 215 234 178 15 8 520 439 97 531 436 449 103 445 338 523 476 516 298 239 347 14 417\n375 190 289 117 252 401 486 151 199 400 484 336 176 10 553 428 330 123 435 356 475 261 368 551\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 206,
        "task_id": 1088,
        "test_case_id": 18,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "12 283\n79 94 106 40 56 35 63 65 68 89 41 140\n109 78 37 38 50 4 70 86 73 74 39 134\n66 130 83 97 2 133 14 87 99 111 60 135\n110 136 21 131 52 84 112 115 100 19 137 143\n5 12 23 62 33 9 6 105 101 113 125 46\n77 18 30 132 15 128 117 43 28 114 126 24\n42 17 57 11 32 67 1 91 93 88 127 139\n8 20 59 90 49 138 16 92 104 118 95 69\n85 54 53 45 7 64 81 103 119 31 129 141\n10 22 82 34 26 124 98 76 75 44 13 3\n121 102 61 47 25 71 27 80 107 116 72 122\n123 55 120 48 29 51 58 96 108 36 142 144\n",
        "output": "350016467\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 207,
        "task_id": 1088,
        "test_case_id": 19,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "7 69\n17 41 47 1 37 48 3\n24 25 15 34 46 42 39\n33 27 40 18 7 13 32\n45 2 44 31 14 30 10\n38 9 11 28 21 16 5\n12 26 4 43 36 23 8\n49 22 19 20 35 29 6\n",
        "output": "288\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 208,
        "task_id": 1088,
        "test_case_id": 20,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "12 274\n119 97 3 4 49 6 13 8 116 38 11 79\n53 14 15 64 37 76 96 20 138 128 130 32\n23 115 27 63 135 30 33 73 31 78 44 62\n17 12 94 40 89 52 57 100 7 66 102 39\n114 46 51 42 136 54 55 56 106 34 2 99\n88 48 50 16 65 86 67 87 140 103 25 60\n5 41 72 18 131 45 21 118 81 82 142 19\n85 92 35 83 22 90 91 75 123 58 36 141\n126 121 93 29 134 105 70 104 71 120 137 108\n26 133 111 112 113 59 10 101 117 80 9 110\n98 122 47 124 74 95 127 28 129 43 77 132\n125 1 68 61 109 84 139 69 107 24 143 144\n",
        "output": "350016467\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 209,
        "task_id": 1088,
        "test_case_id": 21,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "2 5\n1 2\n4 3\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 210,
        "task_id": 1088,
        "test_case_id": 22,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "14 250\n1 15 139 27 135 79 30 99 29 124 141 155 72 183\n125 16 85 97 58 56 122 126 114 173 48 41 142 17\n3 169 31 147 82 73 22 45 78 129 35 128 171 185\n4 66 176 46 64 187 40 14 162 130 144 161 91 186\n5 70 182 18 107 83 92 103 137 132 102 11 180 74\n6 89 151 38 60 111 90 86 13 115 145 160 105 113\n7 21 143 149 184 77 172 76 119 116 67 196 63 98\n8 87 133 50 49 131 24 136 61 134 148 192 32 190\n9 23 37 51 65 33 93 120 117 57 138 163 177 191\n167 20 170 52 47 80 150 108 157 106 94 55 188 62\n127 164 39 75 101 81 34 71 165 158 95 123 159 193\n12 26 88 100 154 59 96 110 104 118 152 166 179 194\n36 43 156 121 69 53 44 42 2 68 175 10 181 195\n146 28 153 112 178 84 189 174 54 140 19 168 25 109\n",
        "output": "144\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 211,
        "task_id": 1088,
        "test_case_id": 23,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "5 26\n14 9 6 21 19\n16 4 8 12 1\n25 5 15 7 18\n20 17 24 10 23\n3 13 11 22 2\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 212,
        "task_id": 1088,
        "test_case_id": 24,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "6 61\n36 22 23 5 33 27\n12 25 1 3 24 7\n30 8 34 28 26 31\n10 32 14 13 6 9\n17 29 16 20 35 11\n21 18 4 2 15 19\n",
        "output": "518400\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 213,
        "task_id": 1088,
        "test_case_id": 25,
        "question": "Given are an N \\times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \\dots, N^2 exactly once.\nSigma can repeat the following two kinds of operation arbitrarily many times in any order.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{i, x} + a_{i, y} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th columns.\n - Pick two integers x, y (1 \\leq x < y \\leq N) that satisfy a_{x, i} + a_{y, i} \\leq K for all i (1 \\leq i \\leq N) and swap the x-th and the y-th rows.\nHow many matrices can he obtain by these operations? Find it modulo 998244353.\n\n-----Constraints-----\n - 1 \\leq N \\leq 50\n - 1 \\leq K \\leq 2 \\times N^2\n - a_{i, j}'s are a rearrangement of 1, 2, \\dots, N^2.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\na_{1, 1} a_{1, 2} ... a_{1, N}\na_{2, 1} a_{2, 2} ... a_{2, N}\n:\na_{N, 1} a_{N, 2} ... a_{N, N}\n\n-----Output-----\nPrint the number of matrices Sigma can obtain modulo 998244353.\n\n-----Sample Input-----\n3 13\n3 2 7\n4 8 9\n1 6 5\n\n-----Sample Output-----\n12\n\nFor example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:\n2 3 7\n8 4 9\n6 1 5\n\nAfter that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:\n6 1 5\n8 4 9\n2 3 7\n",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\ngyou,retu = [],[]\\nans = 1\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        gyou.append((i,j))\\nuf_gyou = UnionFind(N)\\nfor x,y in gyou:\\n    uf_gyou.union(x,y)\\nfor x in uf_gyou.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        retu.append((i,j))\\nuf_retu = UnionFind(N)\\nfor x,y in retu:\\n    uf_retu.union(x,y)\\nfor x in uf_retu.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"import math\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nmod = 998244353\\n\\nclass DSU:\\n    def __init__(self, n):\\n        self.uf = {i: i for i in range(n)}\\n        self.rank = {i: 1 for i in range(n)}\\n\\n    def find(self, x):\\n        if self.uf[x] != x:\\n            self.uf[x] = self.find(self.uf[x])\\n        return self.uf[x]\\n\\n    def union(self, x, y):\\n        px, py = self.find(x), self.find(y)\\n        if px != py:\\n            if self.rank[px] > self.rank[py]:\\n                px, py = py, px\\n            self.rank[py] += self.rank[px]\\n            self.uf[px] = py\\n\\nrow, col = DSU(N), DSU(N)\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(A[i], A[j])):\\n            row.union(i, j)\\nB = list(zip(*A))\\nfor i in range(N):\\n    for j in range(i + 1, N):\\n        if all(a + b <= K for a, b in zip(B[i], B[j])):\\n            col.union(i, j)\\nans = 1\\nfor x in set(row.find(i) for i in range(N)):\\n    ans *= math.factorial(row.rank[x])\\n    ans %= mod\\nfor x in set(col.find(i) for i in range(N)):\\n    ans *= math.factorial(col.rank[x])\\n    ans %= mod\\nprint(ans)\", \"import sys\\nimport math\\n\\ndef input():\\n    return sys.stdin.readline().rstrip()\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n    def all_family_count(self):\\n        return [-min(0,x) for i, x in enumerate(self.parents) ]\\n\\ndef main():\\n    N,K=list(map(int,input().split()))\\n    mod =998244353\\n    A = [[] for _ in range(N)]\\n    for i in range(N):\\n        a = list(map(int,input().split()))\\n        A[i] =a\\n\\n    row = UnionFind(N)\\n    column = UnionFind(N)\\n\\n\\n    #row\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[i][w] +A[j][w] >K:\\n                    break\\n            else:\\n                row.union(i,j)\\n\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            for w in range(N):\\n                if A[w][i] +A[w][j] >K:\\n                    break\\n            else:\\n                column.union(i,j)\\n\\n    root_row  = row.all_family_count()\\n    ans_row =1\\n    for i in range(N):\\n        k = root_row[i]\\n        ans_row *=math.factorial(k)\\n\\n\\n\\n\\n    root_column = column.all_family_count()\\n    ans_column =1\\n    for i in range(N):\\n        k = root_column[i]\\n        ans_column *=math.factorial(k)\\n    \\n\\n\\n\\n    print((ans_column*ans_row%mod))\\n\\n    \\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nufr.allfind()\\nufc.allfind()\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=list(map(int,input().split()))\\nm=998244353\\n\\nP=[-1]*n\\n\\ndef find(x):\\n  if P[x]<0:\\n    return x\\n  P[x]=find(P[x])\\n  return P[x]\\n\\ndef unite(x,y):\\n  x=find(x)\\n  y=find(y)\\n  if x==y:\\n    return\\n\\n  if P[x]>P[y]:\\n    P[y]+=P[x]\\n    P[x]=y\\n  else:\\n    P[x]+=P[y]\\n    P[y]=x\\n\\ndef f(n):\\n  a=1\\n  while n>0:\\n    a*=n\\n    n-=1\\n  return a\\n\\nA=[[int(c) for c in input().split()] for r in range(n)]\\n\\nfor r1 in range(n):\\n  for r2 in range(r1+1,n):\\n    for c in range(n):\\n      if A[r1][c]+A[r2][c]>k:\\n        break\\n    else:\\n      unite(r1,r2)\\n\\na=1\\nfor r in range(n):\\n  if P[r]<0:\\n    a=(a*f(-P[r]))%m\\n\\nP=[-1]*n\\nfor c1 in range(n):\\n  for c2 in range(c1+1,n):\\n    for r in range(n):\\n      if A[r][c1]+A[r][c2]>k:\\n        break\\n    else:\\n      unite(c1,c2)\\n\\nfor c in range(n):\\n  if P[c]<0:\\n    a=(a*f(-P[c]))%m\\n\\nprint(a)\\n\", \"def main():\\n    import sys\\n    from collections import Counter\\n    from math import factorial\\n    input = sys.stdin.readline\\n    MOD = 998244353\\n    N, K = [int(x) for x in input().strip().split()]\\n    A = [0 for n in range(N)]\\n    for n in range(N):\\n        A[n] = [int(x) for x in input().strip().split()]\\n        # print(A[n])\\n    ans = 1\\n    def find(x):\\n        if c[x] == x:\\n            return x\\n        c[x] = find(c[x])\\n        return c[x]\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[n][i] + A[n][j] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n    c = [n for n in range(N)]\\n    for i in range(N-1):\\n        for j in range(i+1, N):\\n            for n in range(N):\\n                if A[i][n] + A[j][n] > K:\\n                    break\\n            else:\\n                if c[j] > c[i]:\\n                    c[j] = c[i]\\n                else:\\n                    c[i] = c[j]\\n    for i in range(N):\\n        find(i)\\n    # print(c)\\n    for d in Counter(c).values():\\n        ans = (ans * factorial(d)) % MOD\\n\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        anc2mem = dict()\\n        for i in range(self._n):\\n            anc = self.leader(i)\\n            if anc in anc2mem:\\n                anc2mem[anc].append(i)\\n            else:\\n                anc2mem[anc] = [i]\\n        return list(anc2mem.values())\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"import sys\\ndef input():\\n\\treturn sys.stdin.readline()[:-1]\\n\\nclass UnionFind():\\n\\tdef __init__(self, size):\\n\\t\\tself.table = [-1 for _ in range(size)]\\n\\t\\tself.size = [1 for _ in range(size)]\\n\\n\\tdef find(self, x):\\n\\t\\twhile self.table[x] >= 0:\\n\\t\\t\\tif self.table[self.table[x]] >= 0:\\n\\t\\t\\t\\tself.table[x] = self.table[self.table[x]]\\n\\t\\t\\tx = self.table[x]\\n\\t\\treturn x\\n\\n\\tdef same(self, x, y):\\n\\t\\treturn self.find(x) == self.find(y)\\n\\n\\tdef unite(self, x, y):\\n\\t\\ts1 = self.find(x)\\n\\t\\ts2 = self.find(y)\\n\\t\\tif s1 != s2:\\n\\t\\t\\tr1 = self.table[s1]\\n\\t\\t\\tr2 = self.table[s2]\\n\\t\\t\\tif r1 <= r2:\\n\\t\\t\\t\\tself.table[s2] = s1\\n\\t\\t\\t\\tif r1 == r2:\\n\\t\\t\\t\\t\\tself.table[s1] -= 1\\n\\t\\t\\t\\tself.size[s1] += self.size[s2]\\n\\t\\t\\t\\tself.size[s2] = 0\\n\\t\\t\\telse:\\n\\t\\t\\t\\tself.table[s1] = s2\\n\\t\\t\\t\\tself.size[s2] += self.size[s1]\\n\\t\\t\\t\\tself.size[s1] = 0\\n\\t\\treturn\\n\\nMOD = 998244353\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nans = 1\\n\\nuf_t = UnionFind(n)\\nuf_y = UnionFind(n)\\n\\nfor s in range(1, n):\\n\\tfor t in range(s):\\n\\t\\tok_y, ok_t = True, True\\n\\t\\tfor i in range(n):\\n\\t\\t\\tif a[s][i] + a[t][i] > k:\\n\\t\\t\\t\\tok_y = False\\n\\t\\t\\tif a[i][s] + a[i][t] > k:\\n\\t\\t\\t\\tok_t = False\\n\\t\\tif ok_y:\\n\\t\\t\\tuf_y.unite(s, t)\\n\\t\\tif ok_t:\\n\\t\\t\\tuf_t.unite(s, t)\\n\\nfact = [1 for _ in range(51)]\\nfor i in range(1, 51):\\n\\tfact[i] = (fact[i-1] * i) % MOD\\n\\nfor i in range(n):\\n\\tif uf_t.size[i] > 0:\\n\\t\\tans *= fact[uf_t.size[i]]\\n\\t\\tans %= MOD\\n\\tif uf_y.size[i] > 0:\\n\\t\\tans *= fact[uf_y.size[i]]\\n\\t\\tans %= MOD\\n\\nprint(ans)\", \"class UnionFind(object):\\n    def __init__(self, n=1):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.size = [1 for _ in range(n)]\\n    def find(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u63a2\\u7d22\\u3057\\u3066\\u89aa\\u3092\\u51fa\\u3059\\u3002\\n        \\\"\\\"\\\"\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d50\\u5408\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.size[x] += self.size[y]\\n    def is_same(self, x, y):\\n        \\\"\\\"\\\"\\n        x \\u3068 y \\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    def get_size(self, x):\\n        \\\"\\\"\\\"\\n        x \\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN,K = map(int,input().split())\\nMOD = 998244353\\n\\nfac = [-1]*(N+1); fac[0] = 1; fac[1] = 1 #\\u968e\\u4e57\\nfinv = [-1]*(N+1); finv[0] = 1; finv[1] = 1 #\\u968e\\u4e57\\u306e\\u9006\\u5143\\ninv = [-1]*(N+1); inv[0] = 0; inv[1] = 1 #\\u9006\\u5143\\nfor i in range(2,N+1):\\n  fac[i] = fac[i-1]*i%MOD\\n  inv[i] = MOD - inv[MOD%i]*(MOD//i)%MOD\\n  finv[i] = finv[i-1]*inv[i]%MOD\\n  \\n  \\nimport numpy as np\\n\\nA = np.array([list(map(int,input().split())) for _ in range(N)])\\n\\nuf0 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf0.union(i,j)\\n\\npar0 = set([])\\nfor i in range(N):\\n  par = uf0.find(i)\\n  par0.add(par)\\n#print(par0)\\n\\nX = 1\\nfor x in par0:\\n  temp = uf0.get_size(x)\\n  X = X*fac[temp]%MOD\\n\\nA = A.T\\n#print(A)\\n\\nuf1 = UnionFind(N)\\nfor i in range(N):\\n  for j in range(N):\\n    if i == j:\\n      continue\\n    for k in range(N):\\n      if A[i,k] + A[j,k] > K:\\n        break\\n    else:\\n      uf1.union(i,j)\\n\\npar1 = set([])\\nfor i in range(N):\\n  par = uf1.find(i)\\n  par1.add(par)\\n\\nY = 1\\nfor y in par1:\\n  temp = uf1.get_size(y)\\n  Y = Y*fac[temp]%MOD\\n#print(Y)\\n\\nans = X*Y%MOD\\nprint(ans)\", \"#!/usr/bin/env python3\\nimport sys\\nfrom collections import deque, Counter\\nfrom heapq import heappop, heappush\\nfrom bisect import bisect_right\\nfrom itertools import accumulate\\n\\nsys.setrecursionlimit(10**6)\\nINF = 10**12\\nm = 998244353\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.parents = list(range(n))\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] == x:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.size[x] < self.size[y]:\\n                x, y = y, x\\n            self.parents[y] = x\\n            self.size[x] += self.size[y]\\n\\n\\ndef main():\\n    N, K = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(N)]\\n    ans = 1\\n\\n    p = 998244353\\n    a = [None] * (N+1)\\n    inva = [None] * (N+1)\\n    a[0] = 1\\n\\n    for i in range(1, N+1):\\n        a[i] = i * a[i-1] % p\\n\\n    inva[N] = pow(a[N], p-2, p)\\n    for i in range(N):\\n        inva[N-i-1] = inva[N-i] * (N-i) % p\\n\\n    rowuf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    break\\n            else:\\n                rowuf.union(x, y)\\n\\n    rows = []\\n    for i in range(N):\\n        rows.append(rowuf.find(i))\\n\\n    # print(rows)\\n    for l in list(Counter(rows).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    coluf = UnionFind(N)\\n    for x in range(N):\\n        for y in range(x + 1, N):\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    break\\n            else:\\n                coluf.union(x, y)\\n    cols = []\\n    for i in range(N):\\n        cols.append(coluf.find(i))\\n\\n    # print(cols)\\n    for l in list(Counter(cols).values()):\\n        ans *= a[l]\\n        ans %= p\\n\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"class union_find:\\n  def __init__(self, n):\\n    self.par = [-1] * n\\n\\n  def find(self, x):#x\\u306e\\u89aa\\u3092\\u898b\\u3064\\u3051\\u308b\\n    if self.par[x] < 0:\\n      return x\\n    else:\\n      self.par[x] = self.find(self.par[x])\\n      return self.par[x]\\n\\n  def unite(self,x,y):#\\u8981\\u7d20x\\u3068\\uff59\\u3092\\u4f75\\u5408\\u3055\\u305b\\u308b\\n    x,y=self.find(x),self.find(y)#x\\u3068y\\u306e\\u89aa\\u306e\\u691c\\u7d22\\n    if x!=y:#\\u89aa\\u304c\\u7570\\u306a\\u308b\\u5834\\u5408\\u4f75\\u5408\\u3055\\u305b\\u308b\\n      if x>y:\\n        x,y=y,x#\\u5c0f\\u3055\\u3044\\u65b9\\u3092x\\u3068\\u3059\\u308b. \\u3053\\u308c\\u306b\\u3088\\u308a\\u8981\\u7d20\\u306e\\u5024\\u304c\\u5c0f\\u3055\\u3044\\u3082\\u306e\\u3092\\u512a\\u5148\\u3057\\u3066\\u6728\\u306e\\u6839\\u3068\\u3059\\u308b. \\n      self.par[x]+=self.par[y] #\\u5024\\u3092\\u7121\\u5411\\u6728\\u306e\\u8981\\u7d20\\u6570\\u306e\\u548c\\u306b\\u3059\\u308b.\\n      self.par[y]=x #\\u679d\\u5074\\u306f\\u6839\\u306e\\u4f4d\\u7f6e\\u3092\\u683c\\u7d0d\\n\\n  def same(self, x, y):#\\u8981\\u7d20x\\u3068\\u8981\\u7d20y\\u304c\\u540c\\u3058\\u7121\\u5411\\u6728\\u306b\\u6240\\u5c5e\\u3057\\u3066\\u3044\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n    return self.find(x) == self.find(y)#\\u540c\\u3058\\u5024\\u3092\\u6301\\u3064\\u304b\\u5426\\u304b\\n\\n  def size(self, x):#\\u8981\\u7d20x\\u304c\\u6240\\u5c5e\\u3059\\u308b\\u7121\\u5411\\u6728\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\n    return-self.par[self.find(x)] \\n\\nimport itertools  \\nmod = 998244353\\ndef main():\\n  n, k = map(int,input().split())\\n  factorial = [1]\\n  for i in range(1, n+1):\\n    factorial.append(factorial[i-1]*i%mod)\\n  a = []\\n  for i in range(n):\\n    a.append(list(map(int, input().split())))\\n  gyou = union_find(n)\\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[x][i] + a[y][i] > k:\\n        flag = False\\n        break\\n    if flag:\\n      gyou.unite(x, y)\\n  retu = union_find(n)\\n  \\n  for x, y in itertools.combinations(range(n), 2):\\n    flag = True\\n    for i in range(n):\\n      if a[i][x] + a[i][y] > k:\\n        flag = False\\n        break\\n    if flag:\\n      retu.unite(x, y)\\n  ans = 1\\n  for i in range(len(retu.par)):\\n    if retu.par[i] < 0:\\n      ans *=factorial[-retu.par[i]]\\n    ans %= mod\\n  for i in range(len(gyou.par)):\\n    if gyou.par[i] < 0:\\n      ans *= factorial[-gyou.par[i]]\\n    ans %= mod\\n  print(ans)  \\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"class dsu():\\n    \\\"\\\"\\\"Data structures and algorithms for disjoint set union problems.\\n    \\n    Given an undirected graph, it processes the following queries in O(alpha(n)) time (amortized).\\n\\n    >   Edge addition\\n    \\n    >   Deciding whether given two vertices are in the same connected component\\n\\n    Each connected component internally has a representative vertex.\\n\\n    When two connected components are merged by edge addition, one of the two representatives of these connected components becomes the representative of the new connected component.\\n    \\\"\\\"\\\"\\n\\n\\n    __slots__ = [\\\"_n\\\", \\\"parent_or_size\\\"]\\n\\n\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\n        It creates an undirected graph with n vertices and 0 edges.\\n        \\n        Constraints\\n        -----------\\n\\n        >   0 <= n <= 10 ** 8\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        self._n = n\\n        self.parent_or_size = [-1] * n\\n    \\n    \\n    def merge(self, a, b):\\n        \\\"\\\"\\\"\\n        It adds an edge (a, b).\\n\\n        If the vertices a and b were in the same connected component, it returns the representative of this connected component. Otherwise, it returns the representative of the new connected component.\\n       \\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n \\n\\n        >   0 <= b < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y:\\n            return x\\n        else:\\n            if self.parent_or_size[y] < self.parent_or_size[x]:\\n                x, y = y, x\\n            self.parent_or_size[x] += self.parent_or_size[y]\\n            self.parent_or_size[y] = x\\n\\n\\n    def same(self, a, b):\\n        \\\"\\\"\\\"\\n        It returns whether the vertices a and b are in the same connected component.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        >   0 <= b < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        # assert 0 <= b < self._n\\n        return self.leader(a) == self.leader(b)\\n\\n\\n    def leader(self, a):\\n        \\\"\\\"\\\"\\n        It returns the representative of the connected component that contains the vertex a.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n\\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        path = []\\n        while self.parent_or_size[a] >= 0:\\n            path.append(a)\\n            a = self.parent_or_size[a]\\n        for child in path:\\n            self.parent_or_size[child] = a\\n        return a\\n\\n    \\n    def size(self, a):\\n        \\\"\\\"\\\"\\n        It returns the size of the connected component that contains the vertex aa.\\n\\n        Constraints\\n        -----------\\n\\n        >   0 <= a < n\\n        \\n        Complexity\\n        ----------\\n\\n        >   O(alpha(n)) amortized\\n        \\\"\\\"\\\"\\n        # assert 0 <= a < self._n\\n        return -self.parent_or_size[self.leader(a)]\\n\\n\\n    def groups(self):\\n        \\\"\\\"\\\"\\n        It divides the graph into connected components and returns the list of them.\\n\\n        More precisely, it returns the list of the \\\"list of the vertices in a connected component\\\". Both of the orders of the connected components and the vertices are undefined.\\n\\n        Complexity\\n        ----------\\n\\n        >   O(n)\\n        \\\"\\\"\\\"\\n        result = [[] for _ in range(self._n)]\\n        for i in range(self._n):\\n            result[self.leader(i)].append(i)\\n        return [g for g in result if g]\\n\\n\\n\\nMOD = 998244353\\ntable_len = 110\\n\\nfac = [1, 1]\\nfor i in range(2, table_len):\\n    fac.append(fac[-1] * i % MOD)\\n\\nfinv = [0] * table_len\\nfinv[-1] = pow(fac[-1], MOD - 2, MOD)\\nfor i in range(table_len-1, 0, -1):\\n    finv[i-1] = finv[i] * i % MOD\\n\\nN, K = list(map(int, input().split()))\\nAs = [list(map(int, input().split())) for _ in range(N)]\\n\\ndef solve_row(mat):\\n    uf = dsu(N)\\n    for i in range(N):\\n        for j in range(i + 1, N):\\n            for k in range(N):\\n                if mat[i][k] + mat[j][k] > K:\\n                    break\\n            else:\\n                uf.merge(i, j)\\n    groups = uf.groups()\\n    ret = 1\\n    for g in groups:\\n        ret *= fac[len(g)]\\n        ret %= MOD\\n    return ret\\n\\ntAs = list(map(list, list(zip(*As))))\\nprint((solve_row(As) * solve_row(tAs) % MOD))\\n\\n\", \"class DSU:\\n    def __init__(self, N):\\n        # stores parent node of given vertex\\n        self.parents = list(range(N))\\n        # gives size of component w given node\\n        self.size = [1] * N\\n\\n    # runtime: amoritized O(1)\\n    # returns root node\\n    def find(self, x):\\n        root = x\\n        # finds parent node at the end of the chain\\n        while self.parents[root] != root:\\n            root = self.parents[root]\\n\\n        # optional: path compression\\n        while (x != root):\\n            nextx = self.parents[x]\\n            self.parents[x] = root\\n            x = nextx\\n        \\n        return root\\n\\n    # runtime: amortized O(1) by combining union by size and path compression\\n    # unifies two components together (the ones containing x and y)\\n    def union(self, x, y):\\n        xr, yr = self.find(x), self.find(y)\\n        # if they're in same group, do nothing\\n        if xr == yr:\\n            return False\\n\\n        if self.size[xr] > self.size[yr]:\\n            xr, yr = yr, xr\\n        # size of xr >= size of yr\\n        # smaller points to the larger\\n        self.parents[xr] = yr\\n        self.size[xr] += self.size[yr]\\n        self.size[yr] = self.size[xr]\\n        return True\\n\\n    def isConnected(self,x,y):\\n        return self.find(x) == self.find(y)\\n\\n    def getSize(self, x):\\n        return self.size[self.find(x)]\\n\\n\\n# from collections import defaultdict, Counter, deque\\n# from heapq import heappop, heappush, heapify\\n# from functools import lru_cache, reduce\\n# import bisect\\n# from itertools import permutations, combinations, combinations_with_replacement\\nfrom math import factorial as f\\n\\nmod = 998244353\\nn, K = list(map(int, input().split()))\\narr = []\\nfor _ in range(n):\\n    arr.append( list(map(int, input().split())) )\\n\\n# num of pairs you can swap\\nrow_dsu = DSU(n)\\ncol_dsu = DSU(n)\\n\\n# find rows\\nfor i in range(n):\\n    for j in range(i):\\n        if all(arr[i][k] + arr[j][k] <= K for k in range(n)):\\n            row_dsu.union(i,j)\\n        if all(arr[k][i] + arr[k][j] <= K for k in range(n)):\\n            col_dsu.union(i,j)\\n    \\nrow_set = set()\\ncol_set = set()\\nfor i in range(n):\\n    row_set.add(row_dsu.find(i))\\n    col_set.add(col_dsu.find(i))\\n\\nrow_prod = col_prod = 1\\nfor ele in row_set:\\n    row_prod *= f(row_dsu.size[ele])\\nfor ele in col_set: \\n    col_prod *= f(col_dsu.size[ele])\\n\\nprint(((row_prod * col_prod) % mod))\\n\\n\", \"import sys\\nfrom math import factorial\\nsys.setrecursionlimit(10**9)\\nread = lambda:sys.stdin.readline()\\n\\ndef read_ints():\\n    return list(map(int,read().split()))\\ndef read_intgrid(h):\\n    return list(list(map(int,read().split()))for i in range(h))\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n        self.rank = [0] * n\\n        self.group_count = n\\n        self.n = n\\n    \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        \\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.rank[x] == self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n            self.rank[x] += 1\\n        \\n        elif self.rank[x] > self.rank[y]:\\n            self.parents[x] += self.parents[y]\\n            self.parents[y] = x\\n        else:\\n            self.parents[y] += self.parents[x]\\n            self.parents[x] = y\\n        \\n        self.group_count -= 1\\n    \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == x]\\n    \\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n \\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parents) if n < 0}\\n\\ndef f(x):\\n    tmp = 1\\n    while x>0:\\n        tmp*=x\\n        x-=1\\n    return tmp\\n\\ndef main():\\n    #input data\\n    n,k = map(int,input().split())\\n    A = read_intgrid(n)\\n\\n    mod = 998244353\\n\\n    #solve\\n    ans = 1\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    # fix by columns\\n    for i in range(n-1):\\n        for j in range(i+1,n):\\n            if all(A[i][c]+A[j][c]<=k for c in range(n)):\\n                uf1.unite(i,j)\\n            if all(A[c][i]+A[c][j]<=k for c in range(n)):\\n                uf2.unite(i,j)\\n\\n    for k,v in uf1.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n\\n    for k,v in uf2.get_all_groups().items():\\n        ans*=f(v)\\n        ans%=mod\\n    \\n    return print(ans)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"class UnionFind:\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n        \\nimport itertools\\n\\nN,K = map(int,input().split())\\nl = [list(map(int,input().split())) for i in range(N)]\\n#print(l)\\na = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[i][v[0]] + l[i][v[1]] > K:\\n            break\\n        if i == N-1:\\n            a.union(v[0],v[1])\\n#print(a)\\n        \\nb = UnionFind(N)\\nfor v in itertools.combinations(range(N),2):\\n    for i in range(N):\\n        if l[v[0]][i] + l[v[1]][i] > K:\\n            break\\n        if i == N-1:\\n            b.union(v[0],v[1])\\n#print(b)\\n\\nans = 1\\n\\nfor x in a.roots():\\n    for i in range(1,a.size(x)+1):\\n        ans = (ans * i)%998244353\\nfor x in b.roots():\\n    for i in range(1,b.size(x)+1):\\n        ans = (ans * i)%998244353\\n    \\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(j)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"n,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nretu=[]\\ngyou=[]\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        for p in range(n):\\n            if a[i][p]+a[j][p]>k:\\n                break\\n        else:\\n            gyou.append([i,j])\\n        for q in range(n):\\n            if a[q][i]+a[q][j]>k:\\n                break\\n        else:\\n            retu.append([i,j])\\n\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\nretuuf=UnionFind(n)\\ngyouuf=UnionFind(n)\\n\\nfor i in retu:\\n    retuuf.union(i[0],i[1])\\nfor i in gyou:\\n    gyouuf.union(i[0],i[1])\\n\\ngyouans=1\\nretuans=1\\n\\nretulist=list(retuuf.all_group_members().values())\\ngyoulist=list(gyouuf.all_group_members().values())\\n\\nimport math\\n\\nfor i in retulist:\\n    retuans*=math.factorial(len(i))\\nfor i in gyoulist:\\n    gyouans*=math.factorial(len(i))\\n\\nprint(retuans*gyouans%998244353)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import bisect, copy, heapq, math, sys\\nfrom collections import *\\nfrom functools import lru_cache\\nfrom itertools import accumulate, combinations, permutations, product\\ndef input():\\n    return sys.stdin.readline()[:-1]\\ndef ruiseki(lst):\\n    return [0]+list(accumulate(lst))\\ndef celi(a,b):\\n    return -(-a//b)\\nsys.setrecursionlimit(5000000)\\nmod=998244353\\nal=[chr(ord('a') + i) for i in range(26)]\\ndirection=[[1,0],[0,1],[-1,0],[0,-1]]\\n\\nn,k=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\n\\nclass WeightedUnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n+1)]\\n        self.rank = [0] * (n+1)\\n        self.weight = [0] * (n+1)\\n        self.sizes = [1] * (n+1)\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            y = self.find(self.par[x])\\n            self.weight[x] += self.weight[self.par[x]]\\n            self.par[x] = y\\n            return y\\n\\n    def union(self, x, y, w=1):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        if self.rank[rx] < self.rank[ry]:\\n            self.sizes[ry] += self.size(rx)\\n            self.par[rx] = ry\\n            self.weight[rx] = w - self.weight[x] + self.weight[y]\\n        else:\\n            self.sizes[rx] += self.size(ry)\\n            self.par[ry] = rx\\n            self.weight[ry] = -w - self.weight[y] + self.weight[x]\\n            if self.rank[rx] == self.rank[ry]:\\n                self.rank[rx] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def diff(self, x, y):\\n        return self.weight[x] - self.weight[y]\\n\\n    def size(self, x):\\n        return self.sizes[self.find(x)]\\n# print(a)\\nretsu=WeightedUnionFind(n)\\ngyo=WeightedUnionFind(n)\\n\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[l][i]+a[l][j]>k:\\n                break\\n        else:\\n            if not retsu.same(i,j):\\n                retsu.union(i,j)\\n# print(retsu)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        for l in range(n):\\n            if a[i][l]+a[j][l]>k:\\n                break\\n        else:\\n            if not gyo.same(i,j):\\n                gyo.union(i,j)\\n\\nans=1\\ndef keisan(ans,m):\\n    for i in range(m):\\n        ans*=i+1\\n        ans%=mod\\n    return ans\\n\\n# print(retsu.par)\\n# print(gyo.par)\\n\\nfor i in range(n):\\n    if i==retsu.find(i):\\n        ans=keisan(ans,retsu.size(i))\\n    if i==gyo.find(i):\\n        ans=keisan(ans,gyo.size(i))\\nprint(ans)\", \"from math import factorial\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    \\n    #\\u8981\\u7d20x\\u304c\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u6839\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u4f75\\u5408\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    #x\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30b5\\u30a4\\u30ba\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nans = 1\\nflag = 1\\n\\nuf = UnionFind(n)\\n# \\u884c\\u65b9\\u5411\\nfor r1 in range(n):\\n    for r2 in range(r1+1, n):\\n        for c in range(n):\\n            flag = 1\\n            if a[r1][c]+a[r2][c] > k:\\n                flag = 0\\n                break\\n        \\n        if flag:\\n            uf.union(r1, r2)\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\n\\nuf = UnionFind(n)\\n\\n# \\u5217\\nfor c1 in range(n):\\n    for c2 in range(c1+1, n):\\n        for r in range(n):\\n            flag = 1\\n            if a[r][c1]+a[r][c2] > k:\\n                flag = 0\\n                break\\n        if flag:\\n            uf.union(c1, c2)\\n\\nfor i in range(n):\\n    if uf.parents[i] < 0:\\n        ans *= factorial(uf.size(i))\\n        ans %= mod\\nprint(ans)\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"n, k = list(map(int, input().split()))\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\ndef Find(x, par):\\n    if par[x] < 0:\\n        return x\\n    else:\\n        par[x] = Find(par[x], par)\\n        return par[x]\\n\\ndef Unite(x, y, par, rank):\\n    x = Find(x, par)\\n    y = Find(y, par)\\n\\n    if x != y:\\n        if rank[x] < rank[y]:\\n            par[y] += par[x]\\n            par[x] = y\\n        else:\\n            par[x] += par[y]\\n            par[y] = x\\n            if rank[x] == rank[y]:\\n                rank[x] += 1\\n\\ndef Same(x, y, par):\\n    return Find(x, par) == Find(y, par)\\n\\ndef Size(x, par):\\n    return -par[Find(x, par)]\\n\\npar1 = [-1]*n\\nrank1 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[x][i]+A[y][i] > k:\\n                break\\n        else:\\n            Unite(x, y, par1, rank1)\\n\\npar2 = [-1]*n\\nrank2 = [0]*n\\nfor x in range(n):\\n    for y in range(n):\\n        for i in range(n):\\n            if A[i][x]+A[i][y] > k:\\n                break\\n        else:\\n            Unite(x, y, par2, rank2)\\n\\nN = 1000\\nmod = 998244353\\nfac = [1]*(N+1)\\nfinv = [1]*(N+1)\\nfor i in range(N):\\n    fac[i+1] = fac[i] * (i+1) % mod\\nfinv[-1] = pow(fac[-1], mod-2, mod)\\nfor i in reversed(list(range(N))):\\n    finv[i] = finv[i+1] * (i+1) % mod\\n\\nans = 1\\nfor i in par1:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nfor i in par2:\\n    if i < 0:\\n        ans *= fac[-i]\\n        ans %= mod\\nprint(ans)\\n\", \"from collections import defaultdict\\nimport math\\nimport numpy as np\\n\\nn, k = map(int, input().split())\\na_lists = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\n\\na_lists = np.array(a_lists)\\n\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\n\\ndef count_point(np_array):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        a = np_array[i]\\n        for j in range(i, n):\\n            b = np_array[j]\\n            if np.count_nonzero(a + b <= k) == n:\\n                uf.union(i, j)\\n    point = 1\\n    for i, j in uf.all_group_members().items():\\n        point *= math.factorial(len(j))\\n        point %= mod\\n    return point\\n\\nans = count_point(a_lists)\\na_lists_T = a_lists.T\\nans *= count_point(a_lists_T)\\nans %= mod\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\ndata=[list(map(int,input().split())) for i in range(N)]\\nimport math\\n#\\u884c\\nans1=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[i][k]+data[j][k]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans1.append([i,j])\\n#\\u5217\\nans2=[]\\nfor i in range(N-1):\\n    for j in range(i+1,N):\\n        m=0\\n        for k in range(N):\\n            if data[k][i]+data[k][j]>K:\\n                m+=1\\n                break\\n        if m==0:\\n            ans2.append([i,j])\\n#\\u884c\\nli1=[[] for i in range(N)]\\nfor i in range(len(ans1)):\\n    li1[ans1[i][0]].append(ans1[i][1])\\n    li1[ans1[i][1]].append(ans1[i][0])\\nL1=[-1]*N\\nfor i in range(N):\\n    if L1[i]!=-1:\\n        continue\\n    L1[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li1[x]:\\n            if L1[j]==-1:\\n                L1[j]=i\\n                deque.append(j)\\nnum1=1\\nl1=list(set(L1))\\nfor i in l1:\\n    num1*=int(math.factorial(L1.count(i)))\\n    num1=num1%998244353\\n#\\u5217\\nli2=[[] for i in range(N)]\\nfor i in range(len(ans2)):\\n    li2[ans2[i][0]].append(ans2[i][1])\\n    li2[ans2[i][1]].append(ans2[i][0])\\nL2=[-1]*N\\nfor i in range(N):\\n    if L2[i]!=-1:\\n        continue\\n    L2[i]=i\\n    deque=[i]\\n    while deque:\\n        x=deque.pop(0)\\n        for j in li2[x]:\\n            if L2[j]==-1:\\n                L2[j]=i\\n                deque.append(j)\\nnum2=1\\nl2=list(set(L2))\\nfor i in l2:\\n    num2*=int(math.factorial(L2.count(i)))\\n    num2=num2%998244353\\nprint((num1*num2)%998244353)\", \"import sys\\nread=sys.stdin.readline\\ndef MAP():\\n    return map(int,read().split())\\ndef I():\\n    return int(read())\\ndef LI():\\n    return list(map(int,read().split()))\\n    \\nMOD=998244353\\n\\nclass UnionFind:\\n    def __init__(self,N):\\n        self.par=[i for i in range(N)]\\n        self.siz=[1 for _ in range(N)]\\n        self.rank=[0 for _ in range(N)]\\n    def find(self,x):\\n        if self.par[x]==x:\\n            return x\\n        else:\\n            self.par[x]=self.find(self.par[x])\\n            return self.par[x]\\n    def union(self,a,b):\\n        a=self.find(a)\\n        b=self.find(b)\\n        if a==b:\\n            return 0\\n        else:\\n            if self.rank[a]>self.rank[b]:\\n                self.par[b]=a\\n                self.siz[a]+=self.siz[b]\\n            else:\\n                self.par[a]=b\\n                self.siz[b]+=self.siz[a]\\n                if self.rank[a]==self.rank[b]:\\n                    self.rank[b]+=1\\n    def size(self,a):\\n        return self.siz[self.find(a)]\\n    def same(self,a,b):\\n        return self.find(a)==self.find(b)\\n\\nN,K=MAP()\\na=[LI() for _ in range(N)]\\nUFg=UnionFind(N)\\nUFr=UnionFind(N)\\nfac=[1]*(N+1)\\nfor i in range(2,N+1):\\n    fac[i]=fac[i-1]*i%MOD\\n\\nfor i in range(N):\\n    for j in range(i):\\n        isokg=True\\n        isokr=True\\n        for k in range(N):\\n            if a[i][k]+a[j][k]>K:\\n                isokg=False\\n            if a[k][i]+a[k][j]>K:\\n                isokr=False\\n        if isokg:\\n            UFg.union(i,j)\\n        if isokr:\\n            UFr.union(i,j)\\n\\nfrom collections import Counter\\ndicg=Counter([UFg.find(i) for i in range(N)])\\ndicr=Counter([UFr.find(i) for i in range(N)])\\n\\nresg,resr=1,1\\nfor x,size in dicg.items():\\n    resg=resg*fac[size]%MOD\\nfor y,size in dicr.items():\\n    resr=resr*fac[size]%MOD\\nprint(resg*resr%MOD)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nckey=set(ufc.par)\\nrkey=set(ufr.par)\\n\\nans=1\\n\\nfor k in ckey:\\n    x=ufc.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rkey:\\n    x=ufr.size(k)\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\\n\", \"class DisjointSetUnion():\\n    def __init__(self, n):\\n        self.n = n\\n        self.par_size = [-1] * n\\n\\n    def merge(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        x = self.leader(a)\\n        y = self.leader(b)\\n        if x == y: return x\\n        if -self.par_size[x] < -self.par_size[y]: x, y = y, x\\n        self.par_size[x] += self.par_size[y]\\n        self.par_size[y] = x\\n        return x\\n\\n    def same(self, a, b):\\n        #assert 0 <= a < self.n\\n        #assert 0 <= b < self.n\\n        return self.leader(a) == self.leader(b)\\n\\n    def leader(self, a):\\n        #assert 0 <= a < self.n\\n        x = a\\n        while self.par_size[x] >= 0:\\n            x = self.par_size[x]\\n        while self.par_size[a] >= 0:\\n            self.par_size[a] = x\\n            a = self.par_size[a]\\n        return x\\n\\n    def size(self, a):\\n        #assert 0 <= a < self.n\\n        return -self.par_size[self.leader(a)]\\n\\ndef build_factorial(n):\\n    fct = [0] * (n + 1)\\n    inv = [0] * (n + 1)\\n    fct[0] = inv[0] = 1\\n    for i in range(n):\\n        fct[i + 1] = fct[i] * (i + 1) % MOD\\n    inv[n] = pow(fct[n], MOD - 2, MOD)\\n    for i in range(n)[::-1]:\\n        inv[i] = inv[i + 1] * (i + 1) % MOD\\n    return fct, inv\\n\\nMOD = 998244353\\nfrom itertools import combinations\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n\\nuf1 = DisjointSetUnion(N)\\nuf2 = DisjointSetUnion(N)\\n\\nfor i, j in combinations(range(N), 2):\\n    for k in range(N):\\n        if A[i][k] + A[j][k] > K:\\n            break\\n    else:\\n        uf1.merge(i, j)\\n        \\n    for k in range(N):\\n        if A[k][i] + A[k][j] > K:\\n            break\\n    else:\\n        uf2.merge(i, j)\\n\\nfct, inv = build_factorial(N)\\nres = 1\\n\\nfor i in range(N):\\n    if uf1.par_size[i] < 0:\\n        res *= fct[-uf1.par_size[i]]\\n        res %= MOD\\n    if uf2.par_size[i] < 0:\\n        res *= fct[-uf2.par_size[i]]\\n        res %= MOD\\n\\nprint(res)\", \"N,K = map(int,input().split())\\n\\nA = [list(map(int,input().split())) for _ in [0]*N]\\nMOD = 998244353\\nB = [[A[j][i] for j in range(N)] for i in range(N)]\\n\\ndef f(A):\\n    import sys\\n    sys.setrecursionlimit(10**7)\\n\\n    class UnionFind:\\n        def __init__(self,N):\\n            self.Parent = list(range(N))\\n            self.size = [1]*N\\n        def get_Parent(self,n):\\n            if self.Parent[n] == n:return n\\n            p = self.get_Parent(self.Parent[n])\\n            self.Parent[n] = p\\n            return p\\n        def get_size(self,n):\\n            return self.size[self.get_Parent(n)]\\n        def merge(self,x,y):\\n            x = self.get_Parent(x)\\n            y = self.get_Parent(y)\\n            if x!=y:\\n                if self.get_size(x) < self.get_size(y):\\n                    x,y = y,x\\n                self.size[x] += self.size[y]\\n                self.Parent[y] = x\\n                return True\\n            return False\\n        def is_united(self,x,y):\\n            return self.get_Parent(x)==self.get_Parent(y)\\n\\n    U_row = UnionFind(N)\\n    for i in range(N):\\n        for j in range(i+1,N):\\n            if U_row.is_united(i,j): continue\\n            for k in range(N):\\n                if A[i][k] + A[j][k] > K:break\\n            else:\\n                U_row.merge(i,j)\\n\\n    ans = 1\\n    for i in range(N):\\n        j = U_row.get_Parent(i)\\n        if i==j:\\n            tmp = 1\\n            s = U_row.get_size(i)\\n            for k in range(2,s+1):\\n                tmp = tmp*k%MOD\\n            ans = ans*tmp%MOD\\n    return ans%MOD\\n\\nans = f(A)*f(B)%MOD\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.par = [i for i in range(n)]\\n        self.rank = [0] * n\\n        self.size = [1] * n\\n\\n    def find(self, x):\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def same_check(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if self.rank[x] < self.rank[y]:\\n            if not self.same_check(x, y):\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            self.par[x] = y\\n        else:\\n            if not self.same_check(x, y):\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n            self.par[y] = x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def siz(self, x):\\n        x = self.find(x)\\n        return self.size[x]\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nUFX = UnionFind(N)\\nUFY = UnionFind(N)\\nmod = 998244353\\n\\nfact = [1]\\nfor i in range(1, N+1):\\n    fact.append(fact[-1] * i)\\n\\nfor i in range(1, N):\\n    for j in range(i):\\n        flag = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFY.union(i, j)\\n        flag = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                flag = False\\n                break\\n        if flag:\\n            UFX.union(i, j)\\nans = 1\\n\\nfor i in range(N):\\n    if UFX.find(i) == i:\\n        ans *= fact[UFX.siz(i)]\\n        ans %= mod\\n    if UFY.find(i) == i:\\n        ans *= fact[UFY.siz(i)]\\n        ans %= mod\\n\\nprint(ans)\", \"class UnionFind:\\n  '''\\n  UnionFind(n) : n\\u9802\\u70b90\\u8fba\\u306e\\u7121\\u5411\\u30b0\\u30e9\\u30d5\\u3092\\u69cb\\u7bc9\\u3059\\u308b O(n)\\n    p:\\u89aa\\u30ce\\u30fc\\u30c9\\u756a\\u53f7(\\u4ee3\\u8868\\u5143\\u4ee5\\u5916)\\u3001\\u6728\\u306e\\u30b5\\u30a4\\u30ba\\u306e\\u8ca0\\u6570(\\u4ee3\\u8868\\u5143)\\u3092\\u683c\\u7d0d\\n  leader(a)    : a\\u306e\\u5c5e\\u3059\\u308b\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  merge(a,b)   : a,b\\u3092\\u8fba\\u3067\\u7d50\\u3073\\u3001\\u4ee3\\u8868\\u5143\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  same(a,b)    : a,b\\u304c\\u9023\\u7d50\\u304b\\u5426\\u304b\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  size(a)      : a\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u30b5\\u30a4\\u30ba\\u3092\\u8fd4\\u3059 O(\\u03b1(n))\\n  count()      : \\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u3092\\u8fd4\\u3059 O(n)\\n  groups()     : \\u30b0\\u30e9\\u30d5\\u3092set\\u306b\\u30b0\\u30eb\\u30fc\\u30d7\\u5206\\u3051\\u3057\\u3066\\u8fd4\\u3059 O(n)\\n  '''\\n  def __init__(self, n):\\n    self.n = n\\n    self.p = [-1]*n\\n  def leader(self, a):\\n    while self.p[a]>=0:\\n      a = self.p[a]\\n    return a\\n  def merge(self, a, b):\\n    x = self.leader(a)\\n    y = self.leader(b)\\n    if x==y:\\n      return x\\n    if self.p[x]>self.p[y]:\\n      x, y = y, x\\n    self.p[x] += self.p[y]\\n    self.p[y] = x\\n    return x\\n  def same(self, a, b):\\n    return self.leader(a)==self.leader(b)\\n  def size(self, a):\\n    return -self.p[self.leader(a)]\\n  def count(self):\\n    return sum(i<0 for i in self.p)\\n  def groups(self):\\n    leader_buf = [0]*self.n\\n    group_size = [0]*self.n\\n    res = [set() for _ in range(self.n)]\\n    for i in range(self.n):\\n      leader_buf[i] = self.leader(i)\\n      group_size[leader_buf[i]] += 1\\n    for i in range(self.n):\\n      res[leader_buf[i]].add(i)\\n    res = [s for s in res if s]\\n    return res\\n\\nf=lambda:map(int,input().split())\\nn,k=f()\\nA=[[*f()] for _ in range(n)]\\nufh,ufw=UnionFind(n),UnionFind(n)\\nfor y in range(n):\\n  for x in range(y):\\n    if all(A[h][x]+A[h][y]<=k for h in range(n)):\\n      ufw.merge(x,y)\\n    if all(A[x][w]+A[y][w]<=k for w in range(n)):\\n      ufh.merge(x,y)\\nM=998244353\\nF=[1]\\nfor i in range(1,51): F+=[i*F[-1]%M]\\nc=1\\nfor i in range(n):\\n  if ufh.p[i]<0: c=c*F[-ufh.p[i]]%M\\n  if ufw.p[i]<0: c=c*F[-ufw.p[i]]%M\\nprint(c)\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        from array import array\\n\\n        self.n = n\\n        self.parent = array('l', (-1 for _ in range(n)))\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_r *= factorial(x)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for gr in uf.groups():\\n        x = len(gr)\\n        cnt_c *= factorial(x)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nimport numpy as np\\nfrom itertools import combinations\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n    \\n    def roots_size(self):\\n        return [-x for x in self.parents if x < 0]\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\ndef main():\\n    mod = 998244353\\n    n, k = map(int, input().split())\\n    A = np.array(sys.stdin.read().split(), dtype=np.int64).reshape((n, -1))\\n    uf_r = UnionFind(n)\\n    uf_c = UnionFind(n)\\n    for i, j in combinations(range(n), 2):\\n        if np.all(A[i, :] + A[j, :] <= k):\\n            uf_r.union(i, j)\\n        if np.all(A[:, i] + A[:, j] <= k):\\n            uf_c.union(i, j)\\n    s = 1\\n    factorial_table = [1]\\n    for i in range(1, n + 1):\\n        s *= i\\n        s %= mod\\n        factorial_table.append(s)\\n    ans = 1\\n    for size in uf_r.roots_size() + uf_c.roots_size():\\n        ans *= factorial_table[size]\\n        ans %= mod\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import itertools\\nimport numpy as np\\nfrom networkx.utils import UnionFind\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([tuple(map(int, input().split())) for _ in range(N)])\\n\\nMOD = 998244353\\nMAX = 50\\nfactorial = [1] * (MAX + 1)\\nfor i in range(1, MAX + 1):\\n    factorial[i] = factorial[i - 1] * i % MOD\\n\\nuf_row = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[:, i] + A[:, j] <= K):\\n        uf_row.union(i, j)\\nuf_col = UnionFind(list(range(N)))\\nfor i, j in itertools.combinations(list(range(N)), 2):\\n    if np.all(A[i] + A[j] <= K):\\n        uf_col.union(i, j)\\n\\nrow_res = 1\\nfor group in uf_row.to_sets():\\n    row_res = row_res * factorial[len(group)] % MOD\\ncol_res = 1\\nfor group in uf_col.to_sets():\\n    col_res = col_res * factorial[len(group)] % MOD\\n\\nprint((row_res * col_res % MOD))\\n\", \"from collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\ndef fact(n, mod=998244353):\\n    ans = 1\\n    for i in range(1, n + 1):\\n        ans *= i\\n        ans %= mod\\n    return ans\\n\\nmod = 998244353\\n\\nn, k = map(int, input().split())\\nlst = [[int(i) for i in input().split()] for _ in range(n)]\\n\\nans = 1\\nun1 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[i][l] + lst[j][l] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un1.union(i, j)\\nfor i in range(n):\\n    if i == un1.find(i):\\n        num = un1.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\n\\nun2 = UnionFind(n)\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if lst[l][i] + lst[l][j] > k:\\n                flag = False\\n                break\\n        if flag:\\n            un2.union(i, j)\\nfor i in range(n):\\n    if i == un2.find(i):\\n        num = un2.size(i)\\n        ans *= fact(num)\\n        ans %= mod\\nprint(ans)\", \"from collections import defaultdict\\nimport math\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nc_pattern = list() # swapable \\u306ac\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\nr_pattern = list() # swapable \\u306ar\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u6570\\n\\nfor c1 in range(N):\\n    for c2 in range(c1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[i][c1] + a[i][c2] > K:\\n                ok = False\\n                break\\n        if ok: c_pattern.append([c1, c2])\\n\\n\\nfor r1 in range(N):\\n    for r2 in range(r1+1, N):\\n        ok = True\\n        for i in range(N):\\n            if a[r1][i] + a[r2][i] > K:\\n                ok = False\\n                break\\n        if ok: r_pattern.append([r1, r2])\\n\\ndef total_pattern(pattern_list):\\n    uf = UnionFind(N)\\n    for p in pattern_list:\\n        uf.union(p[0], p[1])\\n    ans = 1\\n    # print(uf.roots())\\n    for r in uf.roots():\\n        ans *= math.factorial(uf.size(r))\\n    \\n    return ans\\n\\nprint(total_pattern(c_pattern)*total_pattern(r_pattern)%998244353)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.root = [-1]*n\\n        self.rank = [0]*n\\n\\n    def find(self, x):\\n        if self.root[x-1] < 0:\\n            return x\\n        else:\\n            self.root[x-1] = self.find(self.root[x-1])\\n            return self.root[x-1]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x==y:\\n            return\\n        elif self.rank[x-1] > self.rank[y-1]:\\n            self.n-=1\\n            self.root[x-1] += self.root[y-1]\\n            self.root[y-1] = x\\n        else:\\n            self.n-=1\\n            self.root[y-1] += self.root[x-1]\\n            self.root[x-1] = y\\n            if self.rank[x-1] == self.rank[y-1]:\\n                self.rank[y-1] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x)==self.find(y)\\n\\n    def count(self, x):\\n        return -self.root[self.find(x)-1]\\n\\n    def size(self):\\n        return self.n\\n\\n    def roots(self):\\n        return [x+1 for x in range(n) if self.root[x] < 0]\\n\\nmod=998244353\\nn,K=map(int,input().split())\\nA=[list(map(int,input().split())) for _ in range(n)]\\n\\nr=UnionFind(n)\\nc=UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        pr,pc=True,True\\n        for k in range(n):\\n            if A[i][k]+A[j][k]>K:\\n                pr=False\\n            if A[k][i]+A[k][j]>K:\\n                pc=False\\n        if pr: r.unite(i+1,j+1)\\n        if pc: c.unite(i+1,j+1)\\np=[1]*(n+1)\\nfor i in range(1,n+1):\\n    p[i]=(p[i-1]*i)%mod\\nans=1\\nfor x in r.roots():\\n    ans=ans*p[-r.root[x-1]]%mod\\nfor x in c.roots():\\n    ans=ans*p[-c.root[x-1]]%mod\\nprint(ans)\", \"import numpy as np\\n\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.root = list(range(N + 1))\\n        self.size = [1] * (N+1)\\n\\n\\n    def __getitem__(self, x):\\n        root = self.root\\n        while root[x] != x:\\n            root[x] = root[root[x]]\\n            x = root[x]\\n        return x\\n\\n    def merge(self, x, y):\\n        x = self[x]\\n        y = self[y]\\n        if x == y:\\n            return\\n        sx, sy = self.size[x], self.size[y]\\n        if sx < sy:\\n            x, y = y, x\\n            sx, sy = sy, sx\\n        self.root[y] = x\\n        self.size[x] += sy\\n        self.size[y] = 0\\n\\n    def same(self, x, y):\\n        return self[x] == self[y]\\n\\n    def find_max(self):\\n        return max(self.size)\\n\\n\\nN, K = list(map(int, input().split()))\\nA = np.array([list(map(int, input().split())) for _ in range(N)], dtype=np.int64)\\nans = 1\\n# rows and columns\\nfor step in range(2):\\n    if step == 1:\\n        A = A.T\\n\\n    uf = UnionFind(N)\\n    merge = uf.merge\\n    same = uf.same\\n    comb = 1\\n\\n    # swap ok?\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if np.all(A[i, :] + A[j, :] <= K):\\n                merge(i+1, j+1)\\n\\n    # prod of tree-size!\\n    for i in uf.size:\\n        comb *= np.math.factorial(i)\\n        comb %= 998244353\\n\\n    ans *= comb\\n    ans %= 998244353\\n\\nprint(ans)\\n\", \"import sys, bisect, math, itertools, string, queue, copy, heapq, collections, itertools\\n# input = sys.stdin.readline\\nsys.setrecursionlimit(10**8)\\nmod = 998244353\\ndef inp(): return int(input())\\ndef inpm(): return list(map(int,input().split()))\\ndef inpl(): return list(map(int, input().split()))\\ndef inpls(): return list(input().split())\\ndef inplm(n): return list(int(input()) for _ in range(n))\\ndef inplL(n): return [list(input()) for _ in range(n)]\\ndef inplT(n): return [tuple(input()) for _ in range(n)]\\ndef inpll(n): return [list(map(int, input().split())) for _ in range(n)]\\ndef inplt(n): return [tuple(map(int, input().split())) for _ in range(n)]\\ndef inplls(n): return sorted([list(map(int, input().split())) for _ in range(n)])\\n\\n#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n \\n        if x == y:\\n            return\\n \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n        \\nn,k = inpm()\\nA = inpll(n)\\n        \\nuf_r = UnionFind(n)\\nuf_c = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        flg = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_c.union(i,j)\\n            \\n        flg = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flg = False\\n                break\\n        if flg:\\n            uf_r.union(i,j)\\n\\nans = 1\\nfor i in uf_c.roots():\\n    ans = (ans * math.factorial(uf_c.parents[i] * -1)) % mod\\nfor i in uf_r.roots():\\n    ans = (ans * math.factorial(uf_r.parents[i] * -1)) % mod\\n    \\nprint(ans)\\n\", \"from functools import partial, reduce\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0 in range(n-1):\\n    for y1 in range(y0+1, n):\\n        if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n            X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0 in range(n-1):\\n    for x1 in range(x0+1, n):\\n        if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n            Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"mo = 998244353\\nfact = [0] * 100\\nfact[0] = 1\\nfor i in range(1, 100):\\n    fact[i] = fact[i - 1] * i % mo\\nn, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nfa = [i for i in range(n)]\\nfc = [1 for i in range(n)]\\ndef getF(p, u):\\n    if p[p[u]] == p[u]:\\n        return p[u]\\n    p[u] = getF(p, p[u])\\n    return p[u]\\ndef uniF(p, c, u, v):\\n    u = getF(p, u)\\n    v = getF(p, v)\\n    if u == v:\\n        return\\n    p[u] = v\\n    c[v] += c[u]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[i][k] + a[j][k] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fa, fc, i, j)\\nfb = [i for i in range(n)]\\nfd = [1 for i in range(n)]\\nfor i in range(n):\\n    for j in range(n):\\n        f = True\\n        for k in range(n):\\n            if a[k][i] + a[k][j] > K:\\n                f = False\\n                break\\n        if f:\\n            uniF(fb, fd, i, j)\\nans = 1\\nfor i in range(n):\\n    if getF(fa, i) == i:\\n        ans = ans * fact[fc[i]] % mo\\n    if getF(fb, i) == i:\\n        ans = ans * fact[fd[i]] % mo\\nprint(ans)\", \"def main():\\n    law = 998244353\\n    n, k = list(map(int,input().split()))\\n    mat = [list(map(int, input().split())) for i in range(n)]\\n    t_mat = [[mat[j][i] for j in range(n)] for i in range(n)]\\n    print(((line_pattern_counter_mod(mat, n, k, law) * line_pattern_counter_mod(t_mat, n, k, law)) % law))\\n    return\\n\\ndef line_pattern_counter_mod(mat, n, k, law):\\n    min_swapable = [i for i in range(n)]\\n    swappable_count = [0 for _ in range(n)]\\n    ret = 1\\n    for x in range(n):\\n        swappable_array = [x]\\n        min_ind = min_swapable[x]\\n        for y in range(n):\\n            if swappable(mat[x], mat[y], n, k):\\n                swappable_array.append(y)\\n                min_ind = min(min_ind, min_swapable[y])\\n        for ind in swappable_array:\\n            min_swapable[ind] = min_ind\\n    for m in range(n):\\n        swappable_count[min_swapable[m]] += 1\\n    for count in swappable_count:\\n        ret = (ret * fact_mod(count, law)) % law\\n    return ret\\n\\ndef swappable(l_1, l_2, n, k):\\n    for j in range(n):\\n        if l_1[j] + l_2[j] > k:\\n            return False\\n    return True\\n\\ndef fact_mod(m, law, acc = 1):\\n    if m == 0:\\n        return acc\\n    return fact_mod(m - 1, law, (acc * m) % law)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"from math import factorial\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return False\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n        return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        x = self.find(x)\\n        return -self.parents[x]\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\nUF_h = UnionFind(n)\\nUF_w = UnionFind(n)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[i][l] + A[j][l] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_h.union(i, j)\\n\\nfor i in range(n-1):\\n    for j in range(i, n):\\n        flag = True\\n        for l in range(n):\\n            if A[l][i] + A[l][j] > k:\\n                flag = False\\n                break\\n\\n        if flag:\\n            UF_w.union(i, j)\\n\\nDh = {UF_h.find(i):UF_h.size(i) for i in range(n)}\\nDw = {UF_w.find(i):UF_w.size(i) for i in range(n)}\\n\\nans = 1\\nfor i in Dh:\\n    ans *= factorial(Dh[i])\\n    ans %= mod\\nfor i in Dw:\\n    ans *= factorial(Dw[i])\\n    ans %= mod\\n\\nprint(ans)\", \"from itertools import combinations\\nfrom functools import partial\\n\\n\\nclass Mint:\\n    def __init__(self, x, mod=10**9 + 7):\\n        self.x = x.x if isinstance(x, Mint) else x % mod\\n        self.mod = mod\\n        self._mint = partial(Mint, mod=mod)\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" return (g, x, y) such that a*x + b*y = g = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q*y1\\n            x0, x1 = x1, x0 - q*x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g == 1\\n        return x % self.mod\\n\\n    def __str__(self):\\n        return str(self.x)\\n\\n    def __repr__(self):\\n        return repr(self.x)\\n\\n    def __eq__(self, x):\\n        return self.x == self._mint(x).x\\n\\n    def __ne__(self, x):\\n        return self.x != self._mint(x).x\\n\\n    def __int__(self):\\n        return self.x\\n\\n    def __index__(self):\\n        return self.x\\n\\n    def __add__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __radd__(self, x):\\n        return self._mint(self.x + self._mint(x).x)\\n\\n    def __sub__(self, x):\\n        return self._mint(self.x - self._mint(x).x)\\n\\n    def __rsub__(self, x):\\n        return self._mint(self._mint(x).x - self.x)\\n\\n    def __mul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __rmul__(self, x):\\n        return self._mint(self.x * self._mint(x).x)\\n\\n    def __truediv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __floordiv__(self, x):\\n        return self._mint(self.x * self.modinv(self._mint(x).x))\\n\\n    def __pow__(self, x):\\n        return self._mint(pow(self.x, x, self.mod))\\n\\n    def __rpow__(self, x):\\n        return self._mint(pow(self._mint(x).x, self.x, self.mod))\\n\\n\\nclass MintFactorial:\\n    def __init__(self, mod=10**9 + 7):\\n        self.mod = mod\\n        self._factorial = [1]\\n        self._size = 1\\n        self._factorial_inv = [1]\\n        self._size_inv = 1\\n        self._mint = partial(Mint, mod=mod)\\n\\n    def __call__(self, n):\\n        return self.fact(n)\\n\\n    def fact(self, n):\\n        n = self._mint(n).x\\n        \\\"\\\"\\\" n! (mod m) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            return 0\\n        self._make(n)\\n        return self._mint(self._factorial[n])\\n\\n    def _make(self, n):\\n        \\\"\\\"\\\" Calc from self._size to n!^-1 : O(n) \\\"\\\"\\\"\\n        if n >= self.mod:\\n            n = self.mod\\n        if self._size < n+1:\\n            for i in range(self._size, n+1):\\n                self._factorial.append(self._factorial[i-1]*i % self.mod)\\n            self._size = n+1\\n\\n    def fact_inv(self, n):\\n        \\\"\\\"\\\" n!^-1 (mod m) \\\"\\\"\\\"\\n        assert n >= self.mod\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        if self._factorial_inv[n] == -1:\\n            self._factorial_inv[n] = self.modinv(self.fact(n))\\n        return self._mint(self._factorial_inv[n])\\n\\n    def _make_inv(self, n, r=1):\\n        \\\"\\\"\\\" Calc r!^1 ... n!^-1 : O(n-r) \\\"\\\"\\\"\\n        if n >= self.m:\\n            n = self.m - 1\\n        if self._size_inv < n+1:\\n            self._factorial_inv += [-1] * (n+1-self._size_inv)\\n            self._size_inv = n+1\\n        self._factorial_inv[n] = self.modinv(self.fact(n))\\n        for i in range(n, r+1, -1):\\n            self._factorial_inv[i-1] = self._factorial_inv[i]*i % self.mod\\n\\n    @staticmethod\\n    def xgcd(a, b):\\n        \\\"\\\"\\\" Return (gcd(a, b), x, y) such that a*x + b*y = gcd(a, b) \\\"\\\"\\\"\\n        x0, x1, y0, y1 = 0, 1, 1, 0\\n        while a != 0:\\n            (q, a), b = divmod(b, a), a\\n            y0, y1 = y1, y0 - q * y1\\n            x0, x1 = x1, x0 - q * x1\\n        return b, x0, y0\\n\\n    def modinv(self, n):\\n        \\\"\\\"\\\" n^-1 (mod m) \\\"\\\"\\\"\\n        g, x, _ = self.xgcd(n, self.mod)\\n        assert g != 1\\n        return self._mint(x)\\n\\n    def comb(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        t = self(n)*self.fact_inv(n-r) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def comb_(self, n, r):\\n        \\\"\\\"\\\" nCr (mod m) : O(r) \\\"\\\"\\\"\\n        c = 1\\n        for i in range(1, r+1):\\n            c *= (n-i+1) * self.fact_inv(i)\\n            c %= self.mod\\n        return self._mint(c)\\n\\n    def comb_with_repetition(self, n, r):\\n        \\\"\\\"\\\" nHr (mod m) \\\"\\\"\\\"\\n        t = self(n+r-1)*self.fact_inv(n-1) % self.mod\\n        return self._mint(t*self.fact_inv(r))\\n\\n    def perm(self, n, r):\\n        \\\"\\\"\\\" nPr (mod m) \\\"\\\"\\\"\\n        if r > n:\\n            return 0\\n        return self._mint(self(n)*self.fact_inv(n-r))\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self._n = n\\n        self._table = [-1]*n\\n\\n    def _root(self, x):\\n        stack = []\\n        while self._table[x] >= 0:\\n            stack.append(x)\\n            x = self._table[x]\\n        for y in stack:\\n            self._table[y] = x\\n        return x\\n\\n    def unite(self, x, y):\\n        x, y = self._root(x), self._root(y)\\n        if x == y:\\n            return\\n        if x > y:\\n            x, y = y, x\\n        self._table[x] += self._table[y]\\n        self._table[y] = x\\n\\n    def same(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def count_members(self, x):\\n        return -self._table[self._root(x)]\\n\\n    def count_groups(self):\\n        return len({self._root(i) for i in range(self._n)})\\n\\n    def __iter__(self):\\n        return (self._root(i) for i in range(self._n))\\n\\n    def __str__(self):\\n        return str([self._root(i) for i in range(self._n)])\\n\\n    def __repr__(self):\\n        return repr([self._root(i) for i in range(self._n)])\\n\\n    def compress_coordinate(self):\\n        d = {v: i for i, v in enumerate(sorted(set(self)))}\\n        return [d[i] for i in self]\\n\\n    def get_forest(self):\\n        F = [[] for _ in range(self.count_groups())]\\n        d = self.compress_coordinate()\\n        for i in range(self._n):\\n            F[d[i]].append(i)\\n        return F\\n\\n\\nn, k = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nfact = MintFactorial(mod).fact\\n\\nX = UnionFind(n)\\nfor y0, y1 in combinations(range(n), 2):\\n    if all(A[y0][x] + A[y1][x] <= k for x in range(n)): \\n        X.unite(y0, y1)\\n\\nY = UnionFind(n)\\nfor x0, x1 in combinations(range(n), 2):\\n    if all(A[y][x0] + A[y][x1] <= k for y in range(n)): \\n        Y.unite(x0, x1)\\n\\ns = 1\\nfor a in map(fact, map(len, X.get_forest())):\\n    s *= a\\nfor b in map(fact, map(len, Y.get_forest())):\\n    s *= b\\nprint(s)\", \"MOD = 998244353\\n\\ndef dsFind(ds, x):\\n    if ds[x] == x:\\n        return x\\n\\n    x0 = x\\n    while ds[x] != x:\\n        x = ds[x]\\n\\n    ds[x0] = x\\n    return x\\n\\n\\ndef dsUnion(ds, x, y):\\n    xRoot = dsFind(ds, x)\\n    yRoot = dsFind(ds, y)\\n    \\n    if xRoot != yRoot:\\n        ds[yRoot] = xRoot\\n        return True\\n\\n    return False\\n\\n\\ndef isSwappableCols(M, N, K, c1, c2):\\n    for i in range(N):\\n        if M[i][c1] + M[i][c2] > K:\\n            return False\\n    return True\\n\\n\\ndef isSwappableRows(M, N, K, r1, r2):\\n    for i in range(N):\\n        if M[r1][i] + M[r2][i] > K:\\n            return False\\n    return True\\n\\n\\n\\ndef f(M, N, K, isSwappable):\\n    ds = list(range(N))\\n    for i in range(N):\\n        for j in range(i+1, N):\\n            if (dsFind(ds, i) != dsFind(ds, j) and\\n                isSwappable(M, N, K, i, j)):\\n                dsUnion(ds, i, j)\\n    \\n\\n    cnts = {}\\n    \\n    for i in range(N):\\n        root = dsFind(ds, i)\\n        if not(root in cnts):\\n            cnts[root] = 0\\n\\n        cnts[root] += 1\\n\\n    x = 1\\n    for c in list(cnts.values()):\\n        for i in range(2, c+1):\\n            x = x*i%MOD\\n                \\n    return x\\n\\nN, K = list(map(int, input().split()))\\nM  = [list(map(int, input().split())) for _ in range(N)]\\n\\nprint((f(M, N, K, isSwappableCols)*f(M, N, K, isSwappableRows)%MOD))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\nA_T = []\\nfor i in range(N):\\n    x = []\\n    for j in range(N):\\n        x.append(A[j][i])\\n    A_T.append(x)\\n# print(A_T)\\n# print(A)\\nrow_uf = UnionFind(N)\\ncolumn_uf = UnionFind(N)\\nfor i in range(N - 1):\\n    row1 = A[i]\\n    for j in range(i + 1, N):\\n        row2 = A[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(row1, row2)]):\\n            row_uf.union(i, j)\\n# print(row_uf.all_group_members())\\n\\nfor i in range(N - 1):\\n    column1 = A_T[i]\\n    for j in range(i + 1, N):\\n        column2 = A_T[j]\\n        if all([val1 + val2 <= K for val1, val2 in zip(column1, column2)]):\\n            column_uf.union(i, j)\\n# print(column_uf.all_group_members())\\nrow_cnt = 1\\nfor root, member in row_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        row_cnt *= i\\n        row_cnt %= MOD\\n\\ncolumn_cnt = 1\\nfor root, member in column_uf.all_group_members().items():\\n    for i in range(len(member), 0, -1):\\n        column_cnt *= i\\n        column_cnt %= MOD\\nprint((row_cnt * column_cnt) % MOD)\", \"n,K = map(int,input().split())\\nmod = 998244353\\ncnt1 = 0\\nA =[list(map(int,input().split())) for _ in range(n)]\\n#\\u4f7f\\u3048\\u308bUnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n \\n    def group_count(self):\\n        return len(self.roots())\\n \\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n \\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n \\nuf1 = UnionFind(n)\\nuf2 = UnionFind(n)\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[i][k] + A[j][k] <=K for k in range(n)):\\n            uf1.union(i,j)\\ncnt2 = 0\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        if all(A[k][i] + A[k][j] <=K for k in range(n)):\\n            uf2.union(i,j)\\nans = 1\\nfrom math import factorial\\nfor u in uf1.roots():\\n    ans*= factorial(uf1.size(u))%mod\\nfor u in uf2.roots():\\n    ans*= factorial(uf2.size(u))%mod\\nprint(ans%mod)\", \"from sys import setrecursionlimit\\nsetrecursionlimit(10 ** 9)\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.d = [-1] * n\\n\\n    def find(self, x):\\n        if self.d[x] < 0:\\n            return x\\n        else:\\n            self.d[x] = self.find(self.d[x])\\n            return self.d[x]\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return False\\n        else:\\n            if self.d[x] > self.d[y]:\\n                x, y = y, x\\n            self.d[x] += self.d[y]\\n            self.d[y] = x\\n            return True\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n\\n    def size(self, x):\\n        return -self.d[self.find(x)]\\n\\n\\n\\nMOD = 998244353\\ndef permutations(N):\\n    val = 1\\n    for i in range(2,N+1):\\n        val *= i\\n        val %= MOD\\n    return val\\n\\nN,K = list(map(int,input().split()))\\na = [list(map(int,input().split())) for _ in range(N)]\\n\\nufretu = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flg = False\\n        if flg == True:ufretu.unite(i,j)\\nval1 = 1\\nfor i in ufretu.d:\\n    if i < 0:\\n        val1 *= permutations(-i)\\n        val1 %= MOD\\n\\nufgyou = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1,N):\\n        flg = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flg = False\\n        if flg == True:ufgyou.unite(i,j)\\nval2 = 1\\nfor i in ufgyou.d:\\n    if i < 0:\\n        val2 *= permutations(-i)\\n        val2 %= MOD\\nprint((val1 * val2 % MOD))\\n\\n\", \"from collections import defaultdict\\nimport math\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        \\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    \\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n        \\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        \\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    \\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n        \\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    \\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    \\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n    \\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n    \\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\nn, k = list(map(int, input().split()))\\na = [list(map(int, input().split())) for _ in range(n)]\\n\\nmod = 998244353\\n\\ndef c_swapable(a, x, y):\\n    if all(a[i][x] + a[i][y] <= k for i in range(n)):\\n        return True\\n    else:\\n        False\\n\\ndef r_swapable(a, s, t):\\n    if all(a[s][j] + a[t][j] <= k for j in range(n)):\\n        return True\\n    else:\\n        False\\n\\ncolum = UnionFind(n)\\nrow = UnionFind(n)\\n\\nfor hx in range(n - 1):\\n    for hy in range(hx + 1, n):\\n        if c_swapable(a, hx, hy):\\n            colum.union(hx, hy)\\n\\nfor wx in range(n - 1):\\n    for wy in range(wx + 1, n):\\n        if r_swapable(a, wx, wy):\\n            row.union(wx, wy)\\n \\nans = 1\\nfor cg in list(colum.all_group_members().values()):\\n    ans *= math.factorial(len(cg))\\nans %= mod\\n\\nfor rg in list(row.all_group_members().values()):\\n    ans *= math.factorial(len(rg))\\n        \\nprint((ans % mod))\\n\", \"import bisect,collections,copy,heapq,itertools,math,numpy as np,string,sys\\ndef I(): return int(sys.stdin.readline().rstrip())\\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S(): return sys.stdin.readline().rstrip()\\ndef LS(): return list(sys.stdin.readline().rstrip().split())\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\nN,K = LI()\\na = np.array([LI() for _ in range(N)])\\nans = 1\\nuf1 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf1.union(i,j)\\nfor x in uf1.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\na = a.T\\nuf2 = UnionFind(N)\\nfor i,j in itertools.combinations(list(range(N)),2):\\n    if (a[i,:]+a[j,:]<=K).all():\\n        uf2.union(i,j)\\nfor x in uf2.parents:\\n    if x<=-2:\\n        for i in range(2,abs(x)+1):\\n            ans *= i\\n            ans %= 998244353\\nprint(ans)\\n\", \"class TwelvefoldWay:\\n    def __init__(self, n, mod):\\n        self.g1 = [1, 1]\\n        self.g2 = [1, 1]\\n        self.re = [0, 1]\\n        self.md = mod\\n        for i in range(2, n + 1):\\n            self.g1.append((self.g1[-1] * i) % self.md)\\n    def fact(self, n):\\n        return self.g1[n]\\n    def perm(self, n, k):\\n        return (self.g1[n] * self.g2[n - k]) % self.md\\n    def comb(n, k):\\n        if k < 0 or k > n:\\n            return 0\\n        k = min(k, n - k)\\n        return self.g1[n] * self.g2[k] * self.g2[n - k] % self.md\\n    def homo(n, k):\\n        return self.comb(n + k - 1, k)\\n\\n# 1-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nMOD = 998244353\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n\\n    uf = UnionFind(N)\\n    tw = TwelvefoldWay(N ** 2 + 1, MOD)\\n    for a, b in edge:\\n        uf.union(a, b)\\n\\n    ret = 1\\n    for n in uf.size_list(N):\\n        ret = (ret * tw.fact(n)) % MOD\\n    \\n    return ret\\n\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\nA = [[A[i][j] for i in range(N)] for j in range(N)]\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ninf = float('inf')\\nmod = 10 ** 9 + 7\\nmod2 = 998244353\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    \\u4e0b\\u8a18\\u304b\\u3089\\u62dd\\u501f\\n    https://note.nkmk.me/python-union-find/\\n    \\\"\\\"\\\"\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join(\\n            '{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, K, A):\\n    uf_row = UnionFind(N)\\n    uf_col = UnionFind(N)\\n    # grouping row\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[x][i] + A[y][i] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_row.union(x, y)\\n    # grouping col\\n    for x in range(N - 1):\\n        for y in range(x + 1, N):\\n            flg = True\\n            for i in range(N):\\n                if A[i][x] + A[i][y] > K:\\n                    flg = False\\n                    break\\n            if flg:\\n                uf_col.union(x, y)\\n    # calc ans\\n    ans = 1\\n    for gm in list(uf_row.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    for gm in list(uf_col.all_group_members().values()):\\n        for i in range(1, len(gm) + 1):\\n            ans *= i\\n            ans %= mod2\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    N, K = list(map(int, input().split()))\\n    A = [[int(i) for i in input().split()] for _ in range(N)]\\n    solve(N, K, A)\\n\\n    # # test\\n    # from random import randint\\n    # import string\\n    # import tool.testcase as tt\\n    # from tool.testcase import random_str, random_ints\\n    # N, K = 50, 2 * 50 ** 2\\n    # A = [[N * i + j for j in range(1, N + 1)] for i in range(N)]\\n    # solve(N, K, A)\\n\\n__starting_point()\", \"class UnionFind():\\n  def __init__(self, n):\\n    self.n = n\\n    self.parents = [-1] * n\\n\\n  def find(self, x):\\n    if self.parents[x] < 0:\\n      return x\\n    else:\\n      self.parents[x] = self.find(self.parents[x])\\n    return self.parents[x]\\n\\n  def union(self, x, y):\\n    x = self.find(x)\\n    y = self.find(y)\\n\\n    if x == y:\\n      return\\n\\n    if self.parents[x] > self.parents[y]:\\n      x, y = y, x\\n\\n    self.parents[x] += self.parents[y]\\n    self.parents[y] = x\\n\\n  def same(self, x, y):\\n    return self.find(x) == self.find(y)\\n\\n  def roots_nums(self):\\n    return [-x for x in self.parents if x < 0]\\n\\n  def num_roots(self):\\n    return len([i for i, x in enumerate(self.parents) if x < 0])\\n\\n  def members(self, x):\\n    root = self.find(x)\\n    return [i for i in range(self.n) if self.find(i) == root]\\n\\n  def num_members(self,x):\\n    return abs(self.parents[self.find(x)])\\n\\n  def __str__(self):\\n    return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nMOD = 998244353\\n\\nclass ModInt:\\n  def __init__(self, x):\\n    self.x = x % MOD\\n\\n  def __str__(self):\\n    return str(self.x)\\n\\n  __repr__ = __str__\\n\\n  def __add__(self, other):\\n    return (\\n      ModInt(self.x + other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x + other)\\n    )\\n\\n  def __sub__(self, other):\\n    return (\\n      ModInt(self.x - other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x - other)\\n    )\\n\\n  def __mul__(self, other):\\n    return (\\n      ModInt(self.x * other.x) if isinstance(other, ModInt) else\\n      ModInt(self.x * other)\\n    )\\n\\n  def __truediv__(self, other):\\n    return (\\n      ModInt(\\n        self.x * pow(other.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(self.x * pow(other, MOD - 2, MOD))\\n    )\\n\\n  __floordiv__ = __truediv__\\n\\n  def __pow__(self, other):\\n    return (\\n      ModInt(pow(self.x, other.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(self.x, other, MOD))\\n    )\\n\\n  __radd__ = __add__\\n\\n  def __rsub__(self, other):\\n    return (\\n      ModInt(other.x - self.x) if isinstance(other, ModInt) else\\n      ModInt(other - self.x)\\n    )\\n\\n  __rmul__ = __mul__\\n\\n  def __rtruediv__(self, other):\\n    return (\\n      ModInt(\\n        other.x * pow(self.x, MOD - 2, MOD)\\n      ) if isinstance(other, ModInt) else\\n      ModInt(other * pow(self.x, MOD - 2, MOD))\\n    )\\n\\n  def __rpow__(self, other):\\n    return (\\n      ModInt(pow(other.x, self.x, MOD)) if isinstance(other, ModInt) else\\n      ModInt(pow(other, self.x, MOD))\\n    )\\n\\nans = 1\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_row = UnionFind(N)\\nuf_col = UnionFind(N)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        break\\n    else:\\n      uf_row.union(i,j)\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        break\\n    else:\\n      uf_col.union(i,j)\\n\\nfact = [ModInt(1)]*51\\n\\nfor i in range(1,51):\\n  fact[i] = fact[i-1]*i\\nfor p in uf_row.roots_nums():\\n  ans *= fact[p]\\nfor p in uf_col.roots_nums():\\n  ans *= fact[p]\\nprint(ans)\", \"MOD = 998244353\\n\\nN, K = list(map(int, input().split()))\\nAMat = [list(map(int, input().split())) for _ in range(N)]\\n\\nclass UnionFind:\\n    def __init__(self, N):\\n        self.parent = list(range(N))\\n        self.rank = [0] * N\\n        self.size = [1] * N\\n\\n    def find(self, x):\\n        if self.parent[x]==x:\\n            return x\\n        else:\\n            self.parent[x] = self.find(self.parent[x])\\n            return self.parent[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.rank[x] < self.rank[y]:\\n            self.parent[x] = y\\n            self.size[y] += self.size[x]\\n        else:\\n            self.parent[y] = x\\n            self.size[x] += self.size[y]\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def get_size(self, x):\\n        return self.size[self.find(x)]\\n\\nuf_x = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for y in range(N):\\n            if AMat[y][i] + AMat[y][j] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_x.unite(i, j)\\n\\nuf_y = UnionFind(N)\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        flag = True\\n        for x in range(N):\\n            if AMat[i][x] + AMat[j][x] > K:\\n                flag = False\\n                break\\n        if flag:\\n            uf_y.unite(i, j)\\n\\nans_list1 = [0] * N\\nfor i in range(N):\\n    ans_list1[uf_x.find(i)] += 1\\n\\nans_list2 = [0] * N\\nfor i in range(N):\\n    ans_list2[uf_y.find(i)] += 1\\n\\nans_list = ans_list1 + ans_list2\\nans = 1\\nfor a in ans_list:\\n    if a >= 1:\\n        for x in range(1, a+1):\\n            ans *= x\\n            ans %= MOD\\n\\nprint((ans%MOD))\\n\", \"n, k = map(int, input().split())\\na = []\\nfor i in range(n):\\n    a.append(list(map(int, input().split())))\\nmod = 998244353\\nans = 1\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\ndef find(x):\\n    if parent[x - 1] == x:\\n        return x\\n    else:\\n        parent[x - 1] = find(parent[x - 1])\\n        return parent[x - 1]\\n\\ndef unite(x, y):\\n    x = find(x)\\n    y = find(y)\\n    if x == y:\\n        return\\n    if rank[x - 1] < rank[y - 1]:\\n        parent[x - 1] = y\\n        size[y - 1] += size[x - 1]\\n    else:\\n        parent[y - 1] = x\\n        size[x - 1] += size[y - 1]\\n        if rank[x - 1] == rank[y - 1]:\\n            rank[x - 1] += 1\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\n\\nparent = [i + 1 for i in range(n)]\\nrank = [0 for i in range(n)]\\nsize = [1 for i in range(n)]\\n\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        flag = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                flag = False\\n                break\\n        if flag == True:\\n            unite(i + 1, j + 1)\\nfor i in range(n):\\n    if find(i + 1) == i + 1:\\n        for j in range(size[i]):\\n            ans *= j + 1\\n            ans %= mod\\nprint(ans)\", \"mod = 998244353\\nnn = 1010\\nfa = [1] * (nn+1)\\nfainv = [1] * (nn+1)\\nfor i in range(nn):\\n    fa[i+1] = fa[i] * (i+1) % mod\\nfainv[-1] = pow(fa[-1], mod - 2, mod)\\nfor i in range(nn)[::-1]:\\n    fainv[i] = fainv[i+1] * (i+1) % mod\\n\\nN, K = map(int, input().split())\\nX = [[int(a) for a in input().split()] for _ in range(N)]\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.PA = [-1] * n\\n    \\n    def root(self, a):\\n        L = []\\n        while self.PA[a] >= 0:\\n            L.append(a)\\n            a = self.PA[a]\\n        for l in L:\\n            self.PA[l] = a\\n        return a\\n    def unite(self, a, b):\\n        ra, rb = self.root(a), self.root(b)\\n        if ra != rb:\\n            if self.PA[rb] >= self.PA[ra]:\\n                self.PA[ra] += self.PA[rb]\\n                self.PA[rb] = ra\\n            else:\\n                self.PA[rb] += self.PA[ra]\\n                self.PA[ra] = rb\\n    def size(self, a):\\n        return - self.PA[self.root(a)]\\n    def groups(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [g for g in G if g]\\n    def group_size(self):\\n        G = [[] for _ in range(self.n)]\\n        for i in range(self.n):\\n            G[self.root(i)].append(i)\\n        return [len(g) for g in G if g]\\n\\nans = 1\\nuf1 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[i][k] + X[j][k] > K:\\n                break\\n        else:\\n            uf1.unite(i, j)\\nfor a in uf1.group_size():\\n    ans = ans * fa[a] % mod\\n\\nuf2 = UnionFind(N)\\ns = 0\\nfor i in range(N):\\n    for j in range(i):\\n        for k in range(N):\\n            if X[k][i] + X[k][j] > K:\\n                break\\n        else:\\n            uf2.unite(i, j)\\nfor a in uf2.group_size():\\n    ans = ans * fa[a] % mod\\n\\nprint(ans)\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\nn,k = map(int,input().split())\\na = []\\nfor i in range(n):\\n    ai = list(map(int,input().split()))\\n    a.append(ai)\\n\\nu = UnionFind(n)\\nmod = 998244353\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        ai = a[i]\\n        aj = a[j]\\n        bit = False\\n        aij = [i+j for i,j in zip(ai,aj)]\\n        if max(aij)<=k:\\n            bit = True\\n        if bit:\\n            u.union(i,j)\\nans = 1\\nfor i in u.all_group_members():\\n    li = len(u.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\no = UnionFind(n)\\nmod = 998244353\\nb = list(map(list, zip(*a)))\\n\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        bi = b[i]\\n        bj = b[j]\\n        bit = False\\n        bij = [i+j for i,j in zip(bi,bj)]\\n        if max(bij)<=k:\\n            bit = True\\n        if bit:\\n            o.union(i,j)\\n\\nfor i in o.all_group_members():\\n    li = len(o.members(i))\\n    res = 1\\n    for j in range(1,li+1):\\n        res *= j\\n        res %= mod\\n    ans *= res\\n\\nprint(ans%mod)\", \"from collections import deque\\n\\ndef bfs(G, s, j):\\n    q = deque()\\n    q.append(s)\\n    visit[s][j] = 1\\n    p = 1\\n    while q:\\n        u = q.popleft()\\n        for v in G[u]:\\n            if not visit[v][j]:\\n                visit[v][j] = 1\\n                p += 1\\n                q.append(v)\\n    return p\\n\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nmod = 998244353\\nG1 = [[] for _ in range(n)]\\nG2 = [[] for _ in range(n)]\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                f = 0\\n                break\\n        if f:\\n            G1[i].append(j)\\n            G1[j].append(i)\\nfor i in range(n):\\n    for j in range(i + 1, n):\\n        f = 1\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                f = 0\\n                break\\n        if f:\\n            G2[i].append(j)\\n            G2[j].append(i)\\nans = 1\\nvisit = [[0] * 2 for _ in range(n + 5)]\\nfactorial = [1] * (n + 5)\\nfor i in range(2, n + 5):\\n    factorial[i] = factorial[i - 1] * i % mod\\nfor i in range(n):\\n    if not visit[i][0]:\\n        p = bfs(G1, i, 0)\\n        ans *= factorial[p]\\n        ans %= mod\\n    if not visit[i][1]:\\n        p = bfs(G2, i, 1)\\n        ans *= factorial[p]\\n        ans %= mod\\nprint(ans)\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, v):\\n        if self.parents[v] < 0:\\n            return v\\n        else:\\n            self.parents[v] = self.find(self.parents[v])\\n            return self.parents[v]\\n\\n    def unite(self, u, v):\\n        u = self.find(u)\\n        v = self.find(v)\\n\\n        if u == v:\\n            return\\n\\n        if self.parents[u] > self.parents[v]:\\n            u, v = v, u\\n\\n        self.parents[u] += self.parents[v]\\n        self.parents[v] = u\\n\\n    def size(self, v):\\n        return -self.parents[self.find(v)]\\n\\n    def same(self, u, v):\\n        return self.find(u) == self.find(v)\\n\\ndef comb_lists(n, mod):\\n    fact = [1 for _ in range(n+1)]\\n    inv = [1 for _ in range(n+1)]\\n    fact_inv = [1 for _ in range(n+1)]\\n    for i in range(2, n+1):\\n        fact[i] = (fact[i-1]*i) % mod\\n        inv[i] = mod - (inv[mod % i] * (mod // i)) % mod\\n        fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod\\n    \\n    return fact, fact_inv\\n\\nmod = 998244353\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\nuf_c = UnionFind(N)\\nuf_r = UnionFind(N)\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[i][k] + A[j][k] > K:\\n                f = False\\n                break\\n        if f: uf_c.unite(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        f = True\\n        for k in range(N):\\n            if A[k][i] + A[k][j] > K:\\n                f = False\\n                break\\n        if f: uf_r.unite(i, j)\\n\\nfact, _ = comb_lists(N, mod)\\nps = [] \\nans = 1 \\nfor i in range(N):\\n    p = uf_c.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_c.size(i)]\\n        ans %= mod\\n        ps.append(p)\\n\\nps = []\\nfor i in range(N):\\n    p = uf_r.find(i)\\n    if p not in ps:\\n        ans *= fact[uf_r.size(i)]\\n        ans %= mod\\n        ps.append(p)\\nprint(ans)\", \"#UnionFind\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n    \\nn,K = list(map(int,input().split()))\\nmod = 998244353\\na = [list(map(int,input().split())) for i in range(n)]\\n\\ndef factorial_mod(n,mod):\\n    ret = 1\\n    for i in range(1,n+1):\\n        ret *= i\\n        ret %= mod\\n    return ret\\n\\nuf_ver = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[i][k] + a[j][k] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_ver.union(i,j)\\n        \\nuf_hol = UnionFind(n+1)\\nfor i in range(n):\\n    for j in range(n):\\n        is_ok = 1\\n        for k in range(n):\\n            if a[k][i] + a[k][j] <= K:\\n                pass\\n            else:\\n                is_ok = 0\\n                break\\n        if is_ok:\\n            uf_hol.union(i,j)\\nans = 1\\ndic1 = uf_ver.all_group_members()\\nfor v in list(dic1.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\ndic2 = uf_hol.all_group_members()\\nfor v in list(dic2.values()):\\n    ans *= factorial_mod(len(v),mod)\\n    ans %= mod\\nprint(ans)\\n\", \"class UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def size(self, x):\\n        return -self.par[self.find(x)]\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int, input().split())) for _ in range(n)]\\n\\nuf1=UnionFind(n)\\nuf2=UnionFind(n)\\n\\nmod=998244353\\n\\nfct=[1]\\nfor i in range(1,101):\\n    fct.append(fct[-1]*i%mod)\\n\\nfor i in range(n - 1):\\n    for j in range(i + 1, n):\\n        if all(A[c][i] + A[c][j] <= k for c in range(n)):\\n            uf1.unite(i, j)\\n        if all(A[i][c] + A[j][c] <= k for c in range(n)):\\n            uf2.unite(i, j)\\nans = 1\\nfor i in range(n):\\n    if uf1.par[i] < 0:\\n        ans *= fct[-uf1.par[i]]\\n        ans %= mod\\n    if uf2.par[i] < 0:\\n        ans *= fct[-uf2.par[i]]\\n        ans %= mod\\nprint(ans)\\n\\n\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 998244353\\n\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u89aa\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"y\\u3092x\\u306e\\u6839\\u306b\\u7e4b\\u3050\\uff08\\u30de\\u30fc\\u30b8\\u30c6\\u30af\\u6709\\uff09\\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"x\\u3068y\\u304c\\u540c\\u3058\\u9023\\u7d50\\u6210\\u5206\\u304b\\u5224\\u5225\\u3059\\u308b\\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n\\n    def size(self, x):\\n        \\\"\\\"\\\"x\\u306e\\u9023\\u7d50\\u6210\\u5206\\u306e\\u5927\\u304d\\u3055\\u3092\\u8fd4\\u3059\\\"\\\"\\\"\\n        return -self.parents[self.find(x)]\\n\\n    def kruskal(self, edge):\\n        \\\"\\\"\\\"\\n        :param edge: edge = [(\\u30b3\\u30b9\\u30c8, \\u9802\\u70b91, \\u9802\\u70b92),...]\\u306e\\u5f62\\u3067\\u91cd\\u307f\\u4ed8\\u304d\\u96a3\\u63a5\\u30ea\\u30b9\\u30c8\\u3092\\u6e21\\u3057\\u3066\\u4e0b\\u3055\\u3044\\n        :return: \\u6700\\u5c0f\\u5168\\u57df\\u6728\\u306e\\u30b3\\u30b9\\u30c8\\u306e\\u548c\\n        \\\"\\\"\\\"\\n        edge.sort()\\n        cost_sum = 0\\n        for cost, node1, node2 in edge:\\n            if not self.same(node1, node2):\\n                cost_sum += cost\\n                self.union(node1, node2)\\n        return cost_sum\\n\\n\\ndef resolve():\\n    n, k = list(map(int, input().split()))\\n    A = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf_row = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[x][i] + A[y][i] > k:\\n                    break\\n            else:\\n                uf_row.union(x, y)\\n\\n    uf_col = UnionFind(n)\\n    for x in range(n):\\n        for y in range(x + 1, n):\\n            for i in range(n):\\n                if A[i][x] + A[i][y] > k:\\n                    break\\n            else:\\n                uf_col.union(x, y)\\n\\n    fact = [1, 1]\\n    for i in range(2, n + 1):\\n        fact.append(fact[-1] * i % mod)\\n\\n    size_row = [1] * n\\n    for i in range(n):\\n        root = uf_row.find(i)\\n        size_row[root] = uf_row.size(root)\\n\\n    size_col = [1] * n\\n    for i in range(n):\\n        root = uf_col.find(i)\\n        size_col[root] = uf_col.size(root)\\n\\n    tot_row = tot_col = 1\\n    for i, j in zip(size_row, size_col):\\n        tot_row = tot_row * fact[i] % mod\\n        tot_col = tot_col * fact[j] % mod\\n\\n    res = tot_row * tot_col % mod\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from sys import stdin, setrecursionlimit\\nimport bisect, collections, copy, heapq, itertools, math, string\\nsetrecursionlimit(10**8)\\n\\nINF = float(\\\"inf\\\")\\nMOD = 1000000007\\n\\n\\ndef input():\\n    return stdin.readline().strip()\\n\\n#unionfind\\nfrom collections import defaultdict\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = collections.defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\n\\n\\n\\ndef main():\\n\\n    n, mx = list(map(int, input().split()))\\n    a = [list(map(int, input().split())) for _ in range(n)]\\n\\n    uf1 = UnionFind(n)\\n    uf2 = UnionFind(n)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[i][k]+a[j][k] > mx:\\n                    break\\n            else:\\n                uf1.union(i, j)\\n\\n    for i in range(n):\\n        for j in range(i+1, n):\\n            for k in range(n):\\n                if a[k][i]+a[k][j] > mx:\\n                    break\\n            else:\\n                uf2.union(i, j)\\n\\n    ans = 1\\n    mod = 998244353\\n\\n    def factorial(n):\\n        rec = 1\\n        for x in range(2, n+1):\\n            rec *= x\\n            rec %= mod\\n        return rec\\n\\n    for lst in list(uf1.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n\\n    for lst in list(uf2.all_group_members().values()):\\n        ans *= factorial(len(lst))\\n        ans %= mod\\n    \\n    print(ans)\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n    return\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from collections import defaultdict\\n\\n\\nclass DisjoinSet:\\n    def __init__(self, N):\\n        self.par = [-1] * N\\n        self.sz = [1] * N\\n\\n    def root(self, x):\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.root(self.par[x])\\n            return self.par[x]\\n\\n    def unite(self, a, b):\\n        a = self.root(a)\\n        b = self.root(b)\\n        if a == b:\\n            return\\n        if self.sz[a] > self.sz[b]:\\n            a, b = b, a\\n        self.par[a] = b\\n        self.sz[b] += self.sz[a]\\n\\n    def same(self, a, b):\\n        return self.root(a) == self.root(b)\\n\\n    def size(self, x):\\n        return self.sz[self.root(x)]\\n\\n    def groups(self):\\n        clusters = defaultdict(list)\\n        for x in range(N):\\n            clusters[self.root(x)].append(x)\\n        return list(clusters.values())\\n\\n\\nN, K = list(map(int, input().split()))\\nM = 998244353\\nA = [[int(x) for x in input().split()] for _ in range(N)]\\n\\nfact = [1] * (N + 1)\\nfor i in range(1, N + 1):\\n    fact[i] = fact[i - 1] * i % M\\n\\nrow_dsu = DisjoinSet(N)\\nfor r1 in range(N):\\n    for r2 in range(r1, N):\\n        if all(A[r1][c] + A[r2][c] <= K for c in range(N)):\\n            row_dsu.unite(r1, r2)\\n\\ncol_dsu = DisjoinSet(N)\\nfor c1 in range(N):\\n    for c2 in range(c1, N):\\n        if all(A[r][c1] + A[r][c2] <= K for r in range(N)):\\n            col_dsu.unite(c1, c2)\\n\\ncntR = 1\\nfor group in row_dsu.groups():\\n    cntR = cntR * fact[len(group)] % M\\ncntC = 1\\nfor group in col_dsu.groups():\\n    cntC = cntC * fact[len(group)] % M\\nprint((cntR * cntC % M))\\n\", \"from collections import Counter\\nn, k = list(map(int, input().split()))\\n\\na = [tuple(map(int, input().split())) for _ in range(n)]\\n\\nf = [1, 1]\\nmod = 998244353\\nfor i in range(2, n+7):\\n    f.append(f[-1]*i % mod)\\n\\n*p, = list(range(n))\\nr = [0]*(n)\\n\\n\\ndef par(x):\\n    if p[x] == x:\\n        return x\\n    res = p[x] = par(p[x])\\n    return res\\n\\n\\ndef union(x, y):\\n    px = par(x)\\n    py = par(y)\\n    if px == py:\\n        return\\n    if r[px] > r[py]:\\n        p[py] = px\\n        r[py] += 1\\n    elif r[px] < r[py]:\\n        p[px] = py\\n        r[px] += 1\\n    else:\\n        p[px] = py\\n        r[py] += 1\\n\\n\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[i][t]+a[j][t] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)\\nans = 1\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\n*p, = list(range(n))\\nr = [0]*(n)\\nfor i in range(n):\\n    for j in range(i):\\n        chng = True\\n        for t in range(n):\\n            if a[t][i]+a[t][j] > k:\\n                chng = False\\n                break\\n        if chng:\\n            union(i, j)\\nfor i in range(n):par(i)##\\nCp = Counter(p)\\nfor g in Cp:\\n    ans *= f[Cp[g]]\\n    ans %= mod\\nprint(ans)\\n\", \"#!/usr/bin python3\\n# -*- coding: utf-8 -*-\\n\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n        self.ans = n * (n - 1) // 2  ######\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        sx = self.size(x)  ######\\n        sy = self.size(y)  ######\\n        self.ans += sx * (sx - 1) // 2 + sy * (sy - 1) // 2  ######\\n        self.ans -= (sx + sy) * (sx + sy - 1) // 2  ######\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n\\n\\n######\\nmod = 998244353\\npr = [1]\\nfor i in range(1, 50):\\n    pr.append(pr[-1]*i%mod)\\n\\nn, k = list(map(int, input().split()))\\nm = [list(map(int, input().split())) for _ in range(n)]\\nufs = [UnionFind(n) for _ in range(2)]\\n\\nfor x in range(n):\\n    for y in range(n):\\n        fg = True\\n        for i in range(n):\\n            if m[i][x] + m[i][y] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[0].union(x, y)\\n        fg = True\\n        for i in range(n):\\n            if m[x][i] + m[y][i] > k:\\n                fg = False\\n                break\\n        if fg:\\n            ufs[1].union(x, y)\\n\\nret = 1\\nfor uf in ufs:\\n    for r in uf.roots():\\n        ret *= pr[uf.size(r)]\\n        ret %= mod\\nprint(ret)\\n\", \"import sys\\n\\nreadline = sys.stdin.readline\\nINF = float('INF')\\nsys.setrecursionlimit(10 ** 5)\\n\\n\\nclass UnionFind:\\n    \\\"\\\"\\\"\\n    0-indexed\\n    \\\"\\\"\\\"\\n\\n    from typing import List\\n\\n    def __init__(self, n):\\n        self.n = n\\n        self.parent = [-1] * n\\n\\n    def unite(self, x, y) -> int:\\n        x = self.root(x)\\n        y = self.root(y)\\n\\n        if x == y:\\n            return 0\\n\\n        if self.parent[x] > self.parent[y]:\\n            x, y = y, x\\n\\n        self.parent[x] += self.parent[y]\\n        self.parent[y] = x\\n\\n        return self.parent[x]\\n\\n    def is_same(self, x, y) -> bool:\\n        return self.root(x) == self.root(y)\\n\\n    def root(self, x) -> int:\\n        if self.parent[x] < 0:\\n            return x\\n        else:\\n            self.parent[x] = self.root(self.parent[x])\\n            return self.parent[x]\\n\\n    def size(self, x) -> int:\\n        return -self.parent[self.root(x)]\\n\\n    def all_sizes(self) -> List[int]:\\n        sizes = []\\n\\n        for i in range(self.n):\\n            size = self.parent[i]\\n            if size < 0:\\n                sizes.append(-size)\\n        return sizes\\n\\n    def groups(self) -> List[List[int]]:\\n        groups = dict()\\n\\n        for i in range(self.n):\\n            p = self.root(i)\\n            if not groups.get(p):\\n                groups[p] = []\\n            groups[p].append(i)\\n\\n        return list(groups.values())\\n\\n\\ndef main():\\n    def factorial(x):\\n        res = 1\\n        for i in range(1, x + 1):\\n            res *= i\\n            res %= MOD\\n        return res\\n\\n    def judge1(first, second):\\n        for i in range(N):\\n            if grid[first][i] + grid[second][i] > K:\\n                return False\\n        return True\\n\\n    def judge2(first, second):\\n        for i in range(N):\\n            if grid[i][first] + grid[i][second] > K:\\n                return False\\n        return True\\n\\n    MOD = 998244353\\n\\n    N, K = list(map(int, readline().split()))\\n    grid = []\\n\\n    for _ in range(N):\\n        s = list(map(int, readline().split()))\\n        grid.append(s)\\n\\n    cnt_r, cnt_c = 1, 1\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge1(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_r *= factorial(size)\\n        cnt_r %= MOD\\n\\n    uf = UnionFind(N + 1)\\n\\n    for i in range(N):\\n        for j in range(i, N):\\n            if judge2(i, j):\\n                uf.unite(i, j)\\n\\n    for size in uf.all_sizes():\\n        cnt_c *= factorial(size)\\n        cnt_c %= MOD\\n\\n    print(((cnt_r * cnt_c) % MOD))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import numpy as np\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1]*n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x,y = y,x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\nmod = 998244353\\nn,k = map(int,input().split())\\na = np.array([list(map(int,input().split())) for _ in range(n)],dtype=np.int64)\\nans = 1\\nfor _ in range(2):\\n    uf = UnionFind(n)\\n    for i in range(n):\\n        for j in range(i,n):\\n            if i==j:continue\\n            if max(a[i]+a[j])<=k:\\n                uf.union(i,j)\\n    c = uf.all_group_members()\\n    for key,v in c.items():\\n        tmp = 1\\n        for i in range(len(v)):\\n            tmp *= i+1\\n            tmp %= mod \\n        ans *= tmp\\n        ans %= mod\\n    a = a[::-1].T\\nprint(ans)\", \"# -*- coding: utf-8 -*-\\nimport sys\\nsys.setrecursionlimit(10**9)\\nINF=10**18\\nMOD=998244353\\ninput=lambda: sys.stdin.readline().rstrip()\\nYesNo=lambda b: bool([print('Yes')] if b else print('No'))\\nYESNO=lambda b: bool([print('YES')] if b else print('NO'))\\nint1=lambda x:int(x)-1\\n\\nN,K=map(int,input().split())\\na=[list(map(int,input().split())) for _ in range(N)]\\nclass UnionFind:\\n    def __init__(self,n):\\n        self.par=[i for i in range(n)]\\n        self.siz=[1]*n\\n        \\n    def root(self,x):\\n        while self.par[x]!=x:\\n            self.par[x]=self.par[self.par[x]]\\n            x=self.par[x]\\n        return x\\n    \\n    def unite(self,x,y):\\n        x=self.root(x)\\n        y=self.root(y)\\n        if x==y:\\n            return False\\n        if self.siz[x]<self.siz[y]:\\n            x,y=y,x\\n        self.siz[x]+=self.siz[y]\\n        self.par[y]=x\\n        return True\\n    \\n    def is_same(self,x,y):\\n        return self.root(x)==self.root(y)\\n    \\n    def size(self,x):\\n        return self.siz[self.root(x)]\\n    \\n    def get_roots(self):\\n        roots=set()\\n        for i in range(len(self.par)):\\n            roots.add(self.root(i))\\n        return list(roots)\\n\\n    def get_roots_and_size(self):\\n        roots=self.get_roots()\\n        roots_and_size=[[v,self.size(v)] for v in roots]\\n        return roots_and_size\\nuy=UnionFind(N)\\nux=UnionFind(N)\\nfor y0 in range(N):\\n    for y1 in range(N):\\n        for x in range(N):\\n            if a[y0][x]+a[y1][x]>K:\\n                break\\n        else:\\n            uy.unite(y0,y1)\\nfor x0 in range(N):\\n    for x1 in range(N):\\n        for y in range(N):\\n            if a[y][x0]+a[y][x1]>K:\\n                break\\n        else:\\n            ux.unite(x0,x1)\\nans=0\\nry=uy.get_roots_and_size()\\nrx=ux.get_roots_and_size()\\ndef COMinit(n,MOD):\\n    fac,finv,inv=[0]*max(2,n+1),[0]*max(2,n+1),[0]*max(2,n+1)\\n    fac[0]=fac[1]=1\\n    finv[0]=finv[1]=1\\n    inv[1]=1\\n    for i in range(2,(n+1)):\\n        fac[i]=fac[i-1]*i%MOD\\n        inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD\\n        finv[i]=finv[i-1]*inv[i]%MOD\\n    return fac,finv,inv\\n\\nfac,finv,inv=COMinit(N,MOD)\\n\\ndef COM(n, k, MOD=MOD):\\n    if n<k or n<0 or k<0:\\n        return 0\\n    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD\\n\\n\\nans=1\\nfor _,v in ry:\\n    ans*=fac[v]\\n    ans%=MOD\\nfor _,v in rx:\\n    ans*=fac[v]\\n    ans%=MOD\\nprint(ans)\", \"from collections import Counter\\nn, k = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(n)]\\nMOD = 998244353\\n\\nlst1 = [[] for _ in range(n)]\\nlst2 = [[] for _ in range(n)]\\n\\ng1 = [-1] * n\\ng2 = [-1] * n\\n\\nfor i in range(n-1):\\n    for j in range(i+1, n):\\n        jdg1 = True\\n        jdg2 = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                jdg1 = False\\n            if a[l][i] + a[l][j] > k:\\n                jdg2 = False\\n            if (not jdg1) and (not jdg2):break\\n        if jdg1:\\n            lst1[i].append(j)\\n            lst1[j].append(i)\\n            g1[i] = 0\\n            g1[j] = 0\\n        if jdg2:\\n            lst2[i].append(j)\\n            lst2[j].append(i)\\n            g2[i] = 0\\n            g2[j] = 0\\n\\ndef calc(lst, g):\\n    cnt = 1\\n    for i in range(n):\\n        if g[i] != 0: continue\\n        temp = [i]\\n        g[i] = cnt\\n        while temp:\\n            p = temp.pop()\\n            for ip in lst[p]:\\n                if g[ip] != 0:continue\\n                g[ip] = cnt\\n                temp.append(ip)\\n        cnt += 1\\n    return g\\n  \\ng1 = calc(lst1, g1)\\ncnt1 = Counter(g1)\\n\\ng2 = calc(lst2, g2)\\ncnt2 = Counter(g2)\\n\\nans = 1\\n\\nfor i, v in cnt1.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nfor i, v in cnt2.items():\\n    if i==-1: continue\\n    for j in range(1, v+1):\\n        ans *= (j % MOD)\\n    ans %= MOD\\n\\nprint(ans)\", \"\\nimport itertools,math\\nfrom collections import defaultdict\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def all_group_members(self):\\n        group_members = defaultdict(list)\\n        for member in range(self.n):\\n            group_members[self.find(member)].append(member)\\n        return group_members\\n\\n    def __str__(self):\\n        return '\\\\n'.join(f'{r}: {m}' for r, m in list(self.all_group_members().items()))\\nn,k = list(map(int,input().split()))\\na = [list(map(int,input().split())) for i in range(n)]\\na_row = []\\na_column = []\\nfor i in itertools.combinations(list(range(n)),2):\\n    for j in range(n):\\n        if a[i[0]][j] + a[i[1]][j] > k:\\n            break\\n        if j == n - 1:\\n            a_row.append(i)\\n    for j in range(n):\\n        if a[j][i[0]] + a[j][i[1]] > k:\\n            break\\n        if j == n - 1:\\n            a_column.append(i)\\nuf_row = UnionFind(n)\\nuf_column = UnionFind(n)\\nfor i in a_row:\\n    uf_row.union(i[0],i[1])\\nfor i in a_column:\\n    uf_column.union(i[0],i[1])\\nans = 1\\nfor i in list(uf_row.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nfor i in list(uf_column.all_group_members().values()):\\n    ans = ans * math.factorial(len(i)) % 998244353\\nprint(ans)\\n\", \"n,k=map(int, input().split())\\nmat=[]\\nfor i in range(n):\\n    mat.append(list(map(int, input().split())))\\n\\ndef fact(n):\\n    tmp=1\\n    for i in range(2,n+1):\\n        tmp*=i\\n        tmp%=998244353\\n    \\n    return tmp\\n\\ngoto=[[] for i in range(n)]\\nfor gyou1 in range(n):\\n    for gyou2 in range(gyou1+1,n):\\n        OK=True\\n        for retu in range(n):\\n            if mat[gyou1][retu]+mat[gyou2][retu]>k:\\n                OK=False\\n        if OK:\\n            goto[gyou1].append(gyou2)\\n            goto[gyou2].append(gyou1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_gyou=1\\n\\nfor i in range(gro_no+1):\\n    ans_gyou*=fact(gro_cnt[i])\\n\\n\\ngoto=[[] for i in range(n)]\\nfor retu1 in range(n):\\n    for retu2 in range(retu1+1,n):\\n        OK=True\\n        for gyou in range(n):\\n            if mat[gyou][retu1]+mat[gyou][retu2]>k:\\n                OK=False\\n        if OK:\\n            goto[retu1].append(retu2)\\n            goto[retu2].append(retu1)\\n\\nfrom collections import deque\\nque=deque()\\ngro=[-1]*n\\n\\nque.append(0)\\ngro_no=0\\ngro[0]=0\\n\\nfor i in range(n):\\n    if gro[i]==-1:\\n        que.append(i)\\n        gro_no+=1\\n        gro[i]=gro_no\\n\\n    while que:\\n        now=que.popleft()\\n        for j in goto[now]:\\n            if gro[j]==-1:\\n                que.append(j)\\n                gro[j]=gro_no\\n\\ngro_cnt=[0]*(gro_no+1)\\nfor i in range(n):\\n    gro_cnt[gro[i]]+=1\\n\\n\\n\\nans_retu=1\\n\\nfor i in range(gro_no+1):\\n    ans_retu*=fact(gro_cnt[i])\\n\\nans=(ans_gyou*ans_retu)%998244353\\n\\nprint(ans)\", \"class UnionFindTree:\\n    \\\"\\\"\\\"Union-Find Tree\\n\\n    Attributes:\\n        n (int):    \\u9802\\u70b9\\u6570\\n        par (list): \\u8981\\u7d20\\u306e\\u683c\\u7d0d\\u5148\\n    \\\"\\\"\\\"\\n    def __init__(self, n):\\n        \\\"\\\"\\\"\\u521d\\u671f\\u5316 O(1)\\n\\n        Args:\\n            n (int): \\u9802\\u70b9\\u6570\\n        \\\"\\\"\\\"\\n        self.par = [-1] * n\\n\\n    def find(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u691c\\u7d22 O(\\u03b1(N))\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u306e\\u6839\\n        \\\"\\\"\\\"\\n        if self.par[x] < 0:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n\\n\\n    def union(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u4f75\\u5408 O(1)\\n\\n        Args:\\n            x (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n            y (int): \\u4f75\\u5408\\u5bfe\\u8c61\\u306e\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u8981\\u7d20\\n        \\\"\\\"\\\"\\n        x = self.find(x)\\n        y = self.find(y)\\n        \\n        if x == y:\\n            return\\n\\n        if self.par[x] > self.par[y]:\\n            x, y = y, x\\n\\n        self.par[x] += self.par[y]\\n        self.par[y] = x\\n\\n    def same(self, x, y):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u306e\\u5224\\u5b9a O(1)\\n\\n        Args:\\n            x (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n            y (int): \\u5224\\u5b9a\\u5bfe\\u8c61\\u306e\\u8981\\u7d20\\n\\n        Returns:\\n            bool: x\\u3068y\\u304c\\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5426\\u304b\\n        \\\"\\\"\\\"\\n        return self.find(x) == self.find(y)\\n    \\n    def size(self, x):\\n        \\\"\\\"\\\"\\u8981\\u7d20\\u6570\\u306e\\u8a08\\u7b97 O(1)\\n\\n        Args:\\n            x (int): \\u5bfe\\u8c61\\u8981\\u7d20\\n\\n        Returns:\\n            int: x\\u304c\\u5c5e\\u3059\\u308b\\u96c6\\u5408\\u306e\\u8981\\u7d20\\u6570\\n        \\\"\\\"\\\"\\n        return -self.par[self.find(x)]\\n\\n\\nN, K = map(int, input().split())\\na = [list(map(int, input().split())) for _ in range(N)]\\n\\nmod = 998244353\\n\\nuf1 = UnionFindTree(N)\\nuf2 = UnionFindTree(N)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[i][k] + a[j][k] > K:\\n                flag = False\\n        if flag:\\n            uf1.union(i, j)\\n\\nfor i in range(N):\\n    for j in range(i+1, N):\\n        flag = True\\n        for k in range(N):\\n            if a[k][i] + a[k][j] > K:\\n                flag = False\\n        if flag:\\n            uf2.union(i, j)\\n\\nl = [1]\\nfor i in range(1, N+1):\\n    l.append(l[-1] * i % mod)\\n\\nres = 1\\nfor i in range(N):\\n    if i == uf1.find(i):\\n        res = res * l[uf1.size(i)] % mod\\n    if i == uf2.find(i):\\n        res = res * l[uf2.size(i)] % mod\\n\\nprint(res)\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN,K = map(int,readline().split())\\nDIV = 998244353\\nA = [list(map(int,readline().split())) for i in range(N)]\\n\\n# K\\u306e\\u5236\\u7d04\\u304c\\u306a\\u3044\\u5834\\u5408\\n# \\u3069\\u3093\\u306a\\u306b\\u5165\\u308c\\u66ff\\u3048\\u3066\\u3082\\u3001\\u540c\\u3058\\u884c\\u30fb\\u540c\\u3058\\u5217\\u306b\\u5b58\\u5728\\u3059\\u308b\\u6570\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\u5909\\u308f\\u3089\\u306a\\u3044\\n# \\u3064\\u307e\\u308a\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5217\\u306e\\u30da\\u30a2\\u306f\\u9650\\u3089\\u308c\\u3066\\u3044\\u308b\\n# \\u884c\\u30fb\\u5217\\u306b\\u5bfe\\u3057\\u3066\\u3001\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u30da\\u30a2\\u306e\\u901a\\u308a\\u6570\\u3092\\u7b97\\u51fa\\u3057\\u3001\\u305d\\u308c\\u3092\\u639b\\u3051\\u5408\\u308f\\u305b\\u305f\\u3082\\u306e\\u304c\\u7b54\\u3048\\n\\n# \\u884cA\\u3068\\u884cB\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u884cB\\u3068\\u884cC\\u304c\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u5834\\u5408\\u3001\\n# \\u884cA\\u3068\\u884cC\\u304c\\u76f4\\u63a5\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u3067\\u306a\\u304f\\u3066\\u3082\\u64cd\\u4f5c\\u306b\\u3088\\u3063\\u3066\\u884cA,\\u884cC\\u306f\\u5165\\u308c\\u66ff\\u3048\\u308b\\u3053\\u3068\\u304c\\u51fa\\u6765\\u308b\\n# UnionFind\\u3067\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\u306a\\u3082\\u306e\\u540c\\u58eb\\u3092\\u30b0\\u30eb\\u30fc\\u30d4\\u30f3\\u30b0\\u3059\\u308b\\n\\n# by size\\n# 0-indexed\\n\\nclass UnionFind:\\n  N=0\\n  parent=None\\n  size=None\\n  def __init__(self,N):\\n    self.N=N\\n    self.parent=[i for i in range(self.N)]\\n    self.size=[1]*self.N\\n    \\n  def root(self,x):\\n    while x!=self.parent[x]:\\n      self.parent[x]=self.parent[self.parent[x]]\\n      x=self.parent[x]\\n    return x\\n  \\n  def same(self,x,y):\\n    return self.root(x)==self.root(y)\\n  \\n  def unite(self,x,y):\\n    x=self.root(x)\\n    y=self.root(y)\\n    if x==y:\\n      return\\n    if self.size[x]>self.size[y]:\\n      # \\u5927\\u304d\\u3044\\u65b9\\u306b\\u304f\\u3063\\u3064\\u3051\\u308b\\n      self.parent[y]=x\\n      self.size[x]+=self.size[y]\\n    else:\\n      self.parent[x]=y\\n      self.size[y]+=self.size[x]\\n      \\n  def get_group_size(self,x):\\n    return self.size[self.root(x)]\\n  \\n  def get_roots(self):\\n    r=set()\\n    for i in range(self.N):\\n      r.add(self.root(i))\\n    return r\\n  \\n  def show_parent(self):\\n    print(self.parent)\\n    \\n  def show_size(self):\\n    print(self.size)\\n\\nUF_row = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[i][k] + A[j][k] > K:\\n        break\\n    else:\\n      #print(\\\"\\u884c\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_row.unite(i, j)\\n      \\nrow_pat = 1\\nrow_roots = UF_row.get_roots()\\nfor root in row_roots:\\n  siz = UF_row.get_group_size(root)\\n  # siz\\u306e\\u968e\\u4e57\\u901a\\u308a\\u5206\\u7d44\\u307f\\u5408\\u308f\\u305b\\u304c\\u5b58\\u5728\\u3059\\u308b\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  row_pat *= pat\\n  row_pat %= DIV\\n  \\n#print(\\\"row_pat\\\",row_pat)\\n\\nUF_col = UnionFind(N)\\n\\nfor i in range(N - 1):\\n  for j in range(i + 1, N):\\n    for k in range(N):\\n      if A[k][i] + A[k][j] > K:\\n        break\\n    else:\\n      #print(\\\"\\u5217\\\",i,j,\\\"\\u5165\\u308c\\u66ff\\u3048\\u53ef\\u80fd\\\")\\n      UF_col.unite(i, j)\\n\\ncol_pat = 1\\ncol_roots = UF_col.get_roots()\\nfor root in col_roots:\\n  siz = UF_col.get_group_size(root)\\n  #print(\\\"root\\\",root,\\\"siz\\\",siz)\\n  pat = 1\\n  for p in range(1, siz + 1):\\n    pat *= p\\n    pat %= DIV\\n  col_pat *= pat\\n  col_pat %= DIV\\n  \\n#print(\\\"col_pat\\\",col_pat)\\n  \\nprint((row_pat * col_pat) % DIV)\", \"MOD = 998244353\\nfrom math import factorial\\nN, K = list(map(int, input().split()))\\nfield = [list(map(int, input().split())) for i in range(N)]\\n\\nclass Union_Find:\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3068\\u9ad8\\u3055\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u3092\\u521d\\u671f\\u5316\\u3057\\u3001\\n    # \\u8981\\u7d20N\\u500b\\u306eUnion-Find\\u68ee\\u3092\\u4f5c\\u6210\\u3059\\u308b\\u3002\\n    # \\u89aa\\u7ba1\\u7406\\u30ea\\u30b9\\u30c8\\u306f\\u3001\\u57fa\\u672c\\u7684\\u306b\\u306f\\u81ea\\u5206\\u306e\\u3072\\u3068\\u3064\\u4e0a\\u306e\\u89aa\\u3092\\u8868\\u3059\\u304c\\u3001\\n    # \\u5024\\u304c\\u8ca0\\u306e\\u5834\\u5408\\u306b\\u306f\\u3001\\u81ea\\u8eab\\u304c\\u6700\\u4e0a\\u4f4d\\u306e\\u89aa(\\u30ea\\u30fc\\u30c0\\u30fc)\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u8868\\u3057\\u3001\\n    # \\u81ea\\u5206\\u3092\\u542b\\u3081\\u305f\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u7ba1\\u7406\\u3059\\u308b\\u3053\\u3068\\u3068\\u3059\\u308b\\n    def __init__(self, N):\\n        self.parent = [-1] * N\\n        self.rank = [0] * N\\n        self.group_count = N\\n        self.N = N\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u3092\\u8fd4\\u3059\\n    def find(self, x):\\n        # \\u81ea\\u5206\\u81ea\\u8eab\\u304c\\u30ea\\u30fc\\u30c0\\u30fc\\u306a\\u3089\\u3001\\u81ea\\u5206\\u3092\\u8fd4\\u3059\\n        if self.parent[x] < 0:\\n            return x\\n\\n        # \\u518d\\u5e30\\u7684\\u306b\\u635c\\u7d22\\u3057\\u3001\\u898b\\u3064\\u304b\\u308c\\u3070\\u7e4b\\u304e\\u5909\\u3048\\u3066\\u304a\\u304f\\n        # (\\u8a08\\u7b97\\u91cf\\u304c\\u5897\\u3048\\u308b\\uff1d\\u9762\\u5012\\u304f\\u3055\\u3044\\u306e\\u3067)\\u9ad8\\u3055\\u7ba1\\u7406\\u306f\\u884c\\u308f\\u306a\\u3044\\n        par = self.find(self.parent[x])\\n        self.parent[x] = par\\n        return par\\n\\n    # x\\u3068y\\u306e\\u30b0\\u30eb\\u30fc\\u30d7\\u3092\\u7d71\\u5408\\u3059\\u308b\\n    def unite(self, x, y):\\n        # \\u305d\\u308c\\u305e\\u308c\\u306e\\u30ea\\u30fc\\u30c0\\u30fc\\u306b\\u5bfe\\u3059\\u308b\\u64cd\\u4f5c\\u3092\\u884c\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        # \\u30ea\\u30fc\\u30c0\\u30fc\\u304c\\u540c\\u3058\\u306a\\u3089\\u4f55\\u3082\\u3059\\u308b\\u5fc5\\u8981\\u304c\\u306a\\u3044\\n        if x == y:\\n            return\\n\\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u540c\\u3058\\u5834\\u5408\\uff1a\\n        # \\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u4eba\\u6570\\u3092\\u5408\\u8a08\\u3057\\u3064\\u3064\\u9069\\u5f53\\u306b\\u7e4b\\u304e\\u3001\\u7e4b\\u3052\\u3089\\u308c\\u305f\\u65b9\\u306e\\u9ad8\\u3055\\u30921\\u5897\\u3084\\u3059\\n        if self.rank[x] == self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n            self.rank[x] += 1\\n        \\n        # \\u6728\\u306e\\u9ad8\\u3055\\u304c\\u9055\\u3046\\u306a\\u3089\\u3001\\u4f4e\\u3044\\u65b9\\u3092\\u9ad8\\u3044\\u65b9\\u306b\\u3064\\u306a\\u3050\\n        elif self.rank[x] > self.rank[y]:\\n            self.parent[x] += self.parent[y]\\n            self.parent[y] = x\\n        else:\\n            self.parent[y] += self.parent[x]\\n            self.parent[x] = y\\n        \\n        # \\u7d71\\u5408\\u3055\\u308c\\u305f\\u5834\\u5408\\u3001\\u30b0\\u30eb\\u30fc\\u30d7\\u6570\\u306f1\\u6e1b\\u308b\\n        self.group_count -= 1\\n    \\n    # x\\u3068y\\u304c\\u540c\\u3058\\u30b0\\u30eb\\u30fc\\u30d7\\u304b\\u3069\\u3046\\u304b\\u3092\\u8abf\\u3079\\u308b\\n    def samep(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u3092\\u30ea\\u30b9\\u30c8\\u3067\\u8fd4\\u3059\\n    def get_group_member_list(self, x):\\n        x = self.find(x)\\n        return [i for i in range(self.N) if self.find(i) == x]\\n    \\n    # x\\u306e\\u6240\\u5c5e\\u3059\\u308b\\u30b0\\u30eb\\u30fc\\u30d7\\u306e\\u30e1\\u30f3\\u30d0\\u30fc\\u6570\\u3092\\u8fd4\\u3059\\n    def get_group_member_count(self, x):\\n        x = self.find(x)\\n        return -self.parent[x]\\n\\n    # \\u5168\\u3066\\u306e{\\u30ea\\u30fc\\u30c0\\u30fc:\\u30b0\\u30eb\\u30fc\\u30d7\\u30e1\\u30f3\\u30d0\\u30fc\\u6570}\\u3092\\u8f9e\\u66f8\\u5f62\\u5f0f\\u3067\\u8fd4\\u3059\\n    def get_all_groups(self):\\n        return {idx:-n for idx, n in enumerate(self.parent) if n < 0}\\n\\nhg = Union_Find(N)\\nfor i in range(N-1):\\n    h1 = field[i]\\n    for j in range(i,N):\\n        h2 = field[j]\\n        if all([True if x+y <= K else False for x, y in zip(h1, h2)]):\\n            hg.unite(i, j)\\n\\nvg = Union_Find(N)\\nrotated = list(zip(*field))\\nfor i in range(N-1):\\n    v1 = rotated[i]\\n    for j in range(i, N):\\n        v2 = rotated[j]\\n        if all([True if x+y <= K else False for x, y in zip(v1, v2)]):\\n            vg.unite(i, j)\\n\\nresult = 1\\nfor value in list(hg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nfor value in list(vg.get_all_groups().values()):\\n    result *= factorial(value)\\n    result %= MOD\\n\\nprint(result)\\n\", \"import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy\\n\\nsys.setrecursionlimit(10**7)\\ninf=10**20\\nmod=998244353\\ndd=[(-1,0),(0,1),(1,0),(0,-1)]\\nddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]\\n\\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\\n# def LF(): return [float(x) for x in sys.stdin.readline().split()]\\ndef I(): return int(sys.stdin.readline())\\ndef F(): return float(sys.stdin.readline())\\ndef LS(): return sys.stdin.readline().split()\\ndef S(): return input()\\n\\n# Union-Find -- START --\\nclass UnionFind():\\n  def __init__(self,sz):\\n    self.sz=sz\\n    self.data=[-1]*sz\\n    self.amount=[0]*sz\\n\\n  def unite(self,x,y):\\n    x=self.find(x)\\n    y=self.find(y)\\n    if x==y:\\n      return False\\n    self.amount[x]+=self.amount[y]\\n    self.amount[y]+=self.amount[x]\\n    if self.data[x]>self.data[y]:\\n      x,y=y,x\\n    self.data[x]+=self.data[y]\\n    self.data[y]=x\\n    return True\\n\\n  def find(self,k):\\n    if self.data[k]<0:\\n      return k\\n    self.data[k]=self.find(self.data[k])\\n    return self.data[k]\\n\\n  def size(self,k):\\n    return -self.data[self.find(k)]\\n\\n  def set_amount(self,k,k_amount):\\n    self.amount[k]=k_amount\\n\\n  def get_amount(self,k):\\n    return self.amount[k]\\n# Union-Find --- END ---\\n\\ndef main():\\n  n,K=LI()\\n  field=[LI() for _ in range(n)]\\n  uf1=UnionFind(n)\\n  uf2=UnionFind(n)\\n\\n  for i in range(n):\\n    l1=[True]*n\\n    for j in range(i+1,n):\\n      if not l1[i]:\\n        continue\\n      for k in range(n):\\n        # print(field[i][k],field[j][k])\\n        if field[i][k]+field[j][k]>K:\\n          l1[j]=False\\n          break\\n    # print(l1[j])\\n    for j in range(i+1,n):\\n      if l1[j]:\\n        uf1.unite(i,j)\\n\\n    # for i in range(n):\\n    #   print(uf1.find(i))\\n\\n  for i in range(n):\\n    l2=[True]*n\\n    for j in range(i+1,n):\\n      if not l2[i]:\\n        continue\\n      for k in range(n):\\n        if field[k][i]+field[k][j]>K:\\n          l2[j]=False\\n          break\\n    for j in range(i+1,n):\\n      if l2[j]:\\n        uf2.unite(i,j)\\n\\n  # for i in range(n):\\n  #   print(uf2.find(i))\\n\\n  ans1=1\\n  check1=[True]*n\\n  for i in range(n):\\n    sz=uf1.size(i)\\n    pa=uf1.find(i)\\n    if check1[pa]:\\n      check1[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans1*=_ans\\n      ans1%=mod\\n\\n  # print(ans1)\\n\\n  ans2=1\\n  check2=[True]*n\\n  for i in range(n):\\n    sz=uf2.size(i)\\n    pa=uf2.find(i)\\n    if check2[pa]:\\n      check2[pa]=False\\n      _ans=1\\n      for j in range(2,sz+1):\\n        _ans*=j\\n        _ans%=mod\\n      ans2*=_ans\\n      ans2%=mod\\n\\n  return (ans1*ans2)%mod\\n\\n# main()\\nprint((main()))\\n\", \"import sys\\ntry:\\n    import os\\n    f = open('input.txt', 'r')\\n    sys.stdin = f\\nexcept FileNotFoundError:\\n    None\\nfrom math import sqrt, ceil, floor\\nfrom collections import deque, Counter, defaultdict\\n# defaultdict(int)\\ninput=lambda: sys.stdin.readline().strip()\\nsys.setrecursionlimit(11451419)\\nfrom decimal import ROUND_HALF_UP,Decimal  #\\u5909\\u63db\\u5f8c\\u306e\\u672b\\u5c3e\\u6841\\u30920\\u30840.01\\u3067\\u6307\\u5b9a\\n  #Decimal((str(0.5)).quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nfrom functools import lru_cache\\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\\nfrom itertools import combinations as com, permutations as per\\nfrom fractions import Fraction as frac  #frac(a,b)\\u3067\\u6b63\\u78ba\\u306aa/b\\n# @lru_cache(maxsize=10**10)\\n#######\\u3053\\u3053\\u307e\\u3067\\u30c6\\u30f3\\u30d7\\u30ec#######\\n#\\u30bd\\u30fc\\u30c8\\u3001\\\"a\\\"+\\\"b\\\"\\u3001\\u518d\\u5e30\\u306a\\u3089Python3\\u306e\\u65b9\\u304c\\u3044\\u3044\\n#######\\u3053\\u3053\\u304b\\u3089\\u5929\\u3077\\u3089########\\n\\nn,k=list(map(int,input().split()))\\nA=[list(map(int,input().split())) for i in range(n)]\\ncntx=0; cnty=0\\n\\nkai=[1]*70\\nmod=998244353\\nfor i in range(1,65):\\n    kai[i]=(kai[i-1]*i)%mod\\n# print(kai)\\n\\nclass UnionFind():\\n    def __init__(self,num):\\n        self.n = num\\n        self.parents = [-1 for i in range(self.n)]\\n\\n\\n\\n    def find(self,x):\\n        if self.parents[x]<0:\\n            return x\\n        else:\\n            self.parents[x]=self.find(self.parents[x])\\n\\n            return self.parents[x]\\n\\n\\n    def union(self,x,y):\\n        xx=self.find(x)\\n        yy=self.find(y)\\n        if xx==yy:\\n            return\\n        else:\\n            size_xx=abs(self.parents[xx])\\n            size_yy=abs(self.parents[yy])\\n            if size_xx>size_yy:\\n                xx,yy=yy,xx\\n\\n            self.parents[yy]+=self.parents[xx]\\n            self.parents[xx]=yy\\n\\n\\n    def size(self,x):\\n        xx=self.find(x)\\n        return abs(self.parents[xx])\\n\\n\\n    def same(self,x,y):\\n        return 1 if self.find(x)==self.find(y) else 0\\n\\n\\n    def members(self,x):\\n        xx=self.find(x)\\n        return [i for i in range(self.n) if self.find(i)==xx]\\n\\n\\n\\n    def roots(self):\\n        return [i for i,x in enumerate(self.parents) if x < 0]\\n\\n\\n\\n    def all_group_members(self):\\n        return {r:self.members(r) for r in self.roots()}\\n\\n    def state_grouping(self):\\n        return list(self.all_group_members().values())\\n\\n# uf=UnionFind(n)\\nufx=UnionFind(n)\\nufy=UnionFind(n)\\n\\nfor i in range(n):\\n    po=0\\n    for j in range(i):\\n        for p in range(n):\\n            if A[i][p]+A[j][p]>k:\\n                po=1;break\\n        else:\\n            ufx.union(i,j)\\n\\nfor i in range(n):\\n    for j in range(n):\\n        for p in range(n):\\n            if A[p][i]+A[p][j]>k:break\\n        else:\\n            ufy.union(i,j)\\n\\nxx=1; yy=1\\nfor i in ufx.parents:\\n    if i<-1:\\n        xx*=kai[abs(i)]\\n        xx%=mod\\nfor j in ufy.parents:\\n    if j<-1:\\n        yy*=kai[abs(j)]\\n        yy%=mod\\n\\nprint((xx*yy%mod))\\n\", \"class UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n\\n        if x == y:\\n            return\\n\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n\\n    def group_count(self):\\n        return len(self.roots())\\n\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\nmod=998244353\\nn,wa=map(int,input().split())\\na=[list(map(int,input().split())) for i in range(n)]\\nufg=UnionFind(n)\\nufl=UnionFind(n)\\nfor i in range(n-1):\\n  for j in range(i+1,n):\\n    fl=1\\n    fg=1\\n    for k in range(n):\\n      if a[i][k]+a[j][k]>wa:\\n        fg=0\\n        break\\n    for k in range(n):\\n      if a[k][i]+a[k][j]>wa:\\n        fl=0\\n        break\\n    if fg:\\n      ufg.union(i,j)\\n    if fl:\\n      ufl.union(i,j)\\nfrom math import factorial as fa\\nsg=1\\nsl=1\\nfor i in ufg.roots():\\n  sg*=fa(ufg.size(i))\\n  sg%=mod\\nfor i in ufl.roots():\\n  sl*=fa(ufl.size(i))\\n  sl%=mod\\nprint((sl*sg)%mod)\", \"#Union Find Tree\\nclass UnionFind():\\n    def __init__(self, n):\\n        self.n = n\\n        self.parents = [-1] * n\\n    def find(self, x):\\n        if self.parents[x] < 0:\\n            return x\\n        else:\\n            self.parents[x] = self.find(self.parents[x])\\n            return self.parents[x]\\n    def union(self, x, y):\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x == y:\\n            return\\n        if self.parents[x] > self.parents[y]:\\n            x, y = y, x\\n        self.parents[x] += self.parents[y]\\n        self.parents[y] = x\\n    def size(self, x):\\n        return -self.parents[self.find(x)]\\n    def same(self, x, y):\\n        return self.find(x) == self.find(y)\\n    def members(self, x):\\n        root = self.find(x)\\n        return [i for i in range(self.n) if self.find(i) == root]\\n    def roots(self):\\n        return [i for i, x in enumerate(self.parents) if x < 0]\\n    def group_count(self):\\n        return len(self.roots())\\n    def all_group_members(self):\\n        return {r: self.members(r) for r in self.roots()}\\n    def __str__(self):\\n        return '\\\\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())\\n      \\nN,K=map(int,input().split())\\nA=[]\\nfor i in range(N):\\n  a=list(map(int, input().split()))\\n  A.append(a)\\n\\nUF1=UnionFind(N)\\nUF2=UnionFind(N)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[i][k]+A[j][k]>K:\\n        l=1\\n    if l==0:\\n      UF1.union(i,j)\\n\\nfor i in range(N):\\n  for j in range(i+1,N):\\n    l=0\\n    for k in range(N):\\n      if A[k][i]+A[k][j]>K:\\n        l=1\\n    if l==0:\\n      UF2.union(i,j)\\n    \\ndef fac(x):\\n  ans=1\\n  for i in range(1,x+1):\\n    ans*=i\\n    ans%=998244353\\n  return ans\\n    \\nans=1\\nfor i in UF1.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nfor i in UF2.parents:\\n  if i < 0:\\n    ans*=fac(-i)\\n    ans%=998244353\\n    \\nprint(ans)\", \"mod = 998244353\\nfact=[1]\\nfor i in range(1,51):\\n    x = (i*fact[-1])%mod\\n    fact.append(x)\\nn,k = list(map(int,input().split()))\\ndef dfs(node):\\n    if vis[node]:\\n        return 0\\n    vis[node]=1\\n    ans=1\\n    for i in m[node]:\\n        ans+=dfs(i)\\n    return ans\\n\\nl=[]\\nfor i in range(n):\\n    l.append(list(map(int,input().split())))\\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for b in range(n):\\n            if l[i][b]+l[j][b]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\n\\na=1\\nb=1\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    a = (a*fact[x])%mod\\n\\n            \\nm=[]\\nfor i in range(n):\\n    m.append([])\\nfor i in range(n):\\n    for j in range(i+1,n):\\n        e=1\\n        for v in range(n):\\n            if l[v][i]+l[v][j]>k:\\n                e=0\\n                break\\n        if e:\\n            m[i].append(j)\\n            m[j].append(i)\\nvis=[0]*n\\nfor i in range(n):\\n    x = dfs(i)\\n    b = (b*fact[x])%mod\\nans = (a*b)%mod\\nprint(ans)\\n        \\n        \\n\", \"import math\\nfrom math import gcd,pi,sqrt\\nINF = float(\\\"inf\\\")\\nMOD = 10**9 + 7\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**6)\\nimport itertools\\nimport bisect\\nimport re\\nfrom collections import Counter,deque,defaultdict\\ndef iinput(): return int(input())\\ndef imap(): return map(int, input().split())\\ndef ilist(): return list(imap())\\ndef irow(N): return [iinput() for i in range(N)]\\ndef sinput(): return input().rstrip()\\ndef smap(): return sinput().split()\\ndef slist(): return list(smap())\\ndef srow(N): return [sinput() for i in range(N)]\\n\\ndef main():\\n    MOD = 998244353\\n    class UnionFind:\\n        def __init__(self, n):\\n            self.par = [i for i in range(n+1)]\\n            self.rank = [0] * (n+1)\\n            self.size = [1] * (n+1) # \\u89aa\\u306b\\u96c6\\u7d04\\u3055\\u308c\\u308b\\n    \\n        # \\u691c\\u7d22\\n        def find(self, x):\\n            if self.par[x] == x:\\n                return x\\n            else:\\n                self.par[x] = self.find(self.par[x])\\n                return self.par[x]\\n    \\n        # \\u4f75\\u5408\\n        def union(self, x, y):\\n            x = self.find(x)\\n            y = self.find(y)\\n    \\n            if x == y:\\n                return\\n    \\n            if self.rank[x] < self.rank[y]:\\n                self.par[x] = y\\n                self.size[y] += self.size[x]\\n                self.size[x] = 0\\n            else:\\n                self.par[y] = x\\n                self.size[x] += self.size[y]\\n                self.size[y] = 0\\n                if self.rank[x] == self.rank[y]:\\n                    self.rank[x] += 1\\n    \\n        # \\u540c\\u3058\\u96c6\\u5408\\u306b\\u5c5e\\u3059\\u308b\\u304b\\u5224\\u5b9a\\n        def same(self, x, y):\\n            return self.find(x) == self.find(y)\\n    \\n        # \\u3059\\u3079\\u3066\\u306e\\u9802\\u70b9\\u306b\\u5bfe\\u3057\\u3066\\u89aa\\u3092\\u691c\\u7d22\\u3059\\u308b\\n        def all_find(self):\\n            for n in range(len(self.par)):\\n                self.find(n)\\n    N,K = imap()\\n    import numpy as np\\n    A = np.array([ilist() for i in range(N)])\\n    uf_i = UnionFind(N)\\n    uf_r = UnionFind(N)\\n\\n    for i in range(N-1):\\n        for j in range(i+1,N):\\n            if np.all(A[i] + A[j] <= K):\\n                uf_i.union(i+1,j+1)\\n            if np.all(A[:,i] + A[:,j] <= K):\\n                uf_r.union(i+1, j+1)\\n    uf_i.all_find()\\n    uf_r.all_find()\\n    \\n    ans = 1\\n    for i in uf_i.size:\\n        if i in [0,1]:\\n            continue\\n        ans *= math.factorial(i)\\n    for j in uf_r.size:\\n        if j in [0,1]:\\n            continue\\n        ans *= math.factorial(j)\\n    print(ans%MOD)\\n\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"mod = 998244353\\nN, K = list(map(int, input().split()))\\nA = []\\nfor i in range(N):\\n    a = [int(i) for i in input().split()]\\n    A.append(a)\\n\\nmemo = [1]\\nfor i in range(1, 52):\\n    num = memo[-1]\\n    memo.append(num*i%mod)\\n\\nclass UnionFind:\\n    def __init__(self, n):\\n        # \\u8ca0  : \\u6839\\u3067\\u3042\\u308b\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u7d76\\u5bfe\\u5024\\u306f\\u30e9\\u30f3\\u30af\\u3092\\u793a\\u3059\\n        # \\u975e\\u8ca0: \\u6839\\u3067\\u306a\\u3044\\u3053\\u3068\\u3092\\u793a\\u3059\\u3002\\u5024\\u306f\\u89aa\\u3092\\u793a\\u3059\\n        self.table = [-1] * n\\n \\n    def _root(self, x):\\n        stack = []\\n        tbl = self.table\\n        while tbl[x] >= 0:\\n            stack.append(x)\\n            x = tbl[x]\\n        for y in stack:\\n            tbl[y] = x\\n        return x\\n\\n    def count(self, x):\\n        return -self.table[self._root(x)]\\n \\n    def find(self, x, y):\\n        return self._root(x) == self._root(y)\\n\\n    def union(self, x, y):\\n        r1 = self._root(x)\\n        r2 = self._root(y)\\n        if r1 == r2:\\n            return\\n        # \\u30e9\\u30f3\\u30af\\u306e\\u53d6\\u5f97\\n        d1 = self.table[r1]\\n        d2 = self.table[r2]\\n        if d1 <= d2:\\n            self.table[r2] = r1\\n            self.table[r1] += d2\\n        else:\\n            self.table[r1] = r2\\n            self.table[r2] += d1\\n\\nuni1 = UnionFind(N)\\nuni2 = UnionFind(N)\\n\\nfor i in range(N-1):\\n    for j in range(i+1, N):\\n        cur1 = 0\\n        cur2 = 0\\n        for k in range(N):\\n            if A[i][k] + A[j][k] <= K:\\n                cur1 += 1\\n            if A[k][i] + A[k][j] <= K:\\n                cur2 += 1\\n        if cur1 == N:\\n            uni1.union(i, j)\\n        if cur2 == N:\\n            uni2.union(i, j)\\n\\nlsnum = []\\nset1, set2 = set(), set()\\nfor i in range(N):\\n    if uni1._root(i) not in set1:\\n        lsnum.append(uni1.count(i))\\n        set1.add(uni1._root(i))\\n    if uni2._root(i) not in set2:\\n        lsnum.append(uni2.count(i))\\n        set2.add(uni2._root(i))\\n\\nans = 1\\nfor num in lsnum:\\n    ans = ans * memo[num] %mod\\nans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n  px, py = find(x, uf), find(y, uf)\\n  if px != py:\\n    if rank[px] > rank[py]:\\n      px, py = py, px\\n    rank[py] += rank[px]\\n    uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      union(i, j, uf1, rank1)\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      union(i, j, uf2, rank2)\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import math\\nN, K = list(map(int, input().split()))\\nA = []\\nmod = 998244353\\nfor _ in range(N):\\n  A.append(list(map(int, input().split())))\\n\\ndef find(x, uf):\\n  if uf[x] != x:\\n    uf[x] = find(uf[x], uf)\\n  return uf[x]\\n\\ndef union(x, y, uf, rank):\\n    px, py = find(x, uf), find(y, uf)\\n    if px != py:\\n        if rank[px] > rank[py]:\\n            px, py = py, px\\n        rank[py] += rank[px]\\n        uf[px] = py\\n  \\nuf1 = {i: i for i in range(N)}\\nuf2 = {i: i for i in range(N)}\\nrank1 = {i: 1 for i in range(N)}\\nrank2 = {i: 1 for i in range(N)}\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(A[i], A[j])):\\n      px, py = find(i, uf1), find(j, uf1)\\n      if px != py:\\n        if rank1[px] > rank1[py]:\\n          px, py = py, px\\n        rank1[py] += rank1[px]\\n        uf1[px] = py\\nB = list(zip(*A))\\nfor i in range(N):\\n  for j in range(i + 1, N):\\n    if all(a + b <= K for a, b in zip(B[i], B[j])):\\n      px, py = find(i, uf2), find(j, uf2)\\n      if px != py:\\n        if rank2[px] > rank2[py]:\\n          px, py = py, px\\n        rank2[py] += rank2[px]\\n        uf2[px] = py\\nans = 1\\nfor x in set(find(i, uf1) for i in range(N)):\\n  ans *= math.factorial(rank1[x])\\n  ans %= mod\\nfor x in set(find(i, uf2) for i in range(N)):\\n  ans *= math.factorial(rank2[x])\\n  ans %= mod\\nprint(ans)\\n\", \"import collections as co\\ndef searchRoot(n):\\n    par = parList[n]\\n    if n == par:\\n        if len(q) > 0:\\n            rootIn(q,n)\\n        return n\\n    else:\\n        q.append(n)\\n        return(searchRoot(par))\\n\\ndef rootIn(q,root):\\n    while len(q) > 0:\\n        parList[q.popleft()] = root\\n\\ndef UnionFind(n,m,lis):\\n    for i in range(m):\\n        a,b = lis[i]\\n        aRoot = searchRoot(a)\\n        bRoot = searchRoot(b)\\n        if aRoot != bRoot:\\n            parList[max(aRoot,bRoot)] = min(aRoot,bRoot)\\n\\n    ansDic = dict()\\n    rootSet = set()\\n    for i in range(0,n):\\n        root = searchRoot(i)\\n        if root in rootSet:\\n            ansDic[root] += 1\\n        else:\\n            rootSet.add(root)\\n            ansDic[root] = 1\\n\\n    return ansDic\\n\\n\\nn,k = list(map(int,input().split()))\\n\\na = []\\nfor i in range(n):\\n    aRow = list(map(int,input().split()))\\n    a.append(aRow)\\n\\nrowLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[i][l] + a[j][l] > k:\\n                check = False\\n                break\\n        if check:\\n            rowLis.append([i,j])\\n#print(rowLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\nrowDic = UnionFind(n,len(rowLis),rowLis)\\n\\n\\ncolLis = []\\nfor i in range(n-1):\\n    for j in range(i+1,n):\\n        check = True\\n        for l in range(n):\\n            if a[l][i] + a[l][j] > k:\\n                check = False\\n                break\\n        if check:\\n            colLis.append([i,j])\\n#print(colLis)\\nparList = [i for i in range(n+1)]\\nq = co.deque()\\ncolDic = UnionFind(n,len(colLis),colLis)\\n\\nans = 1\\n#print(rowDic)\\n#print(colDic)\\nfor i in rowDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\nfor i in colDic.values():\\n    for j in range(1,i+1):\\n        ans = ans * j\\n\\nans = ans % 998244353\\nprint(ans)\", \"def MI():\\n    return map(int, input().split())\\n\\nn,k= MI()\\nmod=998244353\\nframod=[1]\\ndef framod_calc(n, mod, a=1):\\n    for i in range(1,n+1):\\n        a=a * i % mod\\n        framod.append(a)\\nframod_calc(n+1, mod)\\ndef permmod(n, k, mod):\\n    if n<k: return 0\\n    a=framod[n]\\n    c=framod[n-k]\\n    return (a * pow(c, mod-2, mod)) % mod\\n\\nmat=[]\\nmatinv=[[0]*n for _ in range(n)]\\nfor i in range(n):\\n    mat.append(list(MI()))\\n\\nfor i in range(n):\\n    for j in range(n):\\n        matinv[i][j]=mat[j][i]\\n\\nesrow=[]\\nescol=[]\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if mat[i][p]+mat[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            esrow.append((i,j))\\n\\nfor i in range(n):\\n    for j in range(i+1, n):\\n        flg=True\\n        for p in range(n):\\n            if matinv[i][p]+matinv[j][p]>k:\\n                flg=False\\n                break\\n        if flg:\\n            escol.append((i,j))\\n\\nclass UnionFind(object): # size\\u3092O(1)\\u3067\\u5f15\\u3051\\u308bversion\\n    def __init__(self, n=1):\\n        self.n=n\\n        self.par = [i for i in range(n)]\\n        self.rank = [0 for _ in range(n)]\\n        self.sizebox = [1]*n\\n    def find(self, x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50\\u6210\\u5206\\u306e\\u4ee3\\u8868\\u5143\\n        if self.par[x] == x:\\n            return x\\n        else:\\n            self.par[x] = self.find(self.par[x])\\n            return self.par[x]\\n    def union(self, x, y): # x,y\\u3092\\u9023\\u7d50\\u3001\\u3064\\u3044\\u3067\\u306b\\u30b5\\u30a4\\u30ba\\u3082\\u9023\\u7d50\\n        x = self.find(x)\\n        y = self.find(y)\\n        if x != y:\\n            if self.rank[x] < self.rank[y]:\\n                x, y = y, x\\n            if self.rank[x] == self.rank[y]:\\n                self.rank[x] += 1\\n            self.par[y] = x\\n            self.sizebox[x]+=self.sizebox[y]\\n            self.sizebox[y]=0\\n    def same(self, x, y): # x,y\\u304c\\u9023\\u7d50\\u304b\\u3069\\u3046\\u304b\\n        return self.find(x) == self.find(y)\\n    def size(self,x): # x\\u306e\\u5c5e\\u3059\\u308b\\u9023\\u7d50size\\u3092O(1)\\u3067\\u51fa\\u3059\\n        x = self.find(x)\\n        return self.sizebox[x]\\n    def allfind(self): # find\\u30921\\u5468\\u3059\\u308b\\n        for i in range(self.n):\\n            self.find(i)\\n\\nufr=UnionFind(n)\\nufc=UnionFind(n)\\n\\nfor i,j in esrow:\\n    ufr.union(i,j)\\n\\nfor i,j in escol:\\n    ufc.union(i,j)\\n\\nfor i in range(n):\\n    ufr.find(i)\\n    ufc.find(i)\\n\\nfrom collections import Counter\\ncpar=Counter(ufc.par)\\nrpar=Counter(ufr.par)\\n\\nans=1\\n\\nfor k in cpar.keys():\\n    x=cpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nfor k in rpar.keys():\\n    x=rpar[k]\\n    ans*=permmod(x,x,mod)\\n    ans%=mod\\n\\nprint(ans%mod)\", \"MOD = 998244353\\nSIZE = 10 ** 6\\n\\ng1 = [1, 1]\\ng2 = [1, 1]\\nre = [0, 1]\\nfor i in range(2, SIZE + 1):\\n    g1.append((g1[-1] * i) % MOD)\\ndef fact(n):\\n    return g1[n]\\n\\n\\n# i-index\\nclass UnionFind:\\n    def __init__(self, n):\\n        self.root = [i for i in range(n + 1)]\\n        self.size = [1] * (n + 1)\\n        self.nn = n\\n    def find(self, x):\\n        y = self.root[x]\\n        if x == y:\\n            return x\\n        else:\\n            z = self.find(y)\\n            self.root[x] = z\\n            return z\\n    def union(self, x, y):\\n        rx = self.find(x)\\n        ry = self.find(y)\\n        sx = self.size[rx]\\n        sy = self.size[ry]\\n        if rx == ry:\\n            return 0\\n        else:\\n            if sx >= sy:\\n                self.root[ry] = rx\\n                self.size[rx] = sx + sy\\n            else:\\n                self.root[rx] = ry\\n                self.size[ry] = sx + sy\\n        return sx * sy\\n    def size_list(self, n):\\n        ret = []\\n        cnt = [0] * (n + 1)\\n        for i in range(1, n + 1):\\n            #print(i, self.find(i))\\n            if cnt[self.find(i)] == 0:\\n                cnt[self.find(i)] = 1\\n                ret.append(self.size[self.find(i)])\\n        return ret\\n    def check(self):\\n        print([self.find(i) for i in range(1, self.nn + 1)])\\n\\nN, K = map(int, input().split())\\nA = [list(map(int, input().split())) for _ in range(N)]\\n#print(A)\\n\\n\\ndef f(A):\\n    edge = []\\n    for i in range(N):\\n        ai = A[i]\\n        for j in range(i + 1, N):\\n            aj = A[j]\\n            flag = True\\n            for k in range(N):\\n                if ai[k] + aj[k] > K:\\n                    flag = False\\n                    break\\n            if flag:\\n                edge.append([i + 1, j + 1])\\n    #print(edge)\\n    \\n    for a, b in edge:\\n        uf.union(a, b)\\n    #print(\\\"check\\\")\\n    #uf.check()\\n    \\n    ret = 1\\n    sl = uf.size_list(N)\\n    #print(sl)\\n    for n in sl:\\n        ret = (ret * fact(n)) % MOD\\n    \\n    return ret\\n\\nuf = UnionFind(N)\\nanswer = f(A) % MOD\\n\\n# \\u8ee2\\u7f6e\\ntmp = [[] for _ in range(N)]\\nfor i in range(N):\\n    for j in range(N):\\n        tmp[j].append(A[i][j])\\nA = tmp\\n#print(A)\\n\\nuf = UnionFind(N)\\nanswer = (answer * f(A)) % MOD\\nprint(answer)\"]",
        "difficulty": "interview",
        "input": "8 34\n32 8 36 21 14 13 37 26\n28 22 60 51 48 62 16 25\n40 23 6 33 41 12 42 45\n35 11 4 1 56 59 44 7\n27 52 54 29 46 18 5 2\n63 50 53 55 30 64 61 34\n47 20 38 17 9 31 10 58\n39 43 15 49 24 57 3 19\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/arc107/tasks/arc107_c"
    },
    {
        "id": 214,
        "task_id": 1525,
        "test_case_id": 1,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "1 3 2\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 215,
        "task_id": 1525,
        "test_case_id": 2,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "1 3 1\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 216,
        "task_id": 1525,
        "test_case_id": 3,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "2 3 3\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 217,
        "task_id": 1525,
        "test_case_id": 4,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "2 3 1\n",
        "output": "5\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 218,
        "task_id": 1525,
        "test_case_id": 5,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "7 1 1\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 219,
        "task_id": 1525,
        "test_case_id": 6,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "15 8 5\n",
        "output": "437760187\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 220,
        "task_id": 1525,
        "test_case_id": 7,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "100 8 8\n",
        "output": "467571711\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 221,
        "task_id": 1525,
        "test_case_id": 8,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "100 8 3\n",
        "output": "938282570\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 222,
        "task_id": 1525,
        "test_case_id": 9,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "100 8 1\n",
        "output": "755868507\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 223,
        "task_id": 1525,
        "test_case_id": 10,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "77 7 7\n",
        "output": "237739357\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 224,
        "task_id": 1525,
        "test_case_id": 11,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "98 7 6\n",
        "output": "736412603\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 225,
        "task_id": 1525,
        "test_case_id": 12,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "57 5 1\n",
        "output": "151419294\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 226,
        "task_id": 1525,
        "test_case_id": 13,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "33 4 2\n",
        "output": "938946695\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 227,
        "task_id": 1525,
        "test_case_id": 14,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "86 7 4\n",
        "output": "505044568\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 228,
        "task_id": 1525,
        "test_case_id": 15,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "91 4 3\n",
        "output": "908754076\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 229,
        "task_id": 1525,
        "test_case_id": 16,
        "question": "Amidakuji is a traditional method of lottery in Japan.\nTo make an amidakuji, we first draw W parallel vertical lines, and then draw horizontal lines that connect them. The length of each vertical line is H+1 [cm], and the endpoints of the horizontal lines must be at 1, 2, 3, ..., or H [cm] from the top of a vertical line.\nA valid amidakuji is an amidakuji that satisfies the following conditions:\n - No two horizontal lines share an endpoint.\n - The two endpoints of each horizontal lines must be at the same height.\n - A horizontal line must connect adjacent vertical lines.\n\nFind the number of the valid amidakuji that satisfy the following condition, modulo 1\\ 000\\ 000\\ 007: if we trace the path from the top of the leftmost vertical line to the bottom, always following horizontal lines when we encounter them, we reach the bottom of the K-th vertical line from the left.\nFor example, in the following amidakuji, we will reach the bottom of the fourth vertical line from the left.\n\n-----Constraints-----\n - H is an integer between 1 and 100 (inclusive).\n - W is an integer between 1 and 8 (inclusive).\n - K is an integer between 1 and W (inclusive).\n\n-----Input-----\nInput is given from Standard Input in the following format:\nH W K\n\n-----Output-----\nPrint the number of the amidakuji that satisfy the condition, modulo 1\\ 000\\ 000\\ 007.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\n1\n\nOnly the following one amidakuji satisfies the condition:",
        "solutions": "[\"def check(amidakuji,w):\\n    before=0\\n    flag=True\\n    for _ in range(w-1):\\n        if amidakuji&1==1 and before==1:\\n            flag=False\\n            break\\n        elif amidakuji&1==1:\\n            before=1\\n            amidakuji>>=1\\n        else:\\n            before=0\\n            amidakuji>>=1\\n    return flag\\n\\nfrom sys import stdin\\ndef main():\\n    #\\u5165\\u529b\\n    readline=stdin.readline\\n    mod=10**9+7\\n    h,w,k=map(int,readline().split())\\n\\n    dp=[[0]*w for _ in range(h+1)]\\n    dp[0][0]=1\\n    for i in range(1,h+1):\\n        for bit in range(1<<(w-1)):\\n            if check(bit,w)==False:\\n                continue\\n            else:\\n                for j in range(w):\\n                    if j==0:\\n                        if bit&1==1:\\n                            dp[i][j+1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    elif j==w-1:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                        else:\\n                            dp[i][j]+=dp[i-1][j]\\n                    else:\\n                        if bit&1==1:\\n                            dp[i][j-1]+=dp[i-1][j]\\n                            bit>>=1\\n                        else:\\n                            bit>>=1\\n                            if bit&1==1:\\n                                dp[i][j+1]+=dp[i-1][j]\\n                            else:\\n                                dp[i][j]+=dp[i-1][j]\\n\\n                for j in range(w):\\n                    dp[i][j]%=mod\\n\\n    print(dp[h][k-1])\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\nmod = 10**9+7\\n\\nif w == 1:\\n    print((1))\\n    return\\n\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(1, h+1):\\n    for p in range(2**(w-1)):\\n        L = [0]*(w-1)\\n        for q in range(w-1):\\n            if (p >> q) & 1:\\n                L[q] = 1\\n        flag = True\\n        for q in range(w-2):\\n            if L[q] == 1 and L[q+1] == 1:\\n                flag = False\\n        if not flag:\\n            continue\\n        for j in range(w):\\n            if j == 0:\\n                if L[j] == 1:\\n                    dp[i][j] += dp[i-1][1]\\n                else:\\n                    dp[i][j] += dp[i-1][0]\\n            elif j == w-1:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][w-2]\\n                else:\\n                    dp[i][j] += dp[i-1][w-1]\\n            else:\\n                if L[j-1] == 1:\\n                    dp[i][j] += dp[i-1][j-1]\\n                elif L[j] == 1:\\n                    dp[i][j] += dp[i-1][j+1]\\n                else:\\n                    dp[i][j] += dp[i-1][j]\\n            dp[i][j] %= mod\\n\\n#print(dp)\\nprint((dp[h][k-1]))\\n\", \"h,w,k_=list(map(int,input().split()))\\nmod=pow(10,9)+7\\nif w==1:\\n  print((1))\\n  return\\n# \\u9077\\u79fb\\u306e\\u4ed5\\u65b9\\nsen=[[0]*3 for _ in range(w)]\\nfor j in range(2**(w-1)):\\n  yoko=[0]*(w-1)\\n  for k in range(w-1):\\n    if (j>>k) & 1:\\n      yoko[k]=1\\n  flg=True\\n  for k in range(w-2):\\n    if yoko[k]==1 and yoko[k+1]==1:\\n      flg=False\\n      break\\n  if not flg:continue\\n  for k in range(w):\\n    if k==0:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      else:\\n        sen[k][2]+=1\\n    elif k<w-1:\\n      if yoko[k]==1:\\n        sen[k+1][0]+=1\\n      elif yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n    else:\\n      if yoko[k-1]==1:\\n        sen[k-1][1]+=1\\n      else:\\n        sen[k][2]+=1\\n\\nimport numpy as np \\ndp=np.zeros((h+1,w),int)\\ndp[0,0]=1\\nfor i in range(h):\\n  dp[i+1,0]=sen[0][2]*dp[i,0]+sen[0][1]*dp[i,1]\\n  for j in range(1,w-1):\\n    dp[i+1,j]=sen[j][2]*dp[i,j]+sen[j][1]*dp[i,j+1]+sen[j][0]*dp[i,j-1]\\n  dp[i+1,w-1]=sen[w-1][2]*dp[i,w-1]+sen[w-1][0]*dp[i,w-2]\\n  dp[i+1]%=mod\\nprint((dp[h,k_-1]))\\n#print(dp)\\n\", \"import sys\\ninput = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\n\\ndef main():\\n    H, W, K = map(int, input().split())\\n    dp = [[0] * W for _ in range(H + 1)]  # \\u6570\\u3048\\u4e0a\\u3052\\u554f\\u984c\\u306a\\u306e\\u30670\\u3067\\u521d\\u671f\\u5316\\u3059\\u308b\\n    dp[0][0] = 1  # \\u521d\\u671f\\u6761\\u4ef6\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):  # \\u5de6\\u30d3\\u30c3\\u30c8\\u30b7\\u30d5\\u30c8\\u30672 ** (W-1)\\u3068\\u540c\\u3058\\n            if '11' in bin(bit): continue  # \\u3042\\u308b\\u9802\\u70b9\\u304b\\u3089\\u5de6\\u53f3\\u65b9\\u5411\\u306b\\u68d2\\u304c\\u4f38\\u3073\\u3066\\u3044\\u308b\\u30b1\\u30fc\\u30b9\\u306f\\u30b9\\u30eb\\u30fc\\n            for w in range(W):\\n                # w\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8003\\u3048\\u308b\\n                if w and bit & (1 << (w - 1)):  # left\\u3092\\u898b\\u308b\\u306e\\u30671<<w-1\\u3068\\u78ba\\u8a8d, w=0\\u306e\\u6642\\u306fleft\\u306b\\u3044\\u3051\\u306a\\u3044\\u3053\\u3068\\u306b\\u6ce8\\u610f\\u3059\\u308b\\n                    dp[h + 1][w - 1] += dp[h][w] % MOD\\n                elif bit & (1 << w):  # right\\u3092\\u898b\\u308b\\u306e\\u30671<<w\\u78ba\\u8a8d\\n                    dp[h + 1][w + 1] += dp[h][w] % MOD\\n                else:  # down, \\u5de6\\u53f3\\u3069\\u3061\\u3089\\u306b\\u3082\\u3044\\u304b\\u306a\\u3044\\u6642\\n                    dp[h + 1][w] += dp[h][w] % MOD\\n    # for i in dp:\\n    #     print(*i)\\n    print(dp[H][K - 1] % MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n# \\n# \\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n\\n                def cnt_tmp(n, r, l, flg):\\n                    re = 0\\n                    if n >= W - 2:\\n                        if r <= n <= l:\\n                            return 1\\n                        if flg:\\n                            return 1\\n                        else:\\n                            return 2\\n                    if r <= n <= l:\\n                        return cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, False)\\n                    re += cnt_tmp(n + 1, r, l, True) if not flg else 0\\n                    return re\\n\\n                tmp = cnt_tmp(0, min(w, new_w) - 1, max(w, new_w), False)\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    # for dpi in dp:\\n    #     print(dpi)\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"import sys\\nmod = 7 + 10 ** 9\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    DP = [[0] * W for _ in range(H + 1)]\\n    pattern = [1, 2, 3, 5, 8, 13, 21]\\n    DP[0][0] = 1\\n    for h in range(H):\\n        for w in range(W):\\n            if w == 0:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w+1] * pattern[max(0, W - 3)]) % mod\\n            elif w == W - 1:\\n                DP[h+1][w] += (DP[h][w] * pattern[max(0, W - 2)]) % mod\\n                if W > 1: DP[h+1][w] += (DP[h][w-1] * pattern[max(0, W - 3)]) % mod\\n            else:\\n                DP[h+1][w] += (DP[h][w]  * pattern[max(0, w - 1)] * pattern[max(0, W - w - 2)]) % mod\\n                DP[h+1][w] += (DP[h][w+1] * pattern[max(0, w - 1)] * pattern[max(0, W - w - 3)]) % mod\\n                DP[h+1][w] += (DP[h][w-1] * pattern[max(0, w - 2)] * pattern[max(0, W - w - 2)]) % mod\\n            DP[h+1][w] %= mod\\n    print(DP[H][K - 1])\\n\\n    return 0\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# coding: utf-8\\n\\n# https://atcoder.jp/contests/abc113\\n# 12:01-12:49 give up -> kaisetsu\\n# 11:57-12:25 try again\\n\\n# from pprint import pprint as ppr\\n\\n\\n# def main():\\n#     H, W, K = map(int, input().split())\\n\\n#     v = \\\"v\\\"\\n#     h = \\\"h\\\"\\n#     dp = [[{\\\"v\\\": 0, \\\"h\\\": 0} for _ in range(W)] for _ in range(H)]\\n#     dp[0][0][v] = 1\\n\\n#     for i in range(H):\\n\\n#         for j in range(W):\\n#             # horizontal computation\\n#             if j == 0:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#             elif j == W-1:\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n#             else:\\n#                 dp[i][j+1][h] += dp[i][j][v]\\n#                 dp[i][j-1][h] += dp[i][j][v]\\n\\n#         if i < H-1:\\n#             for j in range(W):\\n#                 # vertical computation\\n#                 dp[i+1][j][v] += dp[i][j][v] + dp[i][j][h]\\n    \\n#     ppr(dp)\\n\\n#     return dp[H-1][K-1][v] + dp[H-1][K-1][h]\\n\\n\\ndef main():\\n    H, W, K = list(map(int, input().split()))\\n\\n    if W == 1:\\n        return 1\\n\\n    dp = [[0]*W for _ in range(H)]\\n    dp[0][0] = 1\\n\\n    bridges_list = []\\n\\n    def preset(i, bridges, n_cand):\\n        if i == n_cand:\\n            bridges_list.append(bridges)\\n            return None\\n\\n        if i-1 in bridges:\\n            preset(i+1, bridges, n_cand)\\n        else:\\n            bridges_1 = bridges[:]\\n            bridges_2 = bridges[:]\\n            bridges_1.append(i)\\n\\n            preset(i+1, bridges_1, n_cand)\\n            preset(i+1, bridges_2, n_cand)\\n\\n    preset(0, [], W-1)\\n\\n    n_bridges = [0] * (W-1)\\n    for bridges in bridges_list:\\n        for x in bridges:\\n            n_bridges[x] += 1\\n\\n    n_all_cands = len(bridges_list)\\n\\n    # ppr(bridges_list)\\n    # ppr(n_bridges)\\n\\n    dp[0][0] = (n_all_cands-n_bridges[0])\\n    dp[0][1] = n_bridges[0]\\n\\n    for i in range(H-1):\\n        for j in range(W):\\n            if j == 0:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j])\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n            elif j == W-1:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n            else:\\n                dp[i+1][j] += dp[i][j] * (n_all_cands-n_bridges[j-1]-n_bridges[j])\\n                dp[i+1][j-1] += dp[i][j] * n_bridges[j-1]\\n                dp[i+1][j+1] += dp[i][j] * n_bridges[j]\\n    # ppr(dp)\\n\\n    return dp[-1][K-1] % (10**9 + 7)\\n\\n\\nprint((main()))\\n\", \"import sys\\nimport math\\nfrom collections import deque\\n\\nsys.setrecursionlimit(1000000)\\nMOD = 10 ** 9 + 7\\ninput = lambda: sys.stdin.readline().strip()\\nNI = lambda: int(input())\\nNMI = lambda: map(int, input().split())\\nNLI = lambda: list(NMI())\\nSI = lambda: input()\\n\\n\\ndef make_grid(h, w, num): return [[int(num)] * w for _ in range(h)]\\n\\n\\ndef main():\\n    H, W, K = NMI()\\n    dp = make_grid(H+1, W, 0)\\n    move = make_grid(W, W, 0)\\n\\n    dp[0][0] = 1\\n\\n    for case in range(2**(W-1)):\\n        bad_case = False\\n        prev_bit = -1\\n        for i in range(W-1):\\n            now_bit = (case >> i) & 1\\n            if now_bit == prev_bit == 1:\\n                bad_case = True\\n            prev_bit = now_bit\\n        if bad_case:\\n            continue\\n\\n        for b in range(W):\\n\\n            if b == 0:\\n                if (case >> 0) & 1:\\n                    move[0][1] += 1\\n                else:\\n                    move[0][0] += 1\\n\\n            elif b == W - 1:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n            else:\\n                if (case >> b - 1) & 1:\\n                    move[b][b - 1] += 1\\n                elif (case >> b) & 1:\\n                    move[b][b + 1] += 1\\n                else:\\n                    move[b][b] += 1\\n\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            for i in range(W):\\n                dp[h][w] += dp[h-1][i] * move[i][w]\\n\\n    print(dp[H][K-1]%MOD)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nmod = 1000000007\\n\\nf = [0]*(W+1)\\nf[0] = 1\\nf[1] = 2\\nfor i in range(2,W+1):\\n    f[i] = f[i-1] + f[i-2]\\n\\ndp = [[0]*(W+2) for _ in range(H+1)]\\ndp[0][K] = 1\\nfor i in range(1,H+1):\\n    for j in range(1,W+1):\\n        dp[i][j] += (dp[i-1][j] * f[max(0,j-2)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j-1] * f[max(0,j-3)] * f[max(0,W-j-1)]\\n                     + dp[i-1][j+1] * f[max(0,j-2)] * f[max(0,W-j-2)] )\\n        dp[i][j] %= mod\\nprint(dp[-1][1])\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * (w + 1) for _ in range(h + 1)]\\nfor i in range(w + 1):\\n    dp[0][i] = 1 if i == 1 else 0\\n\\n\\ndef check_valid_bridge(bridge):\\n    for i in range(1, w-1):\\n        if bridge[i-1] and bridge[i]:\\n            return False\\n    return True\\n\\nfor t in range(1, h + 1):\\n    for i in range(1, w + 1):\\n        X, Y, Z = 0, 0, 0\\n        if w != 1:\\n            p = product([True, False], repeat=w-1)            \\n            for bridge in p:\\n                if check_valid_bridge(bridge):\\n                    if i > 1 and bridge[i-2]:\\n                        X += 1\\n                    elif i < w and bridge[i-1]:\\n                        Y += 1\\n                    elif (i == 1 and not bridge[i-1]) or (i == w and not bridge[i-2]) or (1 < i < w and not bridge[i-2] and not bridge[i-1]):\\n                        Z += 1\\n        else:\\n            Z = 1\\n        # print(f\\\"{X} {Y} {Z}\\\")\\n        pattern_1 = dp[t-1][i-1] * X if i > 1 else 0\\n        pattern_2 = dp[t-1][i+1] * Y if i < w else 0\\n        pattern_3 = dp[t-1][i] * Z\\n        dp[t][i] = (pattern_1 + pattern_2 + pattern_3) % mod\\n\\n# for line in dp:\\n#     print(*line)\\nprint((dp[h][k]))\\n\", \"# D - Number of Amidakuji\\n\\nH, W, K = list(map(int, input().split()))\\nMOD = 10**9 + 7\\n\\ncomb = []\\ndef dfs(n, p):\\n    if len(n) == (W-1):\\n        if len(n) == 0:\\n            n = [0]\\n        comb.append(tuple(n))\\n        return\\n    for i in (0, 1):\\n        if p == 1 and i == 1:\\n            continue\\n        n.append(i)\\n        dfs(n, i)\\n        n.pop()  \\n\\ndfs([], 0)\\n\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        # \\u307e\\u3063\\u3059\\u3050\\u964d\\u308a\\u3066\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        tmp = 0\\n        for i in comb:\\n            if w == 0 and i[w] == 0:\\n                tmp += 1\\n            elif w == (W-1) and i[w-1] == 0:\\n                tmp += 1\\n            elif i[w-1] == 0 and i[w] == 0:\\n                tmp += 1\\n        dp[h+1][w] += dp[h][w] * tmp\\n\\n        # \\u5de6\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != 0:\\n            tmp = 0\\n            for i in comb:\\n                if i[w-1] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w-1] * tmp        \\n\\n        # \\u53f3\\u304b\\u3089\\u304f\\u308b\\u30b1\\u30fc\\u30b9\\n        if w != (W-1):\\n            tmp = 0\\n            for i in comb:\\n                if i[w] == 1:\\n                    tmp += 1\\n            dp[h+1][w] += dp[h][w+1] * tmp  \\n\\nprint((dp[H][K-1]%MOD))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # \\u8fd1\\u63a5\\u3059\\u308b2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u308b\\u304b\\u5224\\u5b9a\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef resolve():\\n    H, W, K = list(map(int, input().split()))\\n    K -= 1\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for bit in range(1 << (W - 1)):\\n                flg = True\\n                for mask in range(W - 2):\\n                    if (bit & (1 << mask)) and (bit & (1 << (mask + 1))):\\n                        flg = False\\n                if flg:\\n                    next_j = j\\n                    if bit & (1 << j):\\n                        next_j = j + 1\\n                    elif j > 0 and (bit & (1 << (j - 1))):\\n                        next_j = j - 1\\n                    dp[i + 1][next_j] = (dp[i + 1][next_j] + dp[i][j]) % mod\\n    print((dp[H][K]))\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\n# h, w, k = 15, 8, 5\\n# h, w, k = 2, 3, 1\\n# h, w, k = 2, 3, 3\\n# h, w, k = 1, 3, 2\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\n# \\u6700\\u7d42\\u7684\\u306bDP[h][k-1]\\u3092\\u6c42\\u3081\\u308b\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j+1]*F[j]*F[w-2-j]\\n        c = DP[i][j]*F[j]*F[w-1-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"h,w,k = list(map(int,input().split()))\\nk -= 1\\ndp = [[0]*w for _ in range(h+1)]\\ndp[0][0] = 1\\nmod = 10**9 + 7\\ndef cnt(n):\\n    if n < 0:\\n        return 1\\n    if 0 <= n < 3:\\n        return n + 1\\n    return n + (n-1)*(n-2)//2 + (n-2)*(n-3)*(n-4)//6 + 1\\n\\nfor i in range(h):\\n    for j in range(w):\\n        if j > 0:\\n            dp[i+1][j-1] += dp[i][j] * cnt(j-2) * cnt(w-2-j)\\n            dp[i+1][j-1] %= mod\\n        if j < w-1:\\n            dp[i+1][j+1] += dp[i][j] * cnt(j-1) * cnt(w-3-j)\\n            dp[i+1][j+1] %= mod\\n        dp[i+1][j] += dp[i][j] * cnt(j-1) * cnt(w-2-j)\\n        dp[i+1][j] %= mod\\nprint((dp[h][k]))\\n\", \"def main():\\n    MOD = 10 ** 9 + 7\\n\\n    H, W, K = list(map(int, input().split()))\\n\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    # \\u6a2a\\u7dda[0,H)\\n    # H->\\u7d42\\u7740\\u70b9\\n\\n    for h in range(H):\\n        for bit in range(1 << (W - 1)):\\n            if '11' in bin(bit): continue\\n            toes = list(range(W))\\n            for j in range(W - 1):\\n                if (bit >> j) & 1:\\n                    toes[j], toes[j + 1] = toes[j + 1], toes[j]\\n            for frm, to in enumerate(toes):\\n                dp[h + 1][to] = (dp[h + 1][to] + dp[h][frm]) % MOD\\n    ans = dp[H][K - 1]\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n# import sys\\n# input = sys.stdin.readline\\n# \\n# sys.setrecursionlimit(10 ** 7)\\n# \\n# (int(x)-1 for x in input().split())\\n# rstrip()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in range(1 << w - 1):\\n        ok = True\\n        for j in range(w - 2):\\n            if bit >> j & 1 and bit >> j + 1 & 1:\\n                ok = False\\n        if ok:\\n            moved = [False] * w\\n            for j in range(w):\\n                if bit >> j & 1:\\n                    next[j + 1] += dp[j]\\n                    next[j] += dp[j + 1]\\n                    moved[j] = moved[j + 1] = True\\n                elif not moved[j]:\\n                    next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h,w,K = map(int,input().split())\\nif w == 1:\\n    print(1)\\n    return\\nK -= 1\\nmod = 1000000007\\ndp = [[0]*(w) for _ in range(h+1)]\\nfor i in range(w): dp[0][0] = 1\\n\\nfor i in range(h):\\n    for j in range(1<<(w-1)):\\n        invalid = False\\n        for k in range(w-1):\\n            if j>>k & 1 and j>>(k+1) & 1:\\n                invalid = True\\n                break\\n        if invalid: continue\\n        used = [False]*w\\n        for k in range(w):\\n            if used[k]: continue\\n            if j>>k & 1:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k+1])%mod\\n                dp[i+1][k+1] = (dp[i+1][k+1]+dp[i][k])%mod\\n                used[k] = True\\n                used[k+1] = True\\n            else:\\n                dp[i+1][k] = (dp[i+1][k]+dp[i][k])%mod\\n                used[k] = True\\n# for i in range(h+1): print(dp[i])\\nprint(dp[h][K])\", \"H,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\nif W==1:\\n  print(1)\\n  return\\n  \\nimport itertools\\nA=list(itertools.product([0,1], repeat=W-1))\\n\\nB=[]\\nfor i in A:\\n  x=0\\n  for j in range(W-2):\\n    if i[j]==1 and i[j+1]==1:\\n      x=1\\n  if x==0:\\n    B.append(i)\\n\\nD=[[0,0,0] for i in range(W)]\\nfor i in B:\\n  for j in range(W-1):\\n    if i[j]==1:\\n      D[j+1][0]+=1\\n      D[j][2]+=1\\n    if j==0 and i[j]==0:\\n      D[j][1]+=1\\n    if j==W-2 and i[j]==0:\\n      D[j+1][1]+=1\\n    if j<W-2:\\n      if i[j]==0 and i[j+1]==0:      \\n        D[j+1][1]+=1\\ndp=[[0]*W for i in range(H+1)]\\nmod=10**9+7\\ndp[0][0]=1\\nfor i in range(H):\\n  for j in range(W):\\n    if j==0:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j+1]*D[j][2]\\n    elif j==W-1:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]\\n    else:\\n      dp[i+1][j]=dp[i][j]*D[j][1]+dp[i][j-1]*D[j][0]+dp[i][j+1]*D[j][2]\\n    dp[i+1][j]%=mod\\nprint(dp[-1][K-1])\", \"import sys\\nimport math\\nimport collections\\nimport bisect\\nimport copy\\n\\n# import numpy as np\\n\\nsys.setrecursionlimit(10 ** 7)\\nINF = 10 ** 16\\nMOD = 10 ** 9 + 7\\n# MOD = 998244353\\n\\nni = lambda: int(sys.stdin.readline())\\nns = lambda: list(map(int, sys.stdin.readline().split()))\\nna = lambda: list(map(int, sys.stdin.readline().split()))\\nna1 = lambda: list([int(x) - 1 for x in sys.stdin.readline().split()])\\n\\n\\n# ===CODE===\\n\\n\\ndef main():\\n    h, w, k = ns()\\n    dp = [[0 for _ in range(w)] for __ in range(h + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2]\\n    for i in range(10):\\n        fibo.append(fibo[-1] + fibo[-2])\\n\\n    for y in range(1, h + 1):\\n        for x in range(w):\\n            if x == 0:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from R\\n                    dp[y][x] += dp[y - 1][x + 1] * fibo[max(0, w - 1 - 2)]\\n            elif x == w - 1:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[max(0, w - 1 - 1)]\\n                if w > 1:\\n                    # from L\\n                    dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, w - 1 - 2)]\\n            else:\\n                # from U\\n                dp[y][x] += dp[y - 1][x] * fibo[x - 1] * fibo[max(0, w - 1 - x - 1)]\\n                # from L\\n                dp[y][x] += dp[y - 1][x - 1] * fibo[max(0, x - 1 - 1)] * fibo[max(0, w - 1 - x - 1)]\\n                # from R\\n                dp[y][x] += dp[y - 1][x + 1] * fibo[x - 1] * fibo[max(0, w - 1 - x - 2)]\\n            dp[y][x] %= MOD\\n\\n    print((dp[h][k - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"#import sys\\n#import numpy as np\\nimport math\\n#from fractions import Fraction\\nimport itertools\\nfrom collections import deque\\nfrom collections import Counter\\n#import heapq\\n#from fractions  import gcd\\n#input=sys.stdin.readline\\n#import bisect\\nMod=10**9+7\\nh,w,K=list(map(int,input().split()))\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nn=2**(w-1)\\nfor i in range(h):\\n    for j in range(w):\\n        for m in range(n):\\n            ok=True\\n            for k in range(w-2):\\n                if (m&(1<<k)) and (m&(1<<(k+1))):\\n                    ok=False\\n            if not ok:\\n                continue\\n            nj=j\\n            if (m & (1<<j)):\\n                nj=j+1\\n            elif j>0 and (m&(1<<(j-1))):\\n                nj=j-1\\n            dp[i+1][nj]+=dp[i][j]\\n            dp[i+1][nj]%=Mod\\nprint((dp[h][K-1]))\\n\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*3))\\n    o(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\n\\ngoal = [0 for i in range(W)]\\ngoal[0] = 1\\noldGoal = [0 for i in range(W)]\\noldGoal[0] = 1\\nfib = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\nfor i in range(H):\\n    for j in range(W):\\n        if j == 0:\\n            a1 = oldGoal[j] * fib[W-1]\\n            a2 = oldGoal[j+1] * fib[W-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        elif j == W - 1:\\n            a1 = oldGoal[j-1] * fib[W-2]\\n            a2 = oldGoal[j] * fib[W-1]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            goal[j] = a1 + a2\\n        else:\\n            a1 = oldGoal[j-1] * fib[j-1] * fib[W-j-1]\\n            a2 = oldGoal[j] * fib[j] * fib[W-j-1]\\n            a3 = oldGoal[j+1] * fib[j] * fib[W-j-2]\\n            a1 = a1 % 1000000007\\n            a2 = a2 % 1000000007\\n            a3 = a3 % 1000000007\\n            goal[j] = a1 + a2 + a3\\n    for k in range(W):\\n        oldGoal[k] = goal[k]\\nprint(goal[K-1] % 1000000007)\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    bf = [0] * (w + 2)\\n    nx = [0] * (w + 2)\\n    bf[1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            nx[j] = c[j - 1] * c[w - j] * bf[j] + c[j - 1] * c[w - j - 1] * bf[j + 1] + c[j - 2] * c[w - j] * bf[j - 1]\\n\\n        bf = nx\\n        nx = [0] * (w + 2)\\n\\n    print((bf[k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for mask in range(1 << (W - 1)):\\n            ok = True\\n            for i in range(W - 2):\\n                if mask & (1 << i) and mask & (1 << (i + 1)):\\n                    ok = False\\n                    break\\n            if not ok:\\n                continue\\n            for i in range(W):\\n                if i > 0 and mask & (1 << (i - 1)):\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and mask & (1 << i):\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,k = map(int,input().split())\\nmod = 10**9+7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\ndp = [[0]*w for i in range(h+1)]\\ndp[0][0] = 1\\n\\nl = [[0]*3 for i in range(w)]\\n\\nfor i in range(2**(w-1)):\\n    if \\\"11\\\" in bin(i):\\n        continue\\n\\n    for j in range(w-1):\\n        if (i >> j) & 1:        \\n            l[j][2] += 1\\n            l[j+1][0] += 1\\n\\nfib = [1,1]\\nfor i in range(10):\\n    fib.append(fib[-1]+fib[-2])\\nfor i in l:\\n    i[1] = fib[w] - sum(i)\\n\\nfor i in range(h):\\n    for j in range(w):\\n        dp[i+1][j] += dp[i][j]*l[j][1]%mod\\n        if j != 0:\\n            dp[i+1][j] += dp[i][j-1]*l[j][0]%mod\\n        if j != w-1:\\n            dp[i+1][j] += dp[i][j+1]*l[j][2]%mod\\n        dp[i+1][j] %= mod\\n\\nprint(dp[-1][k-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\nMOD = 10 ** 9 + 7\\n\\ndef main():\\n    H, W, K = map(int, readline().rstrip().split())\\n    # K -= 1\\n    dp = [[0] * W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for i in range(H):\\n        for j in range(W):\\n            for k in range(2**(W-1)):\\n                b = bin(k)[2:].zfill(W-1)\\n                # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n                flg = True\\n                for l in range(W-2):\\n                    if b[l] == b[l+1] == '1':\\n                        flg = False\\n                        break\\n                if not flg:\\n                    continue\\n                if j >= 1 and b[j-1] == '1':\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j <= W-2 and b[j] == '1':\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u8fbf\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u8fbf\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n\\n    print(dp[H][K-1])\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    H, W, K = [int(x) for x in input().split()]\\n    MOD = 10 ** 9 + 7\\n\\n    if W == 1:\\n        print((1))\\n        return\\n\\n    cnt = [0] * (W - 1)\\n    cntz = [0] * W\\n    for i in range(2 ** (W - 1)):\\n        tmp = [0] * (W - 1)\\n        for j in range(W - 1):\\n            if i >> j & 1:\\n                tmp[j] += 1\\n        # 2\\u8fba\\u9023\\u7d9a\\u3067\\u5f15\\u304b\\u308c\\u3066\\u3044\\u306a\\u3044\\u304b\\u3092\\u30c1\\u30a7\\u30c3\\u30af\\n        for j, k in zip(tmp, tmp[1:]):\\n            if j == k == 1:\\n                break\\n        else:\\n            # \\u30c1\\u30a7\\u30c3\\u30af\\u3092\\u30d1\\u30b9\\u3057\\u305f\\u72b6\\u614b\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n            for j in range(W - 1):\\n                cnt[j] += tmp[j]\\n            for j in range(W):\\n                if j == 0:\\n                    if tmp[j] == 0:\\n                        cntz[j] += 1\\n                elif j == W - 1:\\n                    if tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n                else:\\n                    if tmp[j] == tmp[j - 1] == 0:\\n                        cntz[j] += 1\\n\\n    dp = [[0] * W for j in range(H + 1)]\\n    dp[0][0] = 1\\n\\n    for j in range(H):\\n        for i in range(W):\\n            if i == 0:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n            elif i == W - 1:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n            else:\\n                dp[j + 1][i] += dp[j][i] * cntz[i]\\n                dp[j + 1][i + 1] += dp[j][i] * cnt[i]\\n                dp[j + 1][i - 1] += dp[j][i] * cnt[i - 1]\\n                dp[j + 1][i] %= MOD\\n                dp[j + 1][i + 1] %= MOD\\n                dp[j + 1][i - 1] %= MOD\\n\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def fib(n):\\n    a = 1\\n    b = 0\\n    i = 0\\n    while i < n:\\n        i += 1\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n    mod = 10 ** 9 + 7\\n    \\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    c = [i for i in fib(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            x = c[j - 1] * c[w - j]\\n            y = c[j - 1] * c[w - j - 1]\\n            z = c[j - 2] * c[w - j]\\n\\n            dp[i][j] = (x * dp[i - 1][j] + y * dp[i - 1][j + 1] + z * dp[i - 1][j - 1]) % mod\\n\\n    print((dp[h][k]))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(1, h + 1):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j-1]\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j+1]\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i][j] += dp[i-1][j]\\n\\n\\t\\t\\tdp[i][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    #from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby\\n    #from itertools import product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil\\n    #from operator import itemgetter\\n\\n    #inf = 10**17\\n    mod = 10**9 + 7\\n\\n    h,w,k = map(int, input().split())\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    pattern = []\\n    if w > 2:\\n        for i in range(1<<(w-1)):\\n            for j in range(w-2):\\n                if ((i>>j) & 1) and ((i>>(j+1)) & 1):\\n                    break\\n            else:\\n                pattern.append(i)\\n    else:\\n        print(1)\\n        return\\n    \\n    for i in range(h):\\n        for j in range(w):\\n            for p in pattern:\\n                if j == 0:\\n                    if p & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                elif j == w-1:\\n                    if (p>>(w-2)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n                else:\\n                    if (p>>(j-1)) & 1:\\n                        dp[i+1][j-1] += dp[i][j] % mod\\n                    elif (p>>j) & 1:\\n                        dp[i+1][j+1] += dp[i][j] % mod\\n                    else:\\n                        dp[i+1][j] += dp[i][j] % mod\\n    print(dp[-1][k-1] % mod)\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10 ** 9 + 7\\nh, w, k = list(map(int, input().split()))\\ndp = [0] * w\\ndp[0] = 1\\n\\nfdp = [[0, 0] for _ in range(w)]\\nfdp[0][0] = 1\\nfor i in range(w - 1):\\n    fdp[i+1][0] += fdp[i][0]\\n    fdp[i+1][1] += fdp[i][0]\\n    fdp[i+1][0] += fdp[i][1]\\n\\ndef f(i):\\n    if i < 0:\\n        return 1\\n    return fdp[i][0] + fdp[i][1]\\n\\nfor _ in range(h):\\n    ndp = [0] * w\\n    for i in range(w):\\n        ndp[i] = (ndp[i] + dp[i] * f(i - 1) * f(w - i - 2))  % MOD\\n        if i + 1 < w:\\n            ndp[i+1] = (ndp[i+1] + dp[i] * f(i - 1) * f(w - i - 3)) % MOD\\n        if i - 1 >= 0:\\n            ndp[i-1] = (ndp[i-1] + dp[i] * f(i - 2) * f(w - i - 2)) % MOD\\n    dp = ndp\\nprint((dp[k-1]))\\n\", \"MOD=10**9+7\\nH,W,K=map(int,input().split())\\ndp=[[0]*W for i in range(H+1)]\\ndp[0][0]=1\\n\\nfor i in range(1,H+1):\\n    for k in range(W):\\n        l,c,r=0,0,0\\n        for bit in range(2**(W-1)):\\n            ok=True\\n            for t in range(W-2):\\n                if (bit>>t&1) and (bit>>(t+1)&1):\\n                    ok=False\\n                    break\\n            if not ok:\\n                continue\\n            if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-1 and not(bit>>k&1))or k==W-1):\\n                c+=1\\n            if (k>0):\\n                if ((k>1 and not(bit>>(k-2)&1)) or k==1) and ((k<W-1 and not(bit>>k&1))or k==W-1) and (bit>>(k-1)&1):\\n                    l+=1\\n            if (k<W-1):\\n                if ((k>0 and not(bit>>(k-1)&1)) or k==0) and ((k<W-2 and not (bit>>(k+1)&1))or k==W-2) and (bit>>k&1):\\n                    r+=1\\n        dp[i][k]=(dp[i][k]+dp[i-1][k]*c)%MOD\\n        if k>0:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k-1]*l)%MOD\\n        if k<W-1:\\n            dp[i][k]=(dp[i][k]+dp[i-1][k+1]*r)%MOD\\nprint(dp[H][K-1])\", \"MOD = 10 ** 9 + 7\\nh, w, k = [int(x) for x in input().split()]\\ndp = [[0] * w for _ in range(h+1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for b in range(1 << (w-1)):\\n        ok = True\\n        for s in range(w-2):\\n            if b >> s & 1 and b >> (s+1) & 1:\\n                ok = False\\n        if ok:            \\n            for j in range(w):\\n                if j > 0 and b >> (j-1) & 1:\\n                    dp[i+1][j-1] = (dp[i+1][j-1] + dp[i][j]) % MOD\\n                elif j+1 < w and b >> j & 1:\\n                    dp[i+1][j+1] = (dp[i+1][j+1] + dp[i][j]) % MOD\\n                else:\\n                    dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD\\n\\nprint(dp[h][k-1])\", \"'''3/18 AtCoder\\uff08\\u6f38\\u5316\\u5f0fdp\\uff09\\n\\u4e00\\u756a\\u5de6\\u306e\\u68d2\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3066\\u3001K\\u756a\\u76ee\\u306e\\u68d2\\u306b\\u5230\\u9054\\u3059\\u308b\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306f\\n\\u4f55\\u901a\\u308a\\u4f5c\\u308c\\u307e\\u3059\\u304b\\u3068\\u3044\\u3046\\u8da3\\u65e8\\u306e\\u554f\\u984c\\n\\u307e\\u305a\\u3001\\u3053\\u306e\\u554f\\u984c\\u3092\\u89e3\\u304f\\u3046\\u3048\\u3067\\u4e00\\u756a\\u91cd\\u8981\\u306a\\u306e\\u306f\\u3001\\n\\u300c\\u3042\\u308b\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092\\u6c42\\u3081\\u308b\\u6f38\\u5316\\u5f0f\\u304c\\u7acb\\u3066\\u3089\\u308c\\u308b\\u300d\\u3068\\u3044\\u3046\\u3053\\u3068\\n\\u9ad8\\u3055h\\u3001\\u68d2j\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u306e\\u7dcf\\u6570\\u3092dp[h][j]\\u3068\\u3059\\u308c\\u3070\\u3001\\n\\u9ad8\\u3055h-1\\u304b\\u3089\\u3053\\u306e\\u4f4d\\u7f6e\\u306b\\u81f3\\u308b\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\u306e\\u306f\\u3001\\n\\u68d2j-1,j,j+1\\u306e\\u3044\\u305a\\u308c\\u304b\\u3057\\u304b\\u306a\\u3044\\n\\u3055\\u3089\\u306b\\u3001\\u305d\\u3053\\u306b\\u81f3\\u308b\\u7d4c\\u8def\\u6570\\u3068\\u3044\\u3046\\u306e\\u306f\\u7d50\\u5c40\\n\\u300c\\u307b\\u304b\\u306e\\u68d2\\u306b\\u3069\\u3093\\u306a\\u98a8\\u306b\\u67b6\\u3051\\u6a4b\\uff08\\u6a2a\\u68d2\\uff09\\u304c\\u304b\\u304b\\u3063\\u3066\\u3044\\u308b\\u304b\\u300d\\u306e\\u5834\\u5408\\u306e\\u6570\\u306a\\u306e\\u3067\\u3001\\n\\u305d\\u308c\\u3092dp[h-1][j-1],dp[h-1][j],dp[h-1][j+1]\\u306b\\u304b\\u3051\\u3066\\u3044\\u304f\\u5fc5\\u8981\\u304c\\u3042\\u308b\\n\\u4f8b\\u3048\\u3070\\u3001dp[h-1][j]\\u3092\\u898b\\u3066\\u307f\\u308b\\u3000\\u3053\\u308c\\u306f\\u3001\\u540c\\u3058\\u68d2\\u304b\\u3089\\u4e0b\\u3063\\u3066\\u304f\\u308b\\u3053\\u3068\\u3092\\n\\u610f\\u5473\\u3057\\u3066\\u3044\\u308b\\u304c\\u3001\\u63db\\u8a00\\u3059\\u308c\\u3070\\u300c\\u9ad8\\u3055i-1\\u3068i\\u306b\\u306f\\u3001\\u68d2j\\u304b\\u3089\\u4f38\\u3073\\u308b\\u6a2a\\u68d2\\u306f\\u306a\\u3044\\u300d\\n\\u3068\\u3044\\u3046\\u3053\\u3068\\u3067\\u3042\\u308b\\n\\u3064\\u307e\\u308a\\u3001\\u3053\\u306e\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u3068\\u3044\\u3046\\u306e\\u306f\\n\\u300c\\u68d21~j-1\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u3068\\u300c\\u68d2j+1~\\u68d2W\\u307e\\u3067\\u306e\\u67b6\\u304b\\u308a\\u65b9\\u300d\\u306e\\n\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u3057\\u304b\\u306a\\u3044\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\n\\u3042\\u308b\\u9ad8\\u3055\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u68d2\\u306e\\u304b\\u304b\\u308a\\u65b9\\u3082\\u6f38\\u5316\\u5f0f\\u3067\\u6c42\\u3081\\u3089\\u308c\\u308b\\u3000\\n\\u9ad8\\u3055h\\u306b\\u304a\\u3051\\u308b(\\u6a2a\\u4e00\\u5217\\u306b\\u304b\\u3051\\u6a4b\\u304c\\u4e26\\u3093\\u3067\\u3044\\u308b\\u72b6\\u6cc1\\u3092\\u8003\\u3048\\u308b\\uff09\\u3001\\nn\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570\\u306e\\u7dcf\\u6570\\u3092f(n)\\u3068\\u7f6e\\u304f\\u3068\\u3001\\nf(n) = f(n-1)+f(n-2)\\u3068\\u66f8\\u304f\\u3053\\u3068\\u304c\\u3067\\u304d\\u308b\\n\\u3053\\u308c\\u306f\\u3001f(n)\\u304c\\n\\u2460n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u306a\\u3044\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-2)\\u3068\\u540c\\u3058\\n\\u2461n\\u672c\\u76ee\\u3068n-1\\u672c\\u76ee\\u306e\\u68d2\\u306e\\u9593\\u306b\\u6a4b\\u304c\\u67b6\\u304b\\u3063\\u3066\\u3044\\u308b\\u2192\\u5834\\u5408\\u306e\\u6570\\u306ff(n-1)\\u3068\\u540c\\u3058\\n\\u306e\\u4e8c\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5408\\u8a08\\u3060\\u304b\\u3089\\u3067\\u3042\\u308b\\n\\u3060\\u304b\\u3089\\u3001dp[h-1][j]\\u306b\\u639b\\u3051\\u308b\\u6570\\u306f\\u3044\\u304f\\u3064\\u304b\\u3068\\u3044\\u3046\\u3053\\u3068\\u3092\\u8003\\u3048\\u305f\\u3089\\u3001\\nj-1\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(j-1)\\u3068\\u3001\\nW-j\\u672c\\u306e\\u68d2\\u306e\\u9593\\u306b\\u304b\\u304b\\u308b\\u6a4b\\u306e\\u5834\\u5408\\u306e\\u6570f(W-j)\\u672c\\u3068\\u3044\\u3046\\u3053\\u3068\\u306b\\u306a\\u308b\\u3000\\n\\u3053\\u308c\\u3068\\u540c\\u69d8\\u306b\\u3001\\u6b8b\\u308a\\u4e8c\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3082\\u3044\\u304f\\u3064\\u304b\\u3051\\u308c\\u3070\\u3088\\u3044\\u304b\\u3092\\u8003\\u3048\\u3066\\u3001\\ndp[h][j]]\\u306b\\u5bfe\\u3059\\u308b\\u6f38\\u5316\\u5f0f\\u3092\\u7acb\\u3066\\u308c\\u3070\\u3088\\u3044\\n'''\\nH,W,K = map(int,input().split())\\ndp = []\\nfor i in range(H+1): #\\u9ad8\\u30550\\u306e\\u5206\\u3092\\u4f59\\u5206\\u306b\\u6301\\u3063\\u3066\\u304a\\u304f\\n  L = [0]*W\\n  dp.append(L)\\nfb = [1,1] #\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\uff08f(n)=f(n-1)+f(n-2)\\uff09\\nfor i in range(W-2):\\n  fb.append(fb[i]+fb[i+1])\\ndp[0][0] = 1 #\\u5de6\\u7aef\\u306e\\u68d2\\u306e\\u9ad8\\u30550\\u306f\\u521d\\u671f\\u4f4d\\u7f6e\\u306a\\u306e\\u30671\\u306b\\nif W != 1: #\\u68d2\\u304c\\u4e00\\u672c\\u4ee5\\u4e0a\\u3042\\u308b\\u3068\\u304d\\u306f\\n  for i in range(1,H+1):\\n    for j in range(W): #\\u68d2\\u304c\\u5de6\\u7aef\\u3001\\u53f3\\u7aef\\u3001\\u305d\\u308c\\u4ee5\\u5916\\u3067\\u5834\\u5408\\u5206\\u3051\\n      if 1 <= j <= W-2:\\n        dp[i][j] = dp[i-1][j-1]*fb[j-1]*fb[W-j-1]+dp[i-1][j]*fb[j]*fb[W-j-1]+dp[i-1][j+1]*fb[j]*fb[W-j-2]\\n      elif j == 0:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j+1]*fb[W-2]\\n      else:\\n        dp[i][j] = dp[i-1][j]*fb[W-1]+dp[i-1][j-1]*fb[W-2]\\nelse:\\n  dp[H][0] = 1\\nprint(dp[H][K-1]%(10**9+7)) #\\u9ad8\\u3055H\\uff08\\u4e00\\u756a\\u4e0b\\uff09\\u3001K-1\\u756a\\u76ee\\u306e\\u68d2\\u3092\\u8abf\\u3079\\u308b\", \"H, W, K = list(map(int, input().split()))\\nh_lines = (1, 1, 2, 3, 5, 8, 13, 21, 34)\\nMOD = 10 ** 9 + 7\\n\\ndp = [[0] * 8 for _ in range(H + 1)]\\ndp[0][0] = 1\\nfor h in range(H):\\n    for w in range(W):\\n        dp[h + 1][w] = dp[h][w] * h_lines[w] * h_lines[W - w - 1]\\n        if w > 0:\\n            dp[h + 1][w] += dp[h][w - 1] * h_lines[w - 1] * h_lines[W - w - 1]\\n        if w < W - 1:\\n            dp[h + 1][w] += dp[h][w + 1] * h_lines[w] * h_lines[W - w - 2]\\n        dp[h + 1][w] %= MOD\\nprint((dp[H][K - 1]))\\n\", \"def is_valid(k):\\n    n = k.bit_length()\\n\\n    for i in range(n - 1):\\n        if (k >> i) & 1 and (k >> i + 1) & 1:\\n            return False\\n\\n    return True\\n\\np = 10**9+7\\n\\nH, W, K = map(int, input().split())\\n\\ndp = [[0]*W for _ in range(H + 1)]\\n# dp[i][j] : i\\u6bb5\\u76ee\\u307e\\u3067\\u307f\\u305f\\u3068\\u304dj\\u306b\\u3044\\u304f\\u3088\\u3046\\u306a\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u672c\\u6570\\n\\ndp[0][0] = 1\\n\\nfor i in range(H):\\n    for j in range(1 << (W - 1)):\\n        if not is_valid(j): continue\\n        for k in range(W):\\n            if k < W - 1 and (j >> k) & 1:\\n                dp[i + 1][k + 1] += dp[i][k]\\n                dp[i + 1][k + 1] %= p\\n            elif k > 0 and (j >> (k - 1)) & 1:\\n                dp[i + 1][k - 1] += dp[i][k]\\n                dp[i + 1][k - 1] %= p\\n            else:\\n                dp[i + 1][k] += dp[i][k]\\n                dp[i + 1][k] %= p\\n\\nprint(dp[H][K - 1] % p)\", \"# \\u89e3\\u8aac\\u3068\\u4e0b\\u8a18\\u3092\\u53c2\\u8003\\u306b\\u4f5c\\u6210\\n# https://atcoder.jp/contests/abc113/submissions/15821617\\n# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(H, W, K):\\n    mod = 10 ** 9 + 7\\n    dp = [[0] * W for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n    for h in range(H):\\n        for w in range(W):\\n            if dp[h][w] == 0:\\n                continue\\n            for i in range(3):\\n                new_w = w - 1 + i\\n                if not 0 <= new_w < W:\\n                    continue\\n                l, r = min(w, new_w), max(w, new_w)\\n                tmp = fibo[max(l - 1, 0)] * fibo[max(W - 1 - (r + 1), 0)]\\n                dp[h + 1][new_w] += dp[h][w] * tmp\\n                dp[h + 1][new_w] %= mod\\n    print((dp[-1][K - 1]))\\n\\n\\ndef __starting_point():\\n    H, W, K = list(map(int, input().split()))\\n    solve(H, W, K)\\n\\n    # # test\\n    # from random import randint\\n    # from func import random_str\\n    # solve()\\n\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] O(100*8)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082O(7*7*7))\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"MOD = 10**9+7\\nH, W, K = list(map(int, input().split()))\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for k in range(1<<(W-1)):\\n            # 2\\u3064\\u306e\\u6a2a\\u7dda\\u304c\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u304b\\u8abf\\u3079\\u308b\\n            ok = True\\n            for l in range(W-2):\\n                if (k>>l)&1 and (k>>(l+1))&1:\\n                    ok = False\\n            if ok:\\n                if j>=1 and (k>>(j-1))&1:\\n                    # \\u5de6\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j-1] += dp[i][j]\\n                    dp[i+1][j-1] %= MOD\\n                elif j<W-1 and (k>>j)&1:\\n                    # \\u53f3\\u65b9\\u5411\\u306b\\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u308b\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                else:\\n                    # \\u6a2a\\u7dda\\u3092\\u305f\\u3069\\u3089\\u306a\\u3044\\u30b1\\u30fc\\u30b9\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\nprint((dp[H][K-1]))\\n\", \"h, w, k = list(map(int, input().split()))\\ndp = [0] * w\\nmod = 10 ** 9 + 7\\n\\ncomb = []\\nfor bit in range(1 << w - 1):\\n    ok = True\\n    for j in range(w - 2):\\n        if bit >> j & 1 and bit >> j + 1 & 1:\\n            ok = False\\n    if ok:\\n        comb.append(bit)\\n\\ndp[0] = 1\\nfor i in range(h):\\n    next = [0] * w\\n    for bit in comb:\\n        moved = [False] * w\\n        for j in range(w):\\n            if bit >> j & 1:\\n                next[j + 1] += dp[j]\\n                next[j] += dp[j + 1]\\n                moved[j] = moved[j + 1] = True\\n            elif not moved[j]:\\n                next[j] += dp[j]\\n    dp = next\\nprint((dp[k - 1] % mod))\\n\", \"h, w, k = map(int, input().split())\\np = 10**9+7\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\nF = [1, 2, 3, 5, 8, 13, 21][:w]+[1]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-2]*F[w-2-j]\\n        b = DP[i][j]*F[j-1]*F[w-2-j]\\n        c = DP[i][j+1]*F[j-1]*F[w-3-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint(DP[h][k-1])\", \"H,W,K = map(int,input().split())\\ndp = [[0]*W for i in range(H+1)]\\ndp[0][0] = 1\\nMOD = 10**9+7\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\nprint(dp[-1][K-1] % MOD)\", \"H, W, K = map(int, input().split())\\nmod = 10**9 + 7\\n\\ndp = [0]*W\\ndp[0] = 1\\n\\nOK = [0, 1, 1, 2, 3, 5, 8, 13]\\nNG = [0, 1, 2, 3, 5, 8, 13, 21]\\n\\nif W == 1:\\n  print(dp[K-1])\\nelse:\\n  for _ in range(H):\\n    temp = dp[:]\\n    for i in range(W):\\n      if i == 0:\\n        dp[i] = temp[i] * NG[W-1-i] + temp[i+1] * OK[W-1-i]\\n      elif i == W-1:\\n        dp[i] = temp[i-1] * OK[i] + temp[i] * NG[i]\\n      else:  \\n        dp[i] = temp[i-1] * OK[i] * NG[W-1-i] + temp[i] * NG[i] * NG[W-1-i] + temp[i+1] * NG[i] * OK[W-1-i]\\n      dp[i] %= mod\\n  print(dp[K-1])\", \"fib = [1, 1, 2, 3, 5, 8, 13, 21]\\nmod = 1000000007\\nh, w, k = list(map(int, input().split()))\\nk -= 1\\np = [0] * w\\np[0] = 1\\nfor i in range(h):\\n  q = [0] * w\\n  for j in range(w):\\n    if j > 0:\\n      q[j] += p[j - 1] * fib[j - 1] * fib[w - 1 - j]\\n    if j < w - 1:\\n      q[j] += p[j + 1] * fib[j] * fib[w - j - 2]\\n    if 0 < j < w - 1:\\n      q[j] += p[j] * fib[j] * fib[w - j - 1]\\n    elif j > 0:\\n      q[j] += p[j] * fib[j]\\n    elif j < w - 1:\\n      q[j] += p[j] * fib[w - j - 1]\\n    else:\\n      q[j] += p[j]\\n    q[j] %= mod\\n  p = q\\nprint((p[k]))\\n\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\ndp=[0]*w\\ndp[0]=1\\nfib=[1,1,2,3,5,8,13,21,34,55,89]\\nfor _ in range(h):\\n  t=[0]*w\\n  for i in range(w):\\n    if i>0:\\n      t[i]+=dp[i-1]*fib[i-1]*fib[w-i-1]\\n    t[i]+=dp[i]*fib[i]*fib[w-i-1]\\n    if i<w-1:\\n      t[i]+=dp[i+1]*fib[i]*fib[w-i-2]\\n    t[i]%=mod\\n  dp=t\\nprint(dp[k-1])\", \"h,w,k=map(int,input().split())\\ndp=[0]*(w)\\nl=[1,1,2,3,5,8,13,21,34]#n\\u672c\\u306e\\u7e26\\u7dda\\u306b\\u9ad8\\u30551\\u306evalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u3001\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\u306b\\u306a\\u308b\\n#a_n:=n\\u672c\\u306e\\u7e26\\u7dda\\u306bvalid\\u306a\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\u901a\\u308a\\u306e\\u7dcf\\u6570\\u3001\\u3068\\u3059\\u308c\\u3070\\n#n+1\\u672c\\u306e\\u6642\\u306f1.1\\u30682\\u672c\\u76ee\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\uff082\\u30683\\u306e\\u9593\\u306b\\u5f15\\u3051\\u306a\\u3044\\u306e\\u3067a_n-1\\u901a\\u308a\\uff09\\n#          2.                \\u5f15\\u304b\\u306a\\u3044\\uff08a_n\\u901a\\u308a\\uff09\\n#\\u3088\\u3063\\u3066\\u6f38\\u5316\\u5f0fa_n+1=a_n+a_n-1\\u304c\\u6210\\u7acb\\u3002\\ndp[0]=1\\nmod=10**9+7\\nr=[0]*w\\nfor i in range(h):\\n    for i in range(w):\\n        r[i]=dp[i]*l[i]*l[w-1-i]#\\u5de6\\u53f3\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u304b\\u306a\\u3044\\n        if i>=1:\\n            r[i]+=dp[i-1]*l[i-1]*l[w-1-i]#\\u5de6\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        if i<=w-2:\\n            r[i]+=dp[i+1]*l[i]*l[w-2-i]#\\u53f3\\u306b\\u306e\\u307f\\u6a2a\\u68d2\\u3092\\u5f15\\u304f\\n        r[i]%=mod\\n    dp,r=r,dp\\n\\nprint(dp[k-1])\", \"def fib():\\n    a = 1\\n    b = 0\\n    while 1:\\n        c = a + b\\n        yield c\\n        a = b\\n        b = c\\n\\n\\ndef main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n    f = fib()\\n    c = [f.__next__() for _ in range(w + 1)]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from itertools import product\\n\\nh, w, k = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\npats = [pat for pat in product([1, 0], repeat=w-1)]\\n\\nfor i in range(h):\\n\\tfor j in range(w):\\n\\t\\tfor pat in pats:\\n\\t\\t\\tvalid = True\\n\\t\\t\\tfor e1, e2 in zip(pat, pat[1:]):\\n\\t\\t\\t\\tif e1 and e2:\\n\\t\\t\\t\\t\\tvalid = False\\n\\n\\t\\t\\tif not valid:\\n\\t\\t\\t\\tcontinue\\n\\n\\t\\t\\tif j - 1 >= 0 and pat[j-1]:\\n\\t\\t\\t\\tdp[i+1][j-1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j-1] %= mod\\n\\n\\t\\t\\telif j <= w - 2 and pat[j]:\\n\\t\\t\\t\\tdp[i+1][j+1] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j+1] %= mod\\n\\n\\t\\t\\telse:\\n\\t\\t\\t\\tdp[i+1][j] += dp[i][j]\\n\\t\\t\\t\\tdp[i+1][j] %= mod\\n\\nans = dp[h][k-1]\\nprint(ans)\\n#print(*dp, sep=\\\"\\\\n\\\")\\n\", \"h,w,k = [int(i) for i in input().split()]\\n\\nmod = 10**9 + 7\\n   \\n\\ndp = [[0 for _ in range(w)] for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(h):\\n    for bit in range(1<<(w-1)):\\n        if '11' in bin(bit) : continue\\n        for j in range(w):\\n            if j > 0 and bit & (1 << (j-1)):\\n                dp[i+1][j-1] += dp[i][j] % mod \\n            elif bit & (1 << j):\\n                dp[i+1][j+1] += dp[i][j] % mod\\n            else:\\n                dp[i+1][j] += dp[i][j] % mod\\n                \\nprint(dp[h][k-1]%mod)\", \"H, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\n\\ndef check(bit):\\n  pre_b = '0'\\n  for b in bit:\\n    if b == '1' and pre_b == '1':\\n      return False\\n    pre_b = b\\n  return True\\n\\n# dp[h][w]:\\u4e0a\\u304b\\u3089h\\u6bb5\\u76ee\\u3067\\u306e\\u64cd\\u4f5c\\u3092\\u7d42\\u4e86\\u3057\\u305f\\u6642\\u70b9\\u3067w\\u756a\\u76ee\\u306e\\u3042\\u307f\\u3060\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0]*(W+2) for h in range(H+1)]\\ndp[0][1] = 1\\n\\n# \\u3042\\u308b\\u6bb5\\u306b\\u304a\\u3051\\u308b\\u6a2a\\u7dda\\u306e\\u914d\\u7f6e\\u3092\\u5168\\u63a2\\u7d22\\u3057\\u3066w-1 <-> w\\u306b\\u6a2a\\u7dda\\u304c\\u3042\\u308b\\u6570\\nlines = [0] * (W+1)\\nc = 0\\nfor i in range(2**(W-1)):\\n  if not check(bin(i)[2:]):\\n    continue\\n  c += 1\\n  for w in range(W-1):\\n    lines[w+1] += (i & 1<<w) > 0\\n\\n\\n# \\u914d\\u308bDP\\nfor h in range(H):\\n  for w in range(1, W+1):\\n    x, z = lines[w-1], lines[w]\\n    y = c - x - z\\n    dp[h+1][w-1] = (dp[h+1][w-1] + dp[h][w]*x % MOD) % MOD\\n    dp[h+1][w] = (dp[h+1][w] + dp[h][w]*y % MOD) % MOD\\n    dp[h+1][w+1] = (dp[h+1][w+1] + dp[h][w]*z % MOD) % MOD\\n\\nprint(dp[-1][K])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nmod = 10 ** 9 + 7\\nif w == 1:\\n    print(1)\\n    return\\nrow = [0 for i in range(w + 1)]\\nrow[0] = 1\\nrow[1] = 1\\nfor i in range(w - 1):\\n    row[i + 2] = row[i + 1] + row[i]\\n\\ndp = [[0 for i in range(w)] for j in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(h):\\n    for j in range(w):\\n        if j == 0:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j + 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        elif j == w - 1:\\n            dp[i + 1][j] = dp[i][j] * row[w - 1] + dp[i][j - 1] * row[w - 2]\\n            dp[i + 1][j] %= mod\\n        else:\\n            dp[i + 1][j] = dp[i][j - 1] * row[j - 1] * row[w - j - 1] + dp[i][j] * row[j] * row[w - j - 1] + dp[i][j + 1] * row[j] * row[w - j - 2]\\n            dp[i + 1][j] %= mod\\nprint(dp[h][k - 1])\", \"import sys\\nh, w, k = map(int, input().split())\\n\\nmod = 10 ** 9 + 7\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nn_join = [0 for i in range(w-1)]\\nn_unjoin = [0 for i in range(w-1)]\\ncnt = 0\\n\\nfor i in range(2 ** (w-1)):\\n    p = 0\\n    f = 1\\n    tmp_join = []\\n    tmp_unjoin = []\\n    for j in range(w-1):\\n        c = i & (1 << j)\\n        if c:\\n            tmp_join.append(j)\\n        if not (c or p):\\n            tmp_unjoin.append(j)\\n        if p and c:\\n            f = 0\\n            break\\n        p = c\\n    if f:\\n        cnt += 1\\n        for j in tmp_join:\\n            n_join[j] += 1\\n        for j in tmp_unjoin:\\n            n_unjoin[j] += 1\\n\\nn_unjoin.append(cnt - n_join[-1])\\n\\ndp = [[0 for j in range(w)] for i in range(h)]\\ndp[0][0] = n_unjoin[0]\\ndp[0][1] = n_join[0]\\n\\nfor i in range(1,h):\\n    for j in range(w):\\n        dp[i][j] += dp[i-1][j] * n_unjoin[j] % mod\\n        dp[i][j] %= mod\\n        if j > 0:\\n            dp[i][j] += dp[i-1][j-1] * n_join[j-1] % mod\\n            dp[i][j] %= mod\\n        if j < w - 1:\\n            dp[i][j] += dp[i-1][j+1] * n_join[j] % mod\\n            dp[i][j] %= mod\\n        \\nprint(dp[h-1][k-1])\", \"#float\\u578b\\u3092\\u8a31\\u3059\\u306a\\n#numpy\\u306fpython\\u3067\\nimport sys\\ninput = sys.stdin.readline\\nsys.setrecursionlimit(10**7)\\nfrom collections import Counter, deque\\nfrom collections import defaultdict\\nfrom itertools import combinations, permutations, accumulate, groupby, product\\nfrom bisect import bisect_left,bisect_right\\nfrom heapq import heapify, heappop, heappush\\nfrom math import floor, ceil,pi,factorial\\nfrom operator import itemgetter\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\ndef SI(): return input().rstrip()\\ndef printns(x): print(('\\\\n'.join(x)))\\ndef printni(x): print(('\\\\n'.join(list(map(str,x)))))\\ninf = 10**17\\nmod = 10**9 + 7\\n\\nh,w,k=MI()\\ndp=[[0]*w for i in range(h+1)]\\ndp[0][0]=1\\na=0\\nb=1\\nweight=[]\\nfor i in range(100):\\n    weight.append(a+b)\\n    a,b=b,a+b\\n#print(weight)    \\nfor i in range(h):\\n    for j in range(w):\\n        if 0<=j+1<w:\\n            left=max(j-1,0)\\n            right=max(w-j-3,0)\\n            dp[i+1][j+1]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j<w:\\n            left=max(j-1,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j]+=(dp[i][j]*weight[left]*weight[right])%mod\\n        if 0<=j-1<w:\\n            left=max(j-2,0)\\n            right=max(w-j-2,0)\\n            dp[i+1][j-1]+=(dp[i][j]*weight[left]*weight[right])%mod\\nprint((dp[-1][k-1]%mod))\\n\\n\\n\", \"H,W,K = map(int,input().split())\\nmod = 10**9+7\\ndp = W*[0]\\ndp[0] = 1\\nfib = [1,1,2,3,5,8,13,21,34,55,89]\\n\\nfor h in range(H):\\n  t = W*[0]\\n  for w in range(W):\\n    if 0<w:\\n      t[w]+=dp[w-1]*fib[w-1]*fib[W-w-1]\\n    t[w]+=dp[w]*fib[w]*fib[W-w-1]\\n    \\n    if w<W-1:\\n      t[w]+=dp[w+1]*fib[w]*fib[W-w-2]\\n    t[w]%=mod\\n  dp = t\\n\\nprint(dp[K-1])\", \"\\nfrom itertools import product\\n\\n\\ndef patterns(w):\\n    res = []\\n    for pt in product([0, 1], repeat=w):\\n        valid = True\\n        for i in range(w - 1):\\n            if pt[i] == pt[i + 1] == 1:\\n                valid = False\\n                break\\n        if valid:\\n            res.append(pt)\\n    return res\\n\\n\\ndef submit():\\n    h, w, k = [int(e) for e in input().split()]\\n    dp = [[0 for _ in range(w)] for _ in range(h + 1)]\\n    dp[0][0] = 1\\n    modp = 10 ** 9 + 7\\n\\n    pts = patterns(w - 1)\\n\\n    for i in range(1, h + 1):\\n        for j in range(w):\\n            for pt in pts:\\n                if j > 0 and pt[j - 1] == 1: # j -> j - 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j - 1] += dp[i - 1][j]\\n                    dp[i][j - 1] %= modp\\n                elif j < w - 1 and pt[j] == 1:  # j -> j + 1\\u306b\\u9077\\u79fb\\u3059\\u308b\\n                    dp[i][j + 1] += dp[i - 1][j]\\n                    dp[i][j + 1] %= modp\\n                else:\\n                    dp[i][j] += dp[i - 1][j]\\n                    dp[i][j] %= modp\\n\\n\\n    print(dp[h][k - 1])\\n\\n\\nsubmit()\", \"from itertools import product\\nH, W, K = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nif W == 1:\\n    print((1))\\n    return\\n\\nup = [0] * W\\nright = [0] * W\\nleft = [0] * W\\n\\nfor b in range(1 << (W - 1)):\\n    bridge = bin(b)[2:].zfill(W - 1)\\n    if \\\"11\\\" in bridge:\\n        continue\\n\\n    # \\u5de6\\u306e\\u68d2\\n    if bridge[0] == \\\"0\\\":\\n        up[0] += 1\\n    else:\\n        right[0] += 1\\n\\n    # \\u53f3\\u306e\\u68d2\\n    if bridge[-1] == \\\"0\\\":\\n        up[W - 1] += 1\\n    else:\\n        left[W - 1] += 1\\n\\n    # \\u771f\\u3093\\u4e2d\\n    for i in range(1, W - 1):\\n        if bridge[i - 1] == \\\"0\\\" and bridge[i] == \\\"1\\\":\\n            right[i] += 1\\n        elif bridge[i - 1] == \\\"1\\\" and bridge[i] == \\\"0\\\":\\n            left[i] += 1\\n        else:\\n            up[i] += 1\\n\\nup = [0] + up + [0]\\nright = [0] + right + [0]\\nleft = [0] + left + [0]\\n\\ndp = [0] * (W + 2)\\ndp[K] = 1\\nfor _ in range(H):\\n    newDP = [0] * (W + 2)\\n    for i in range(1, W + 1):\\n        newDP[i] += dp[i - 1] * right[i - 1]\\n        newDP[i] += dp[i] * up[i]\\n        newDP[i] += dp[i + 1] * left[i + 1]\\n        newDP[i] %= mod\\n    dp = newDP\\n\\nans = dp[1]\\nprint(ans)\\n\", \"w = [1, 2]\\nfor i in range(6):\\n    w.append(w[-2] + w[-1])\\nH, W, K = map(int,input().split())\\nmod = 10 ** 9 + 7\\ndp = [[0 for i in range(W)] for j in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        if j >= 1:\\n            k = 1\\n            if j - 2 >= 0:\\n                k *= w[j - 2]\\n            if W - j - 2 >= 0:\\n                k *= w[W - j - 2]\\n            dp[i+1][j-1] += k * dp[i][j]\\n            dp[i+1][j-1] %= mod\\n        k = 1\\n        if j - 1 >= 0:\\n            k *= w[j - 1]\\n        if  W - j - 2 >= 0:\\n            k *= w[W - j - 2]\\n        dp[i+1][j] += k * dp[i][j]\\n        dp[i+1][j] %= mod\\n        if j <= W - 2:\\n            k = 1\\n            if j - 1 >= 0:\\n                k *= w[j - 1]\\n            if W - j - 3 >= 0:\\n                k *= w[W - j - 3]\\n            dp[i+1][j+1] += k * dp[i][j]\\n            dp[i+1][j+1] %= mod\\n\\nprint(dp[H][K-1] % mod)\", \"h,w,k=map(int,input().split())\\ndp=[[0 for _ in range(w)]for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n    for bit in range(2**(w-1)):\\n        bit=bin(bit)[2:].zfill(w-1)\\n        f=0\\n        for j in range(w-2):\\n            if bit[j]=='1' and bit[j+1]=='1':\\n                f=1\\n                break\\n        if f:\\n            continue\\n        for j in range(w):\\n            if j==0:\\n                dp[i+1][j]+=dp[i][j+1] if bit[0]=='1' else dp[i][j]\\n            elif j==w-1:\\n                dp[i+1][j]+=dp[i][j-1] if bit[-1]=='1' else dp[i][j]\\n            else:\\n                dp[i+1][j]+=dp[i][j]*(bit[j-1]=='0' and bit[j]=='0')\\n                dp[i+1][j]+=dp[i][j-1]*(bit[j-1]=='1')\\n                dp[i+1][j]+=dp[i][j+1]*(bit[j]=='1')\\n            dp[i+1][j]%=mod\\nprint(dp[-1][k-1])\", \"# Python3 (3.4.3)\\nimport sys\\ninput = sys.stdin.readline\\n\\n# -------------------------------------------------------------\\n# function\\n# -------------------------------------------------------------\\n\\n\\n# -------------------------------------------------------------\\n# main\\n# -------------------------------------------------------------\\nH,W,K = map(int,input().split())\\n\\nmod = 10**9+7\\n\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nj = [0,1,1,2,3,5,8,13];\\n# \\u5de6(\\u3042\\u308b\\u3044\\u306f\\u53f3)\\u306bn\\u672c\\u306e\\u7e26\\u68d2\\u304c\\u3042\\u308a\\u3001\\u771f\\u6a2a\\u3068\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u306a\\u3044\\u6642\\u306e\\u5834\\u5408\\u306e\\u6570\\nm = [1,1,2,3,5,8,13,21];\\n \\n# dp[h][w] : h\\u884c\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067w\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\ndp = [[0 for _ in range(W)] for _ in range(H+1)]\\ndp[0][0] = 1\\n \\nfor h in range(H+1):\\n    for w in range(W):\\n        # \\u53f3\\u306b\\u79fb\\u52d5\\n        if w != 0:\\n            dp[h][w] += dp[h-1][w-1] * j[w] * m[W-1-w]\\n        # \\u5de6\\u306b\\u79fb\\u52d5\\n        if w != W-1:\\n            dp[h][w] += dp[h-1][w+1] * m[w] * j[W-1-w]\\n        # \\u771f\\u4e0b\\u306b\\u79fb\\u52d5\\n        dp[h][w] += dp[h-1][w] * m[w] * m[W-1-w]\\n        \\n        dp[h][w] %= mod;\\n\\n    \\nprint(dp[H][K-1])\", \"H, W, K = list(map(int, input().split()))\\n\\n# \\u9023\\u7d9a\\u3059\\u308bn\\u533a\\u9593\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5\\u306f\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\n# kakekata[b][i] : b\\u304c0\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u306a\\u3044\\u65b9\\u6cd5 b\\u304c1\\u306e\\u6642\\u306fi\\u533a\\u9593\\u76ee\\u306b\\u6a4b\\u3092\\u304b\\u3051\\u308b\\u65b9\\u6cd5 \\u304c\\u4f55\\u901a\\u308a\\u3042\\u308b\\u304b\\nkakekata = [[0] * 10] + [[0] * 10]\\nkakekata[0][0] = 1\\nfor i in range(8):\\n    kakekata[0][i + 1] = kakekata[0][i] + kakekata[1][i]\\n    kakekata[1][i + 1] = kakekata[0][i]\\n\\n\\nMOD = 10 ** 9 + 7\\nclass modint:\\n    def __init__(self, x):\\n        self.x = x.x if isinstance(x, modint) else x % MOD\\n    def __str__(self): return str(self.x)\\n    __repr__ = __str__\\n    def __int__(self): return self.x\\n    __index__ = __int__\\n    def __add__(self, other): return modint(self.x + modint(other).x)\\n    def __sub__(self, other): return modint(self.x - modint(other).x)\\n    def __mul__(self, other): return modint(self.x * modint(other).x)\\n    def __pow__(self, other): return modint(pow(self.x, modint(other).x, MOD))\\n    def __floordiv__(self, other): return modint(self.x * pow(modint(other).x, MOD - 2, MOD))\\n    def __eq__(self, other): return self.x == modint(other).x\\n    def __ne__(self, other): return self.x != modint(other).x\\n    def __inv__(self): return pow(self.x, MOD - 2, MOD)\\n\\n\\ndp = [[modint(0)] * (W + 2) for h in range(H + 1)]\\ndp[0][1] += 1\\nfor h in range(H):\\n    for w in range(1, W + 1):\\n        # \\u5de6\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b \\u53f3\\u306b\\u4f55\\u533a\\u9593\\u3042\\u308b\\u304b\\n        l, r = w - 1, W - w\\n\\n        # \\u305d\\u306e\\u307e\\u307e\\u6e21\\u3059\\n        dp[h + 1][w] += dp[h][w] * kakekata[0][l] * kakekata[0][r]\\n        # \\u53f3\\u306b\\u6e21\\u3059\\n        dp[h + 1][w + 1] += dp[h][w] * kakekata[0][l] * kakekata[1][r]\\n        # \\u5de6\\u306b\\u6e21\\u3059\\n        dp[h + 1][w - 1] += dp[h][w] * kakekata[1][l] * kakekata[0][r]\\n\\nprint((dp[H][K]))\\n\", \"h,w,K=list(map(int,input().split()))\\ndef two(x):\\n\\treturn \\\"0\\\"*(w-1-len(bin(x)[2:]))+bin(x)[2:]\\ndp=[[0]*w for _ in range(h+1)]\\ndp[0][0]=1\\nmod=10**9+7\\nfor i in range(h):\\n\\tfor j in range(2**(w-1)):\\n\\t\\tr=two(j)\\n\\t\\tf=1\\n\\t\\tfor k in range(w-2):\\n\\t\\t\\tif r[k]==r[k+1]==\\\"1\\\":\\n\\t\\t\\t\\tf=0\\n\\t\\t\\t\\tbreak\\n\\t\\tif f:\\n\\t\\t\\tfor k in range(w):\\n\\t\\t\\t\\tif k+1<w:\\n\\t\\t\\t\\t\\tif r[k]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k+1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tif k>0:\\n\\t\\t\\t\\t\\tif r[k-1]==\\\"1\\\":\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]+=dp[i][k]\\n\\t\\t\\t\\t\\t\\tdp[i+1][k-1]%=mod\\n\\t\\t\\t\\t\\t\\tcontinue\\n\\t\\t\\t\\tdp[i+1][k]+=dp[i][k]\\n\\t\\t\\t\\tdp[i+1][k]%=mod\\nprint((dp[h][K-1]))\\n\\n\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            #dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"import sys\\nreadline = sys.stdin.readline\\n\\n# 0-indexed\\u3067\\u8003\\u3048\\u308b\\n# \\u7e26\\u68d2\\u306fW\\u672c\\u3001\\u6a2a\\u68d2\\u3092\\u7f6e\\u3051\\u308b\\u5834\\u6240\\u306f\\u4e00\\u884c\\u3042\\u305f\\u308aW - 1\\u7b87\\u6240\\u3068\\u306a\\u308b\\n# \\u30fbi\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\n# \\u30fbi\\u304b\\u3089\\u79fb\\u52d5\\u305b\\u305a\\u306b\\u305d\\u306e\\u307e\\u307e\\u306b\\u306a\\u308b\\u5834\\u5408\\u306e\\u6570\\n# \\u3092\\u305d\\u308c\\u305e\\u308c\\u6c42\\u3081\\u308b\\n\\n# LINE[i] = i\\u3068i + 1\\u306e\\u9593\\u306b\\u6a2a\\u68d2\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u6570\\u3002\\n# POINT[i] = i\\u304b\\u3089\\u6a2a\\u68d2\\u304c\\u51fa\\u3066\\u3044\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\n# \\u305d\\u308c\\u305e\\u308cDP\\u3067\\u6c42\\u3081\\u308b\\n\\nH,W,K = list(map(int,readline().split()))\\nDIV = 1000000007\\n\\n# dp[i][j] = \\u9593\\u9694i\\u307e\\u3067\\u51e6\\u7406\\u3057\\u305f\\u3068\\u304d\\u306b\\u3001j\\u756a\\u76ee\\u306e\\u9593\\u9694\\u306b\\u68d2\\u304c\\u3042\\u308b(0,1)\\u5834\\u5408\\u306e\\u6570\\nLINE = [-1] * (W - 1)\\nfor i in range(W - 1):\\n  # i\\u3068i + 1\\u306e\\u9593\\u306b\\u68d2\\u304c\\u3042\\u308b\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W - 1)]\\n  if i == 0:\\n    dp[0][0] = 0\\n    dp[0][1] = 1\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W - 1):\\n    if j == i:\\n      dp[j][0] = 0\\n      dp[j][1] = dp[j - 1][0]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      dp[j][1] += dp[j - 1][0]\\n  LINE[i] = dp[-1][0] + dp[-1][1]\\n  LINE[i] %= DIV\\n\\nPOINT = [-1] * W\\n# \\u70b9i\\u304b\\u3089\\u307e\\u3063\\u3059\\u3050\\u4e0b\\u304c\\u308b\\u5834\\u5408\\u306e\\u6570\\n# i\\u304b\\u3089\\u53f3\\u306b\\u68d2\\u3092\\u5f15\\u304f/\\u5f15\\u304b\\u306a\\u3044\\u5834\\u5408\\u306e\\u6570\\u3092\\u6570\\u3048\\u308b\\nfor i in range(W):\\n  # i - 1\\u306b\\u3082i\\u306b\\u3082\\u68d2\\u304c\\u306a\\u3044\\u5834\\u5408\\n  dp = [[0] * 2 for j in range(W)]\\n  if i - 1 == 0 or i == 0:\\n    dp[0][0] = 1\\n    dp[0][1] = 0\\n  else:\\n    dp[0][0] = 1\\n    dp[0][1] = 1\\n  for j in range(1, W):\\n    if j == i - 1 or j == i:\\n      dp[j][1] = 0\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n    else:\\n      dp[j][0] += dp[j - 1][0] + dp[j - 1][1]\\n      if j == W - 1:\\n        dp[j][1] = 0\\n      else:\\n        dp[j][1] += dp[j - 1][0]\\n  POINT[i] = dp[-1][0] + dp[-1][1]\\n  POINT[i] %= DIV\\n  \\n# \\u3053\\u3053\\u304b\\u3089DP\\n# dp[i][j] = \\u3042\\u307f\\u3060\\u306ei\\u6bb5\\u76ee\\u3067j\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\n\\ndp = [[0] * W for i in range(H + 1)]\\ndp[0][0] = 1\\n\\nfor i in range(1, len(dp)):\\n  for j in range(W):\\n    # j\\u3092\\u51fa\\u767a\\u70b9\\u306b\\u3057\\u3066\\u9077\\u79fb\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i][j] += dp[i - 1][j - 1] * LINE[j - 1]\\n    dp[i][j] += dp[i - 1][j] * POINT[j]\\n    if j + 1 < W:\\n      dp[i][j] += dp[i - 1][j + 1] * LINE[j]\\n      \\n    dp[i][j] %= DIV\\n    \\nprint((dp[H][K - 1]))\\n\", \"H, W, K = [int(x) for x in input().split()]\\np = 10 ** 9 + 7\\n\\n# H = 1, \\u7e26\\u68d2W\\u672c\\u306e\\u3042\\u307f\\u3060\\u304f\\u3058\\u306e\\u6570\\u3000\\u2192\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\nh1amida = [1, 1, 2] + [None] * 6\\nfor i in range(3, 9):\\n    h1amida[i] = h1amida[i - 2] + h1amida[i - 1]\\n\\n# dp[h][k] = \\u7e26\\u68d2\\u306e\\u9577\\u3055h+1\\u3001\\u7e26\\u68d2\\u306e\\u672c\\u6570W\\u3001\\u30b4\\u30fc\\u30eb\\u306e\\u68d2k\\u3068\\u306a\\u308b\\u3042\\u307f\\u3060\\u306e\\u6570\\n# dp[0][*]\\u3068dp[*][0]\\u306f\\u30c0\\u30df\\u30fc\\ndp = [[0 for _ in range(W + 1)] for _ in range(H + 1)]\\n\\nfor k in range(1, W + 1):\\n    if k == 1:\\n        dp[1][k] = h1amida[W - 1]\\n    elif k == 2:\\n        dp[1][k] = h1amida[W - 2]\\n    else:\\n        dp[1][k] = 0\\n\\nfor h in range(2, H + 1):\\n    for k in range(1, W + 1):\\n        if k > 1:\\n            dp[h][k] += (dp[h - 1][k - 1] * h1amida[k - 2] % p) * h1amida[W - k] % p\\n        dp[h][k] += (dp[h - 1][k] * h1amida[k - 1] % p) * h1amida[W - k] % p\\n        if k < W:\\n            dp[h][k] += (dp[h - 1][k + 1] * h1amida[k - 1] % p) * h1amida[W - k - 1] % p\\n        dp[h][k] %= p\\n\\nprint((dp[H][K]))\\n\", \"def isok(n):\\n    for i in range(w-2):\\n        if n >> i & 1 and n >> (i+1) & 1:\\n            return False\\n    return True\\nmod = 10**9+7\\nh,w,k = map(int,input().split())\\nh += 1\\nif w == 1:\\n    print(1)\\n    return\\nif w == 2:\\n    print(2**(h-2))\\n    return\\ndp = [[0]*(w+1) for _ in range(h+1)]\\ndp[1][1] = 1\\namida = [0]*(w)\\nnoamida = [0]*(w+1)\\nfor i in range(2**(w-1)):\\n    if isok(i):\\n        for j in range(w-1):\\n            amida[j+1] += i >> j & 1\\n        for j in range(w-2):\\n            if i >> j & 1 == 0 and i >> (j+1) & 1 == 0:\\n                noamida[j+2] += 1\\n        if i >> 0 & 1 == 0:\\n                noamida[1] += 1\\n        if i >> (w-2) & 1 == 0:\\n                noamida[w] += 1\\nfor i in range(1,h):\\n    dp[i+1][1] = (dp[i][2]*amida[1]+dp[i][1]*noamida[1]) % mod\\n    dp[i+1][w] = (dp[i][w-1]*amida[w-1]+dp[i][w]*noamida[w]) % mod\\n    for j in range(2,w):\\n        dp[i+1][j] = (dp[i][j-1]*amida[j-1]+dp[i][j+1]*amida[j]+dp[i][j]*noamida[j]) % mod\\nprint(dp[h][k])\", \"from functools import lru_cache\\n\\nH, W, K = map(int, input().split())\\nMOD = 10**9 + 7\\nK -= 1\\n\\nif W == 1:\\n    print(1)\\n    return\\n\\n@lru_cache(maxsize=None)\\ndef fib(width):\\n    if width < -1:\\n        return 0\\n    if width == -1:\\n        return 1\\n    return (fib(width - 1) + fib(width - 2)) % MOD\\n\\ndp = [0] * W\\ndp[0] = 1\\n\\nfor _ in range(H):\\n    newDp = [0] * W\\n\\n    newDp[0] = (dp[0] * fib(W - 2) + dp[1] * fib(W - 3)) % MOD\\n    newDp[W - 1] = (dp[W - 1] * fib(W - 2) + dp[W - 2] * fib(W - 3)) % MOD\\n\\n    for w in range(1, W - 1):\\n        left = dp[w - 1] * max(1, fib(w - 2)) * max(1, fib(W - 1 - w - 1))\\n        right = dp[w + 1] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 2))\\n        mid = dp[w] * max(1, fib(w - 1)) * max(1, fib(W - 1 - w - 1))\\n        newDp[w] = (left + mid + right) % MOD\\n    dp = newDp\\n\\nprint(dp[K])\", \"from itertools import combinations\\n\\nH,W,K=map(int,input().split())\\ndp=[[0 for i in range(W)] for j in range(H+1)]\\n\\nmod=10**9+7\\n\\nif W==1:\\n  if K==1:print(1)\\n  else:print(0)\\n  return\\n\\nmemo={}\\ndef is_separate(c):\\n  for i in range(len(c)-1):\\n    if c[i+1]-c[i] == 1:\\n      return False\\n  return True\\n\\ndef n_select(occupied):\\n  if memo.get(occupied):\\n    return memo[occupied]\\n  else:\\n    count=1\\n    if len(occupied)==1:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c:\\n            if is_separate(c):\\n              count += 1\\n    if len(occupied)==2:\\n      for r in range(1,W//2+1):\\n        for c in combinations(range(W-1),r=r):\\n          if occupied[0]-1 not in c and occupied[0] not in c and occupied[0]+1 not in c:\\n            if is_separate(c):count += 1\\n  memo[occupied] = count\\n  return count\\n\\ndp[0][0]=1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    if j==0:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))\\n    elif j==W-1:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j-1]*n_select((j-1,j))\\n    else:\\n      dp[i][j] = dp[i-1][j]*n_select((j,))+dp[i-1][j+1]*n_select((j,j+1))+dp[i-1][j-1]*n_select((j-1,j))\\n\\nprint(dp[-1][K-1] % mod)\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n    res *= P[(W - 1) - (R + 1)]\\n    res %= DIV\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"H,W,K = map(int, input().split())\\n\\nif W == 1:\\n    print(1 if K == 1 else 0)\\n    return\\n\\nMOD = 10 ** 9 + 7\\n\\nstates = [0]\\nfor state in range(1, 1 << (W - 1)):\\n    flag = True\\n    for j in range(1, W - 1):\\n        if ((state >> j - 1) & 1) and ((state >> j) & 1):\\n            flag = False\\n    if flag: states.append(state)\\n\\ndp = [[0] * W for _ in range(H + 1)]\\n\\ndp[0][0] = 1\\n\\n# \\u8cb0\\u3046DP\\nfor i in range(H):\\n    for state in states:\\n        for j in range(W - 1):\\n            if (state >> j) & 1:\\n                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j + 1]) % MOD\\n                dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % MOD\\n            else:\\n                if j == 0:\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                elif not ((state >> j - 1) & 1):\\n                    dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % MOD\\n                if j == W - 2:\\n                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j + 1]) % MOD\\n\\nprint(dp[H][K - 1])\", \"import itertools\\n\\n\\ndef amida_patterns(w):\\n    # (0, 1, 2, ... , w - 1) -> ?\\n    ret = list()\\n    for bars in itertools.product([0, 1], repeat=w-1):\\n        if sum([b * bb for b, bb in zip(bars[1:], bars[:-1])]) > 0:\\n            continue\\n        location = list(range(w))\\n        for i in range(w):\\n            if i > 0 and bars[i - 1] == 1:\\n                location[i] = i - 1\\n            elif i < w - 1 and bars[i] == 1:\\n                location[i] = i + 1\\n        ret.append(location)\\n    return ret\\n\\n\\ndef main():\\n    MOD = 10**9 + 7\\n    H, W, K = list(map(int, input().split(' ')))\\n    ap_list = amida_patterns(W)\\n    dp = [[0 for _ in range(W)] for _ in range(H + 1)]\\n    dp[0][0] = 1\\n    for h in range(1, H + 1):\\n        for a in ap_list:\\n            for w in range(W):\\n                dp[h][a[w]] += dp[h - 1][w]\\n                dp[h][a[w]] %= MOD\\n    print(dp[H][K - 1])\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import sys\\n\\ndef comb(n, r, mod=None):\\n    if r == 0 or r == n:\\n        return 1\\n    r = min([r, n-r])\\n    x, y = 1, 1\\n    ans = 1\\n    for i in range(1, r+1):\\n        if mod:\\n            x *= n+1-i\\n            y *= i\\n            x %= mod\\n            y %= mod\\n        else:\\n            ans *= n+1-i\\n            ans //= i\\n    ans = x*pow(y, mod-2, mod)%mod if mod else ans\\n    return ans\\n\\n\\ndef main():\\n    h, w, k = map(int, input().split())\\n    mod = pow(10,9)+7\\n    \\n    if w == 1:\\n        print(1)\\n        return\\n    \\n    comb_list = [[0]*11 for _ in range(11)]\\n    for i in range(11):\\n        for j in range(11):\\n            if i >= j:\\n                comb_list[i][j] = comb(i, j)\\n    \\n    key_list = [1]*10\\n    for i in range(1, 10):\\n        key = 0\\n        for j in range(1, 10):\\n            if i < j*2-1:\\n                break\\n            key += comb_list[i-j+1][j]\\n        key_list[i] += key\\n    \\n    \\n    dp = [[0]*w for _ in range(h)]\\n    for i in range(h):\\n        if i == 0:\\n            dp[0][0] = key_list[w-2]\\n            dp[0][1] = key_list[w-3] if w != 2 else 1\\n            continue\\n        if w == 2:\\n            dp[i][0] = (dp[i-1][0]+dp[i-1][1])%mod\\n            dp[i][1] = (dp[i-1][0]+dp[i-1][1])%mod\\n            continue\\n            \\n        for j in range(w):\\n            if j == 0:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j+1]*key_list[w-3])%mod\\n            elif j == w-1:\\n                dp[i][j] = (dp[i-1][j]*key_list[w-2]+dp[i-1][j-1]*key_list[w-3])%mod\\n            else:\\n                dp[i][j] = 0\\n                dp[i][j] += (dp[i-1][j-1]*key_list[max([0, j-2])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j]*key_list[max([0, j-1])]*key_list[max([0, w-2-j])])%mod\\n                dp[i][j] += (dp[i-1][j+1]*key_list[max([0, j-1])]*key_list[max([0, w-3-j])])%mod\\n                dp[i][j] %= mod\\n    print(dp[h-1][k-1])\\n                                                                           \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"\\\"\\\"\\\"\\n    dp[h][w]: h\\u756a\\u76ee\\u306erow(h: 0~H(\\u7d42\\u7740))\\u3067\\u68d2w(w: 0~W-1)\\u306b\\u3044\\u308b\\u72b6\\u614b\\u306b\\u306a\\u308b\\u305f\\u3081\\u306e\\u6a2a\\u7dda(0~h)\\u306e\\u7d44\\u5408\\u305b\\u6570\\n    dp[h][w] = A*dp[h-1][w-1] + B*dp[h-1][w] + C*dp[h-1][w+1] o(1000)\\n    A, B, C\\u306f\\u306a\\u3093\\u304b\\u3046\\u307e\\u3044\\u3053\\u3068\\u6c7a\\u3081\\u308c\\u305d\\u3046\\u3002(\\u5168\\u63a2\\u7d22\\u3067\\u3082max7*7*3\\u901a\\u308a)o(1000) \\n    \\u3069\\u3046\\u3084\\u3063\\u3066\\u3082O(10**6)\\u306b\\u306f\\u5165\\u308a\\u305d\\u3046\\n    \\\"\\\"\\\"\\ndef main():\\n    import sys\\n    input = sys.stdin.readline\\n    H, W, K = map(int, input().split())\\n    dp = [[0]*W for _ in range(H+1)]\\n    dp[0][0] = 1\\n    for h in range(1, H+1):\\n        for w in range(W):\\n            A, B, C = 0, 0, 0\\n            for i in range(2 ** (W-1)):\\n                lines = []\\n                for j in range(W-1):\\n                    if ((i >> j) & 1):\\n                        if lines and lines[-1]:\\n                            break\\n                        lines.append(True)\\n                    else:\\n                        lines.append(False)\\n                else:\\n                    if w-1 >= 0 and lines[w-1]:\\n                        A += 1\\n                    elif w <= W-2 and lines[w]:\\n                        C += 1\\n                    else:\\n                        B += 1\\n            if w-1 >= 0:\\n                dp[h][w] += dp[h-1][w-1] * A\\n            dp[h][w] += dp[h-1][w] * B\\n            if w+1 <= W-1:\\n                dp[h][w] += dp[h-1][w+1] * C\\n    print(dp[H][K-1] % (10**9+7))\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"h,w,k=map(int,input().split())\\nmod=10**9+7\\nR=[[],[1],[1,1],[2,1,2],[3,2,2,3],[5,3,4,3,5],[8,5,6,6,5,8],[13,8,10,9,10,8,13]]\\nT=[1,2,3,5,8,13,21,34]\\nr=R[w-1]\\nt=T[w-1]\\nA=[0]*w\\nA[0]=1\\nif w==1:\\n    print(1)\\nelse:\\n    for i in range(h):\\n        C=[0]*w\\n        for i in range(w):\\n            if i==0:\\n                C[0]+=(t-r[0])*A[0]\\n                C[1]+=r[0]*A[0]\\n            elif i==w-1:\\n                C[w-1]+=(t-r[w-2])*A[w-1]\\n                C[w-2]+=r[w-2]*A[w-1]\\n            else:\\n                C[i-1]+=r[i-1]*A[i]\\n                C[i]+=(t-r[i-1]-r[i])*A[i]\\n                C[i+1]+=r[i]*A[i]\\n        for i in range(w):\\n            C[i]%=mod\\n        A=C\\n    print(A[k-1])\", \"import sys\\n\\nh, w, k = map(int, input().split())\\nMOD = 1000000007\\n\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\n\\nfn = [1, 1, 2, 3, 5, 8, 13, 21, 34]\\n\\nif w == 1:\\n    print(1)\\n    return\\n\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        dp[i][j] = dp[i - 1][j] * fn[j] * fn[w - j - 1]\\n        if j < w - 1:\\n            dp[i][j] += dp[i - 1][j + 1] * fn[j] * fn[w - j - 2]\\n        if 0 < j:\\n            dp[i][j] += dp[i - 1][j - 1] * fn[j - 1] * fn[w - j - 1]\\n        dp[i][j] %= MOD\\n\\nprint(dp[-1][k - 1] % MOD)\", \"#!/usr/bin/env python\\n# -*- coding: utf-8 -*-\\n\\n#number of amidakuji\\n\\nh,w,k=list(map(int,input().split()))\\n\\ndp=[[0 for i in range(w+1)] for i in range(h+1)]\\n\\n#dp[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u3067j\\u3068\\u3044\\u3046\\u3068\\u3053\\u308d\\u306b\\u3044\\u304f\\u305f\\u3081\\u306b\\u5fc5\\u8981\\u306a\\u65b9\\u6cd5\\u306e\\u7dcf\\u548c\\n#\\u6c42\\u3081\\u308b\\u306e\\u306fdp[h][k]\\u3067\\u3042\\u308b\\ndp[0][1] = 1\\nmod=10**9+7\\nif w>1:\\n    for i in range(1,h+1):\\n        for j in range(2**(w-1)):\\n            st=format(j,\\\"0%ib\\\"%(w-1))\\n            flag=True\\n            for _ in range(w-2):\\n                if st[_]==\\\"1\\\" and st[_+1]==\\\"1\\\":\\n                    flag=False\\n            connect=[False for kyopuro in range(w+1)]\\n            if flag:\\n                li=[]\\n                for ss in range(w-1):\\n                    if st[ss]==\\\"1\\\":\\n                        li.append(ss+1)\\n                        connect[ss+1]=True\\n                        connect[ss+2]=True\\n\\n                for some in li:\\n                    dp[i][some+1]+=dp[i-1][some]\\n                    dp[i][some+1]%=mod\\n                    dp[i][some]+=dp[i-1][some+1]\\n                    dp[i][some]%=mod\\n                for number in range(1,w+1):\\n                    if connect[number]==False:\\n                        dp[i][number]+=dp[i-1][number]\\n                        dp[i][number]%=mod\\n    print((dp[h][k]%mod))\\n                \\n        \\nelse:\\n    print((1))\\n\\n\\n\", \"'''Yoshichi\\u306e\\u65e5\\u8a18\\n\\u3042\\u307f\\u3060\\u304f\\u3058\\u3002\\n0\\u672c\\u76ee\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\u3057\\u3001W\\u672c\\u306e\\u9577\\u3055H + 1\\u307e\\u3067\\u306b\\u3092\\u4efb\\u610f\\u306e\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u6642\\nK\\u672c\\u76ee\\u306b\\u305f\\u3069\\u308a\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306f\\u4f55\\u30d1\\u30bf\\u30fc\\u30f3\\u3042\\u308b\\u304b\\u7b54\\u3048\\u3088\\u3002\\n\\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u72b6\\u614b\\u3067\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u3092\\u5168\\u5217\\u6319\\u3057\\u3001DP(\\u30e1\\u30e2\\u5316\\u518d\\u5e30)\\u3092\\u7528\\u3044\\u3066\\u7b54\\u3048\\u308b\\u3002\\nx \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\ny \\u2192 \\u73fe\\u5728\\u306e\\u9032\\u307f\\u5177\\u5408\\nfor\\u5206\\u306ei \\u2192 \\u73fe\\u5728\\u306e\\u4f4d\\u7f6e\\u306b\\u3044\\u308b\\u6642\\u306e\\u7dda\\u306e\\u914d\\u7f6e\\u72b6\\u614b(1\\u304c\\u96a3\\u63a5\\u3078\\u3064\\u306a\\u304c\\u3063\\u3066\\u3044\\u308b\\u3068\\u304d)\\nfor\\u5206\\u306ej \\u2192 NG\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u5217\\u6319(\\u96a3\\u3078\\u7e4b\\u304c\\u3063\\u3066\\u3044\\u308b\\u304b\\u3064\\u3001\\n                   \\u6b21\\u306e\\u96a3\\u3078\\u3082\\u7dda\\u304c\\u5f15\\u304b\\u308c\\u3066\\u3044\\u308b\\u72b6\\u614b)\\n'''\\nfrom collections import defaultdict\\nh, w, k = map(int, input().split())\\nmemo = defaultdict(lambda:defaultdict(int))\\ndef dfs(x, y):\\n    if y == h:\\n        if x == k - 1:\\n            return 1\\n        else:\\n            return 0\\n    if y in memo[x]:\\n        return memo[x][y]\\n    ans = 0\\n    for i in range(1 << w - 1):\\n        flg = True\\n        for j in range(w - 2):\\n            if i & (1 << j) and i & (1 << j + 1):\\n                flg = False\\n                break\\n        if flg:\\n            nx = x\\n            if x > 0 and i & (1 << x - 1):\\n                nx = x - 1\\n            elif i & (1 << x):\\n                nx = x + 1\\n            ans += dfs(nx, y + 1)\\n            ans %= 1000000000 + 7\\n    memo[x][y] = ans\\n    return ans\\nprint(dfs(0, 0))\", \"#\\u5b9f\\u306fDP\\u3068\\u5272\\u308a\\u5207\\u308b\\u3068\\u308f\\u304b\\u308a\\u3084\\u3059\\u3044\\nmod=10**9+7\\nh,w,K=map(int,input().split())\\ndp=[[0]*w for j in range(h+1)]\\ndp[0][0]=1\\nfor i in range(1,h+1):\\n    for k in range(2**(w-1)):\\n        for l in range(w-2):\\n            if ((k>>l)&1) and ((k>>(l+1))&1):\\n                break\\n        else:\\n            for l in range(w):\\n                if l==0:\\n                    if ((k>>l)&1):\\n                        dp[i][l+1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                elif l==w-1:\\n                    if ((k>>(l-1))&1):\\n                        dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n                else:\\n                    if ((k>>l)&1) or ((k>>(l-1))&1):\\n                        if ((k>>l)&1):\\n                            dp[i][l+1]+=dp[i-1][l]\\n                        else:\\n                            dp[i][l-1]+=dp[i-1][l]\\n                    else:\\n                        dp[i][l]+=dp[i-1][l]\\n            dp[i][l]%=mod\\nprint(dp[h][K-1]%mod)\", \"H, W, K = list(map(int, input().split()))\\n\\nWW = [0]*(W+1)\\nWW[0] = 1\\nWW[1] = 1\\nfor i in range(2, W+1):\\n    WW[i] = WW[i-1] + WW[i-2]\\nDP = [[0]*W for i in range(H+1)]\\nDP[0][0] = 1\\nmod = 10**9+7\\nfor i in range(1, H+1):\\n    for j in range(W):\\n        if j == 0:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j+1]*WW[W-2]\\n        elif j == W-1:\\n            DP[i][j] = DP[i-1][j]*WW[W-1]\\n            if W > 1:\\n                DP[i][j] += DP[i-1][j-1]*WW[W-2]\\n        else:\\n            DP[i][j] = DP[i-1][j]*WW[j]*WW[W-1-j]+DP[i-1][j-1] * \\\\\\n                WW[j-1]*WW[W-1-j]+DP[i-1][j+1]*WW[j]*WW[W-2-j]\\n\\n        DP[i][j] %= mod\\n# print(DP, WW)\\nprint((DP[-1][K-1]))\\n\", \"import sys\\nfrom itertools import product\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    H, W, K = list(map(int, readline().split()))\\n\\n    A = product((0, 1), repeat=W - 1)\\n    B = []\\n    for bars in A:\\n        ok = True\\n        for i in range(W - 2):\\n            if bars[i] and bars[i + 1]:\\n                ok = False\\n                break\\n        if ok:\\n            B.append(bars)\\n\\n    dp = [0] * W\\n    dp[0] = 1\\n\\n    for _ in range(H):\\n        dp, dp_prev = [0] * W, dp\\n        for bars in B:\\n            for i in range(W):\\n                if i > 0 and bars[i - 1]:\\n                    dp[i - 1] = (dp[i - 1] + dp_prev[i]) % MOD\\n                elif i < W - 1 and bars[i]:\\n                    dp[i + 1] = (dp[i + 1] + dp_prev[i]) % MOD\\n                else:\\n                    dp[i] = (dp[i] + dp_prev[i]) % MOD\\n\\n    print((dp[K - 1]))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h,w,K=map(int,input().split())\\nmod=10**9+7\\ndp=[[0 for i in range(w)] for j in range(h+1)]\\nfor i in range(2**(w-1)):dp[0][0]=1\\nfor i in range(1,h+1):\\n    for j in range(2**(w-1)):\\n        s=format(j,\\\"b\\\").zfill(w-1)\\n        if \\\"11\\\" in s:continue\\n        exchanged=[False]*w\\n        for k in range(w-1):\\n            if s[k]==\\\"1\\\":\\n                dp[i][k]+=dp[i-1][k+1]\\n                dp[i][k+1]+=dp[i-1][k]\\n                dp[i][k]%=mod\\n                dp[i][k+1]%=mod\\n                exchanged[k]=True\\n                exchanged[k+1]=True\\n        for k in range(w):\\n            if exchanged[k]:continue\\n            dp[i][k]+=dp[i-1][k]\\n            dp[i][k]%=mod\\n\\nprint(dp[-1][K-1])\", \"# |-| | | | |\\n# \\u306e\\u3088\\u3046\\u306b\\u4e00\\u756a\\u5de6\\u306e\\u4e00\\u672c\\u304c\\u6c7a\\u307e\\u3063\\u305f\\u3068\\u304d\\u3001\\u6b8b\\u308a\\u306e\\n#     | | | |\\n# \\u306b\\u306f\\u3001\\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304c3\\u3064\\u3042\\u308b\\n# \\u7dda\\u3092\\u5f15\\u304f\\u5834\\u6240\\u304cN\\u500b\\u3042\\u308b\\u3068\\u304d\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\u306e\\u7d44\\u307f\\u5408\\u308f\\u305b\\u306f\\n# A[1] = 2, A[2] = 3, A[N] = A[N - 2] + A[N - 1]\\n# \\u306e\\u307b\\u307c\\u30d5\\u30a3\\u30dc\\u30ca\\u30c3\\u30c1\\u6570\\u5217\\n# 2,3,5,8,13...\\n# \\u3053\\u308c\\u3092\\u3042\\u3089\\u304b\\u3058\\u3081\\u6700\\u5927\\u6570\\u3076\\u3093\\u6c42\\u3081\\u3066\\u304a\\u304f\\n# \\u6a2a\\u68d2W\\u672c\\u306b\\u5bfe\\u3057\\u3066\\u3001W - 1\\u500b\\u306e\\u9593\\u9694\\u304c\\u3042\\u308a\\u3001\\u305d\\u306e\\u3046\\u3061\\u7aef\\u306e2\\u304b\\u6240\\u304c\\u57cb\\u307e\\u3063\\u305f\\u72b6\\u614b\\u304c\\u6700\\u5927\\u306a\\u306e\\u3067W - 3\\n# \\u3053\\u308c\\u3092\\u6c42\\u3081\\u308b\\n\\nimport sys\\nreadline = sys.stdin.readline\\n\\nDIV = 10 ** 9 + 7\\nH,W,K = map(int,readline().split())\\n\\nP = [0] * max(W - 2 + 1,3)\\nP[1],P[2] = 2,3\\nfor i in range(3, len(P)):\\n  P[i] = P[i - 1] + P[i - 2]\\n  \\n# [0, 2, 3, 5, 8, 13, 21, 34, ...]\\n\\n# \\u901a\\u3089\\u306a\\u3044\\u7dda\\u306f\\u4e0a\\u8a18\\u3067\\u7b97\\u51fa\\u3067\\u304d\\u308b\\u306e\\u3067\\u3001\\u901a\\u308b\\u7dda\\u3092\\u8003\\u3048\\u308b\\n# \\u4e0a\\u304b\\u3089i\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001\\u7e26\\u68d2j\\u306b\\u3044\\u308b\\u3068\\u304d\\u306e\\u5834\\u5408\\u306e\\u6570\\u3067DP\\u3059\\u308b\\n\\ndp = [[0 for j in range(W)] for i in range(H + 1)]\\n\\ndp[0][0] = 1 # \\u4e0a\\u304b\\u30890\\u6bb5\\u76ee\\u3092\\u7d42\\u3048\\u305f\\u6642\\u70b9(\\u307e\\u3060\\u4f55\\u3082\\u3057\\u3066\\u3044\\u306a\\u3044)\\u3068\\u304d\\u306b0\\u306b\\u3044\\u308b\\u306e\\u30671\\u901a\\u308a\\n\\ndef calc(L,R): # L\\u3068R\\u306e\\u9593\\u306b\\u7dda\\u3092\\u5f15\\u3044\\u305f\\u5834\\u5408\\u306e\\u3001\\u6b8b\\u308a\\u306e\\u7dda\\u306e\\u5f15\\u304d\\u65b9\\n#  print(\\\"calc L\\\",L,\\\"R\\\",R)\\n  res = 1\\n  if 1 < L:\\n    # | | |-| L\\u304c2\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1 (L - 1)\\u3067\\u304d\\u308b\\n    res *= P[L - 1]\\n#    print(\\\"P[L - 2]\\\",P[L - 2],\\\"res\\\",res)\\n    res %= DIV\\n  if (W - 1) - (R + 1) >= 1:\\n    # |-| | | R + 2 = W - 1\\u306e\\u3068\\u304d\\u306f\\u3058\\u3081\\u3066\\u30b9\\u30da\\u30fc\\u30b9\\u304c1(W - R)\\u3067\\u304d\\u308b\\n#    print(min((W - 1) - (R + 1),len(P)))\\n    res *= P[(W - 1) - (R + 1)]\\n#    print(\\\"P[(W - 1) - (R + 1)]\\\",min((W - 1) - (R + 1),len(P)),\\\"res\\\",res)\\n    res %= DIV\\n#  print(res,\\\"\\u901a\\u308a\\\")\\n  return res\\n  \\n# \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\u3001\\u4f55\\u3082\\u3057\\u306a\\u3044\\u3001\\u306e3\\u901a\\u308a\\u3067DP\\nfor i in range(H):\\n  for j in range(W):\\n    # \\u53f3\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j + 1 < W:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n      dp[i + 1][j + 1] += dp[i][j] * calc(j, j + 1)\\n      dp[i + 1][j + 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j + 1\\\",j + 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j + 1]\\\",dp[i + 1][j + 1])\\n    # \\u5de6\\u306b\\u79fb\\u52d5\\u3059\\u308b\\n    if j - 1 >= 0:\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n      dp[i + 1][j - 1] += dp[i][j] * calc(j - 1,j)\\n      dp[i + 1][j - 1] %= DIV\\n#      print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i + 1\\\",i + 1,\\\"j - 1\\\",j - 1,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j - 1]\\\",dp[i + 1][j - 1])\\n    # \\u4f55\\u3082\\u3057\\u306a\\u3044\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3059\\u308b dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n    dp[i + 1][j] += dp[i][j] * calc(j,j) # \\u5de6\\u7aef\\u3082\\u53f3\\u7aef\\u3082\\u540c\\u3058\\n    dp[i + 1][j] % DIV\\n#    print(\\\"i\\\",i,\\\"j\\\",j,\\\"\\u304b\\u3089i\\\",i,\\\"j\\\",j,\\\"\\u306b\\u79fb\\u52d5\\u3057\\u305f dp[i][j]\\\",dp[i][j],\\\"dp[i + 1][j]\\\",dp[i + 1][j])\\n#  for d in dp:\\n#    print(dp)\\n\\n    \\n# i = H\\u6bb5\\u76ee\\u307e\\u3067\\u7d42\\u3048\\u305f\\u6642\\u70b9\\u3067\\u3001j = K - 1\\u306b\\u3044\\u308b\\u5834\\u5408\\u306e\\u6570\\nprint(dp[H][K - 1] % DIV)\", \"def main():\\n    mod = 10**9 + 7\\n    h, w, k = map(int, input().split())\\n\\n    if w == 1:\\n        print(1)\\n        return\\n    if w == 2:\\n        print(pow(2, h-1, mod))\\n        return\\n\\n    k -= 1\\n\\n    fibo = [1, 2, 3, 5, 8, 13, 21]\\n\\n    dp = [0] * w\\n    dp[0] = 1\\n    for _ in range(h):\\n        new_dp = [0] * w\\n        new_dp[0] = (dp[0] * fibo[w-2] + dp[1] * fibo[w-3]) % mod\\n        new_dp[1] = (dp[0] * fibo[w-3]) % mod\\n        new_dp[w-1] = (dp[w-1] * fibo[w-2] + dp[w-2] * fibo[w-3]) % mod\\n        new_dp[w-2] += (dp[w-1] * fibo[w-3]) % mod\\n        for i in range(1, w-1):\\n            new_dp[i] += ((fibo[i-1] * fibo[w-i-2]) * dp[i]) % mod\\n        for i in range(1, w-2):\\n            new_dp[i] += (fibo[i-1] * fibo[w-i-3]) * dp[i+1]\\n            new_dp[i] %= mod\\n            new_dp[i+1] += (fibo[i-1] * fibo[w-i-3]) * dp[i]\\n            new_dp[i+1] %= mod\\n        dp = new_dp\\n\\n    print(dp[k] % mod)\\n\\nmain()\", \"#!/usr/bin/env python3\\nfrom itertools import product\\nimport sys\\n\\ntry:\\n    from typing import List, Tuple\\nexcept ImportError:\\n    pass\\n\\n\\nMOD = 1000000007  # type: int\\n\\n\\ndef isvalid(ptn: \\\"Tuple[bool]\\\"):\\n    return not any(h1 and h2 for h1, h2 in zip(ptn, ptn[1:]))\\n\\n\\ndef solve(H: int, W: int, K: int):\\n    validptns = [\\n        ptn\\n        for ptn in product((False, True), repeat=W - 1)\\n        if isvalid(ptn)\\n    ]  # type: List[Tuple[bool]]\\n    dp = [1 if i == K - 1 else 0 for i in range(W)]  # type: List[int]\\n    for _ in range(H):\\n        newdp = [0] * W  # type: List[int]\\n        for ptn in validptns:\\n            for s in range(W):\\n                t = s\\n                if s < W - 1 and ptn[s]:\\n                    t = s + 1\\n                elif s > 0 and ptn[s - 1]:\\n                    t = s - 1\\n                newdp[t] += dp[s]\\n                newdp[t] %= MOD\\n        dp = newdp\\n\\n    print((dp[0]))\\n\\n\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    H = int(next(tokens))  # type: int\\n    W = int(next(tokens))  # type: int\\n    K = int(next(tokens))  # type: int\\n    solve(H, W, K)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"h, w, k = list(map(int, input().split()))\\np = 10**9+7\\n# DP[i][j]=i\\u6bb5\\u76ee\\u307e\\u3067\\u898b\\u30660\\u304b\\u3089j\\u306b\\u7740\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u6570\\nDP = [[0 for j in range(w+1)] for i in range(h+1)]\\nDP[0][0] = 1\\n# F[k]=k\\u500b\\u306e\\u67a0\\u306b\\u96a3\\u308a\\u5408\\u308f\\u306a\\u3044\\u3088\\u3046\\u306b\\u7dda\\u3092\\u5f15\\u304f\\u30d1\\u30bf\\u30fc\\u30f3\\u306e\\u6570\\nF = [1, 1, 2, 3, 5, 8, 13, 21]\\nfor i in range(h):\\n    for j in range(w):\\n        a = DP[i][j-1]*F[j-1]*F[w-1-j]\\n        b = DP[i][j]*F[j]*F[w-1-j]\\n        c = DP[i][j+1]*F[j]*F[w-2-j]\\n        DP[i+1][j] = (a+b+c) % p\\nprint((DP[h][k-1]))\\n\", \"def f(i):\\n  if i == W-1:\\n    for j in range(W-2):\\n      if s[j] == s[j+1] == 1:\\n        return\\n    nonlocal x\\n    for j in range(W):\\n      if j == 0:\\n        if s[0] == 1:\\n          x[0][1] += 1\\n        else:\\n          x[0][0] += 1\\n      elif j == W - 1:\\n        if s[W-2] == 1:\\n          x[W-1][W-2] += 1\\n        else:\\n          x[W-1][W-1] += 1\\n      else:\\n        if s[j-1] == 1:\\n          x[j][j-1] += 1\\n        elif s[j] == 1:\\n          x[j][j+1] += 1\\n        else:\\n          x[j][j] += 1 \\n    return\\n  s[i] = 1\\n  f(i + 1)\\n  s[i] = 0\\n  f(i + 1)\\n\\nH,W,K=map(int, input().split())\\nMOD = pow(10, 9) + 7\\ns = [0] * (W - 1)\\nx = [[0] * W for _ in range(W)]\\nif not W == 1:\\n  f(0)\\nelse:\\n  print(1)\\n  return\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(1,H+1):\\n  for j in range(W):\\n    for l in range(W):\\n      dp[i][j]+=dp[i-1][l]*x[l][j]\\n      dp[i][j]%=MOD\\nprint(dp[H][K-1])\", \"import sys\\ninput=sys.stdin.readline\\nINF = 10**9\\nMOD = 10**9 + 7\\n\\ndef main():\\n    h,w,k = list(map(int,input().split()))\\n\\n    dp = [[0]*w for _ in range(h+1)]\\n    dp[0][0] = 1\\n\\n    for i in range(h):\\n        for bit in range(1<<(w-1)):\\n            flag = False\\n            before = -2\\n            line = [0] * (w-1)\\n            for j in range(w-1):\\n                if (bit>>j)&1:\\n                    if  before + 1 == j:\\n                        flag = True\\n                        break\\n                    \\n                    else:\\n                        before = j\\n                        line[j] = 1\\n  \\n\\n            if flag:\\n                continue\\n\\n            j = 0\\n            while j < w:\\n                if j == w-1:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    break\\n                if line[j]:\\n                    dp[i+1][j] += dp[i][j+1]\\n                    dp[i+1][j] %= MOD\\n                    dp[i+1][j+1] += dp[i][j]\\n                    dp[i+1][j+1] %= MOD\\n                    j += 2\\n                else:\\n                    dp[i+1][j] += dp[i][j]\\n                    dp[i+1][j] %= MOD\\n                    j += 1\\n\\n    print((dp[-1][k-1]%MOD))\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"H,W,K = list(map(int,input().split()))\\nMOD = 10**9+7\\n\\ndp = [[0]*W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for b in range(1<<(W-1)):\\n        if '11' in bin(b): continue\\n        for k in range(W):\\n            if k and b&(1<<(k-1)):\\n                dp[i+1][k-1] += dp[i][k]\\n            elif b&(1<<k):\\n                dp[i+1][k+1] += dp[i][k]\\n            else:\\n                dp[i+1][k] += dp[i][k]\\n\\nprint((dp[-1][K-1] % MOD))\\n\", \"#!/usr/bin/env python3\\n\\nimport itertools\\nmod = 1000000007\\n\\nh, w, k = list(map(int, input().split()))\\n\\ndp = [[0]*(w) for _ in range(h+1)]\\n\\ndp[0][0] = 1\\n\\nfor h_ in range(1, h+1):\\n    for bridges in itertools.product([0, 1], repeat=w-1):\\n        flag = 0\\n        for j in range(len(bridges)-1):\\n            if bridges[j] == 1 and bridges[j+1] == 1:\\n                flag = 1\\n                continue\\n        if flag == 1:\\n            continue\\n        # print(bridges)\\n        for w_ in range(w):\\n            if w_ > 0:\\n                if bridges[w_-1] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_-1] % mod\\n                    continue\\n            if w_ < w-1:\\n                if bridges[w_] == 1:\\n                    dp[h_][w_] += dp[h_-1][w_+1] % mod\\n                    continue\\n            dp[h_][w_] += dp[h_-1][w_] % mod\\n\\n# print(dp)\\n\\nprint((dp[-1][k-1] % mod))\\n\", \"h,w,k=map(int,input().split())\\nf=[1,1,2,3,5,8,13,21]\\nm=10**9+7\\ndp=[[1]+[0]*(w-1)for i in range(h+1)]\\nh=0if w==1else h\\nfor i in range(1,h+1):\\n for j in range(w):\\n  if j==0:dp[i][0]=(dp[i-1][0]*f[w-1] + dp[i-1][1]*f[w-2])%m;\\n  elif j==w-1:dp[i][w-1]=(dp[i-1][w-1]*f[w-1] + dp[i-1][w-2]*f[w-2])%m\\n  else:dp[i][j]=(dp[i-1][j]*f[j]*f[w-j-1]+dp[i-1][j-1]*f[j-1]*f[w-j-1]+dp[i-1][j+1]*f[j]*f[w-j-2])%m\\nprint(dp[h][k-1])\", \"H, W, K = list(map(int, input().split()))\\n\\nmod = 10**9 + 7\\ndp = [[0] * W for _ in range(H+1)]\\ndp[0][0] = 1\\nfor i in range(H):\\n    for j in range(W):\\n        for bit in range(1 << (W-1)):\\n            ok = True\\n            for k in range(W-2):\\n                if bit & (1 << k) and bit & (1 << (k+1)):\\n                    ok = False\\n            if not ok:\\n                continue\\n\\n            jj = j\\n            if j > 0 and bit & (1 << (j-1)):\\n                jj -= 1\\n            elif j < W - 1 and bit & (1 << j):\\n                jj += 1\\n            dp[i+1][jj] += dp[i][j]\\n            dp[i+1][jj] %= mod\\n\\n\\nprint((dp[H][K-1]))\\n\", \"def main():\\n    h, w, k = list(map(int, input().split()))\\n\\n    dp = [[0] * (w + 2) for _ in range(h + 1)]\\n    dp[0][1] = 1\\n\\n    c = [1, 1, 2, 3, 5, 8, 13, 21]\\n\\n    for i in range(1, h + 1):\\n        for j in range(1, w + 1):\\n            dp[i][j] = c[j - 1] * c[w - j] * dp[i - 1][j] + c[j - 1] * c[w - j - 1] * dp[i - 1][j + 1] + c[j - 2] * c[w - j] * dp[i - 1][j - 1]\\n\\n    print((dp[h][k] % (10 ** 9 + 7)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def f(i):\\n    if i == w - 1:\\n        for j in range(w - 2):\\n            if s[j] == s[j + 1] == 1:\\n                return\\n        nonlocal x\\n        for j in range(w):\\n            if j == 0:\\n                if s[0] == 1:\\n                    x[0][1] += 1\\n                else:\\n                    x[0][0] += 1\\n            elif j == w - 1:\\n                if s[w - 2] == 1:\\n                    x[w - 1][w - 2] += 1\\n                else:\\n                    x[w - 1][w - 1] += 1\\n            else:\\n                if s[j - 1] == 1:\\n                    x[j][j - 1] += 1\\n                elif s[j] == 1:\\n                    x[j][j + 1] += 1\\n                else:\\n                    x[j][j] += 1 \\n        return\\n    s[i] = 1\\n    f(i + 1)\\n    s[i] = 0\\n    f(i + 1)\\n\\nh, w, k = map(int, input().split())\\nmod = pow(10, 9) + 7\\ns = [0] * (w - 1)\\nx = [[0] * w for _ in range(w)]\\nif not w == 1:\\n    f(0)\\nelse:\\n    print(1)\\n    return\\ndp = [[0] * w for _ in range(h + 1)]\\ndp[0][0] = 1\\nfor i in range(1, h + 1):\\n    for j in range(w):\\n        for l in range(w):\\n            dp[i][j] += dp[i - 1][l] * x[l][j]\\n            dp[i][j] %= mod\\nprint(dp[h][k - 1])\"]",
        "difficulty": "interview",
        "input": "92 8 6\n",
        "output": "127339651\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc113/tasks/abc113_d"
    },
    {
        "id": 230,
        "task_id": 1663,
        "test_case_id": 1,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "107\n",
        "output": "42\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 231,
        "task_id": 1663,
        "test_case_id": 2,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "100500100500\n",
        "output": "428101984\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 232,
        "task_id": 1663,
        "test_case_id": 3,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "1\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 233,
        "task_id": 1663,
        "test_case_id": 4,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "22098174938\n",
        "output": "647942793\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 234,
        "task_id": 1663,
        "test_case_id": 5,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "1403665305\n",
        "output": "765601706\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 235,
        "task_id": 1663,
        "test_case_id": 6,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "75109\n",
        "output": "37263\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 236,
        "task_id": 1663,
        "test_case_id": 7,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "2\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 237,
        "task_id": 1663,
        "test_case_id": 8,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "68947\n",
        "output": "39697\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 238,
        "task_id": 1663,
        "test_case_id": 9,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "117223418\n",
        "output": "132461189\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 239,
        "task_id": 1663,
        "test_case_id": 10,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "631782284\n",
        "output": "587995301\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 240,
        "task_id": 1663,
        "test_case_id": 11,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "999999999\n",
        "output": "987654276\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 241,
        "task_id": 1663,
        "test_case_id": 12,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "4858009126122882427521828524340976437888697258902645644032745782648911868553409977869361928273673714911638246440203138033678\n",
        "output": "327724338\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 242,
        "task_id": 1663,
        "test_case_id": 13,
        "question": "Sometimes it is not easy to come to an agreement in a bargain. Right now Sasha and Vova can't come to an agreement: Sasha names a price as high as possible, then Vova wants to remove as many digits from the price as possible. In more details, Sasha names some integer price $n$, Vova removes a non-empty substring of (consecutive) digits from the price, the remaining digits close the gap, and the resulting integer is the price.\n\nFor example, is Sasha names $1213121$, Vova can remove the substring $1312$, and the result is $121$.\n\nIt is allowed for result to contain leading zeros. If Vova removes all digits, the price is considered to be $0$.\n\nSasha wants to come up with some constraints so that Vova can't just remove all digits, but he needs some arguments supporting the constraints. To start with, he wants to compute the sum of all possible resulting prices after Vova's move.\n\nHelp Sasha to compute this sum. Since the answer can be very large, print it modulo $10^9 + 7$.\n\n\n-----Input-----\n\nThe first and only line contains a single integer $n$ ($1 \\le n < 10^{10^5}$).\n\n\n-----Output-----\n\nIn the only line print the required sum modulo $10^9 + 7$.\n\n\n-----Examples-----\nInput\n107\n\nOutput\n42\n\nInput\n100500100500\n\nOutput\n428101984\n\n\n\n-----Note-----\n\nConsider the first example.\n\nVova can choose to remove $1$, $0$, $7$, $10$, $07$, or $107$. The results are $07$, $17$, $10$, $7$, $1$, $0$. Their sum is $42$.",
        "solutions": "[\"s=input();M=10**9+7;o=u=v=0;n=len(s)\\nfor i in range(n):c=int(s[i]);u+=v;v=(10*v+c)%M;o+=pow(10,n-i-1,M)*((i*i+i)//2*c+u)\\nprint(o%M)\", \"mod = int(1e9+7)\\ns = input()\\nn = len(s)\\npref = [0] * (n+1)\\nfor i in range(n):\\n    pref[i+1] = (int(s[i]) + pref[i]*10) % mod\\nfor i in range(n):\\n    pref[i+1] = (pref[i+1] + pref[i]) % mod\\n\\nres = 0\\nacc = 0\\nfor i in range(n, 0, -1):\\n    res += pref[i-1] * pow(10, n-i, mod) + i*acc\\n    res %= mod\\n    acc = acc + int(s[i-1]) * pow(10, n-i, mod) % mod\\nprint(res)\\n\", \"import sys\\nz=sys.stdin.readline\\nM=10**9+7\\nn=[*map(int,z().strip())]\\nl=len(n)\\np=[0]\\nfor i in range(l):p.append(p[-1]+n[i])\\ns=0\\nv=(l*l-l)//2\\nd=1\\nfor i in range(1,l):\\n    r=p[l-i]*i+v*n[l-i]\\n    s=(s+r*d)%M\\n    d=(d*10)%M\\n    v-=l-i\\nprint(s)\", \"n = input().strip()\\nM = 1000000007\\nl = len(n)\\n\\na = 0\\nb = 0\\nfor i,c in enumerate(n[::-1]):\\n\\tc = int(c)\\n\\tp = l - 1 - i\\n\\ta += p * (p + 1) // 2 * c * pow(10, i, M)\\n\\ta += b * c\\n\\ta %= M\\n\\tb += (i+1) * pow(10, i, M)\\n\\tb %= M\\nprint(a)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nMOD = 10 ** 9 + 7\\nN = 10 ** 5 + 100\\n\\nfact = [0 for _ in range(N)]\\ninvfact = [0 for _ in range(N)]\\nfact[0] = 1\\nfor i in range(1, N):\\n    fact[i] = fact[i - 1] * i % MOD\\n\\ninvfact[N - 1] = pow(fact[N - 1], MOD - 2, MOD)\\n\\nfor i in range(N - 2, -1, -1):\\n    invfact[i] = invfact[i + 1] * (i + 1) % MOD\\ndef nCk(n, k):\\n    if k < 0 or n < k:\\n        return 0\\n    else:\\n        return fact[n] * invfact[k] * invfact[n - k] % MOD\\n\\ndef main():\\n    n = input().strip()\\n    ans = 0\\n    l = len(n)\\n    plus = 0\\n    plus2 = 1\\n    plus3 = 1\\n    for i, str_num in enumerate(n[::-1]):\\n        num = int(str_num)\\n        j = l - i - 1\\n        ans += nCk(j + 1, 2) * pow(10, i, MOD) * num\\n        ans %= MOD\\n        ans += num * plus\\n        ans %= MOD\\n        plus += plus2 * plus3\\n        plus2 *= 10\\n        plus3 += 1\\n        plus %= MOD\\n        plus2 %= MOD\\n        plus3 %= MOD\\n\\n    print(ans)\\n        \\n        \\nmain()\\n\", \"n = list(input())\\nl = len(n)\\nx = 1\\ny = 0\\nz = 0\\nmod = pow(10, 9) + 7\\nans = 0\\nfor i in range(l):\\n    m = int(n[l - i - 1])\\n    ans += x * m * ((l - i) * (l - i - 1) // 2)\\n    ans %= mod\\n    ans += z * m\\n    ans %= mod\\n    y += 1\\n    z += x * y\\n    z %= mod\\n    x *= 10\\n    x %= mod\\nprint(ans)\", \"import sys\\n\\ndef minp():\\n\\treturn sys.stdin.readline().strip()\\n\\ndef mint():\\n\\treturn int(minp())\\n\\ndef mints():\\n\\treturn list(map(int, minp().split()))\\n\\n#from math import ceil\\n\\ndef solve():\\n\\tMOD = int(1e9+7)\\n\\ts = minp()\\n\\tn = len(s)\\n\\tp = [0]*(n+1)\\n\\tpp = [1]*(n+1)\\n\\tp10 = 1\\n\\tfor i in range(1,n+1):\\n\\t\\tp[i] = (p[i-1]+p10*i)%MOD\\n\\t\\tpp[i] = p10\\n\\t\\tp10 = (p10*10)%MOD\\n\\tres = (int(s[0])*p[n-1])%MOD\\n\\t#print(res)\\n\\tfor i in range(1,n):\\n\\t\\t#print(int(s[i])*pp[n-i],int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))\\n\\t\\tres = (res+int(s[i])*(p[n-1-i] + pp[n-i]*(i)*(i+1)//2))%MOD\\n\\tprint(res)\\n\\n#for i in range(mint()):\\nsolve()\\n\", \"import sys\\ninput = sys.stdin.readline\\nfrom itertools import accumulate\\n\\nS=input().strip()\\nmod=10**9+7\\nLEN=len(S)\\n\\nANS=[0]*(LEN+1)\\nANS2=[0]*(LEN+1)\\nANS3=[0]*(LEN+1)\\n\\nfor i in range(LEN):\\n    x=int(S[LEN-1-i])\\n    \\n    k=LEN-i-1\\n    p=k*(k+1)//2\\n    ANS[i]+=x*p\\n\\n    \\n    ANS2[0]+=x\\n    ANS2[i]-=x\\n    ANS3[i]-=i*x\\n\\nANS2=list(accumulate(ANS2))\\nfor i in range(LEN+1):\\n    ANS2[i]+=ANS3[i]\\nANS2=list(accumulate(ANS2))\\n\\n#print(ANS)\\n#print(ANS2)\\n\\nA=0\\nfor i in range(LEN):\\n    A+=(ANS[i]+ANS2[i])*pow(10,i,mod)\\n    A%=mod\\n\\nprint(A)\\n\", \"s=input()\\nans=0\\nmod=10**9+7\\nn=len(s)\\nps=[0]\\ncp=1\\nfor i in range(n-1,-1,-1):\\n\\tps.append((ps[-1]+int(s[i])*cp)%mod)\\n\\tcp=cp*10%mod\\nps.reverse()\\nprefs=0\\nlastpref=0\\nfor i in range(n):\\n\\tnextdigs=ps[i+1]\\n\\tans=(ans+prefs*pow(10,n-i-1,mod)%mod+nextdigs*(i+1))%mod\\n\\tlastpref=(lastpref*10+int(s[i]))%mod\\n\\tprefs=(prefs+lastpref)%mod\\nprint(ans)\", \"s = [int(c) for c in input()][::-1]\\nn = len(s)\\n\\nmod = 1000000007\\ndef inv(x):\\n    return pow(x, mod - 2, mod)\\nteninv = inv(10)\\n\\nP = [0]\\np = 1\\nfor x in s:\\n    P.append((P[-1] + x*p) % mod)\\n    p = p*10 % mod\\n\\nQ = [0]\\nfor i in range(n+1):\\n    Q.append((Q[-1] + P[i]*pow(teninv, i, mod))%mod) \\n\\ns = 0\\nfor l in range(n):\\n    first = P[l] - P[0]\\n    s += (n - l)*first % mod\\n    s += P[n] * inv(9) % mod * (1 - inv(pow(10, n-l, mod))) % mod\\n    d = Q[n+1] - Q[l+1]\\n\\n    s = (s - d*inv(pow(teninv,l,mod))%mod) % mod\\nprint(s%mod)\\n\", \"def inv(x):\\n    return pow(x,1000000005,1000000007)\\ns=input()\\nans=0\\nn=len(s)\\nfor i in range(n-1,-1,-1):\\n    z=pow(10,n-1-i,1000000007)*int(s[i])\\n    z=z*((i)*(i+1))//2\\n    ans+=z\\n    ans%=1000000007\\n    k=n-1-i\\n    op=0\\n    op+=(pow(10,k,1000000007)*(9*k-1))\\n    op%=1000000007\\n    op+=1\\n    op=op*inv(81)\\n    op%=1000000007\\n    op=op*int(s[i])\\n    ans+=op\\n    ans%=1000000007\\nprint(ans)\\n\", \"import sys\\nimport random\\nfrom fractions import Fraction\\nfrom math import *\\n \\ndef input():\\n    return sys.stdin.readline().strip()\\n \\ndef iinput():\\n    return int(input())\\n\\ndef finput():\\n    return float(input())\\n\\ndef tinput():\\n    return input().split()\\n\\ndef linput():\\n    return list(input())\\n \\ndef rinput():\\n    return list(map(int, tinput()))\\n\\ndef fiinput():\\n    return list(map(float, tinput()))\\n \\ndef rlinput():\\n    return list(map(int, input().split()))\\ndef trinput():\\n    return tuple(rinput())\\n\\ndef srlinput():\\n    return sorted(list(map(int, input().split())))\\n\\ndef NOYES(fl):\\n    if fl:\\n        print(\\\"NO\\\")\\n    else:\\n        print(\\\"YES\\\")\\ndef YESNO(fl):\\n    if fl:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n    \\ndef main():\\n    #n = iinput()\\n    #k = iinput() \\n    #m = iinput() \\n    #n = int(sys.stdin.readline().strip()) \\n    #n, k = rinput()\\n    #n, m = rinput()\\n    #m, k = rinput()\\n    #n, k, m = rinput()\\n    #n, m, k = rinput()\\n    #k, n, m = rinput()\\n    #k, m, n = rinput() \\n    #m, k, n = rinput()\\n    #m, n, k = rinput()\\n    #q = rlinput()\\n    #q = linput()\\n    s = input(); n = len(s)\\n    mod = int(1e9) + 7\\n    q = [0 for i in range(100100)]\\n    w = [0 for i in range(100100)]\\n    q[0] = 1; w[0] = 1; res = 1\\n    for i in range(1, 100100):\\n        res = (res * 10) % mod\\n        q[i] = q[i - 1] + res\\n        q[i] %= mod\\n        w[i] = w[i - 1] * 10\\n        w[i] %= mod\\n    l, res, r = 0, 0, 0\\n    for i in range(n - 1):\\n        l *= 10\\n        l += int(s[i])\\n        l %= mod\\n        res += l * q[n - 2 - i] % mod\\n        res %= mod\\n    for i in range(n - 1, 0, -1):\\n        r += w[n - 1 - i] * int(s[i])\\n        r %= mod\\n        res += r * i % mod\\n        res %= mod\\n    print(res)\\n    \\n    \\n        \\n\\n            \\n        \\n    \\n                \\n    \\n    \\n    \\n            \\n    \\n        \\n    \\n\\nfor i in range(1):\\n    main()\\n\"]",
        "difficulty": "interview",
        "input": "8965386960152006591809984225293942587326198640196778753062530086068570301147990585166466362559764049574872079130299053141640988917032932849227639889087132375588014401073399470647913290891872985556578647384795621167114212145376047533262867548922177976893208381027336566491937276936855437908355709002439339533374267351887912532392361653303035981314497638285914959457892764665757142443996340214934182387692044841385048241173328760613302269019024624710759003987341917110042233934\n",
        "output": "36469735\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1422/C"
    },
    {
        "id": 243,
        "task_id": 2293,
        "test_case_id": 1,
        "question": "Dora the explorer has decided to use her money after several years of juicy royalties to go shopping. What better place to shop than Nlogonia?\n\nThere are $n$ stores numbered from $1$ to $n$ in Nlogonia. The $i$-th of these stores offers a positive integer $a_i$.\n\nEach day among the last $m$ days Dora bought a single integer from some of the stores. The same day, Swiper the fox bought a single integer from all the stores that Dora did not buy an integer from on that day.\n\nDora considers Swiper to be her rival, and she considers that she beat Swiper on day $i$ if and only if the least common multiple of the numbers she bought on day $i$ is strictly greater than the least common multiple of the numbers that Swiper bought on day $i$.\n\nThe least common multiple (LCM) of a collection of integers is the smallest positive integer that is divisible by all the integers in the collection.\n\nHowever, Dora forgot the values of $a_i$. Help Dora find out if there are positive integer values of $a_i$ such that she beat Swiper on every day. You don't need to find what are the possible values of $a_i$ though.\n\nNote that it is possible for some values of $a_i$ to coincide in a solution.\n\n\n-----Input-----\n\nThe first line contains integers $m$ and $n$ ($1\\leq m \\leq 50$, $1\\leq n \\leq 10^4$) — the number of days and the number of stores.\n\nAfter this $m$ lines follow, the $i$-th line starts with an integer $s_i$ ($1\\leq s_i \\leq n-1$), the number of integers Dora bought on day $i$, followed by $s_i$ distinct integers, the indices of the stores where Dora bought an integer on the $i$-th day. The indices are between $1$ and $n$.\n\n\n-----Output-----\n\nOutput must consist of a single line containing \"possible\" if there exist positive integers $a_i$ such that for each day the least common multiple of the integers bought by Dora is strictly greater than the least common multiple of the integers bought by Swiper on that day. Otherwise, print \"impossible\".\n\nNote that you don't have to restore the integers themselves.\n\n\n-----Examples-----\nInput\n2 5\n3 1 2 3\n3 3 4 5\n\nOutput\npossible\n\nInput\n10 10\n1 1\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n\nOutput\nimpossible\n\n\n\n-----Note-----\n\nIn the first sample, a possible choice for the values of the $a_i$ is $3, 4, 3, 5, 2$. On the first day, Dora buys the integers $3, 4$ and $3$, whose LCM is $12$, while Swiper buys integers $5$ and $2$, whose LCM is $10$. On the second day, Dora buys $3, 5$ and $2$, whose LCM is $30$, and Swiper buys integers $3$ and $4$, whose LCM is $12$.",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\n\\nm, n = list(map(int, input().split()))\\nDora = []\\nSwiper = []\\nall = set([i for i in range(1, n+1)])\\nfor _ in range(m):\\n    a = set(list(map(int, input().split()))[1:])\\n    Dora.append(a)\\n    Swiper.append(all.difference(a))\\n\\nflag = 1\\nfor i in range(m):\\n    for j in range(m):\\n        if Dora[i] | Swiper[j] == Swiper[j]:\\n            flag = 0\\n            break\\n    if flag == 0:\\n        break\\n\\nif flag == 1:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"# stdin=open('input.txt')\\nfrom sys import stdin, stdout\\ndef input():\\n\\treturn stdin.readline()[:-1]\\n\\n\\n# stdout=open('output.txt',mode='w+')\\n\\n# def print(x, end='\\\\n'):\\n# \\tstdout.write(str(x) +end)\\n\\n\\n# a, b = map(int, input().split())\\n\\n# l = list(map(int, input().split()))\\n\\n# n = int(input())\\n\\n\\n\\n\\n\\n# CODE BEGINS HERE.................\\n\\n# import copy\\nimport math\\n# import sys\\n# sys.setrecursionlimit(10**7)\\n\\nm, n = list(map(int, input().split()))\\n\\ndays = []\\nfor i in range(m):\\n\\tdays.append(set(list(map(int, input().split()))[1:]))\\npossible = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tpossible = False\\n\\t\\t\\tbreak\\n\\tif not possible:\\n\\t\\tbreak\\n\\nif possible:\\n\\tprint('possible')\\nelse:\\n\\tprint('impossible')\\n\\n#CODE ENDS HERE....................\\n\\n\\n#stdout.close()\\n\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nm,n=list(map(int,input().split()))\\n\\nD=[set(list(map(int,input().split()))[1:]) for i in range(m)]\\n\\n\\nfor i in range(m-1):\\n    for j in range(1,m):\\n        if D[i] & D[j]== set():\\n            print(\\\"impossible\\\")\\n            return\\nelse:\\n    print(\\\"possible\\\")\\n\\n\", \"def check(arr1, arr2):\\n    i1 = 0\\n    i2 = 0\\n    while True:\\n        if i1 == len(arr1) or i2 == len(arr2):\\n            return False\\n        elif arr1[i1] == arr2[i2]:\\n            return True\\n        elif arr1[i1] < arr2[i2]:\\n            i1 += 1\\n        else:\\n            i2 += 1\\n\\n\\nm, n = (int(x) for x in input().split())\\n\\nday___set = []\\nfor i in range(m):\\n    x = sorted([int(x) for x in input().split()][1:])\\n    day___set.append(x)\\n\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not check(day___set[i], day___set[j]):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nkok = {i for i in range(1, n + 1)}\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"inp = lambda cast=int: list(map(cast, input().split()))\\nprintf = lambda s='', *args, **kwargs: print(str(s).format(*args), flush=True, **kwargs)\\nm, n = inp()\\nA = []\\nfor _ in range(m ):\\n    l = inp()\\n    A.append(set(l[1:]))\\nfor i in range(m):\\n    for j in range(m):\\n        if i == j: continue\\n        if not A[i].intersection(A[j]):\\n            print('impossible')\\n            return\\nprint('possible')\", \"M, N = list(map(int, input().split()))\\nX = []\\nfor i in range(M):\\n    X.append(set(list(map(int, input().split()))[1:]))\\n\\nflg = 1\\nfor i in range(M):\\n    for j in range(i):\\n        if len(X[i] & X[j]) == 0:\\n            flg = 0\\n            break\\n    if flg == 0:\\n        break\\n\\nif flg:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\n#print(m,n)\\nfor i in range(m):\\n\\tl+=[list(map(int,input().split()))]\\nl=[set(i[1:]) for i in l]\\n#k=0\\n#print(n,m)\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\t#print(a,b,a.intersection(b))\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\n\\t\\\"\\\"\\\"count=0\\n\\t\\t\\t\\tfor j in range(m):\\n\\t\\t\\t\\t\\tif i in l[j]:\\n\\t\\t\\t\\t\\t\\tcount+=1\\n\\t\\t\\t\\tif count==m:\\n\\t\\t\\t\\t\\tprint('possible')\\n\\t\\t\\t\\t\\treturn\\\"\\\"\\\"\\nprint('possible')\", \"m,n=map(int,input().split())\\nsets=[]\\nfor i in range(m):\\n    a=list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood=True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good=False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"import math\\nm,n = list(map(int,input().split()))\\ndays = []\\nfor z in range(m):\\n\\tt = set(list(map(int,input().split()))[1:])\\n\\tdays.append(t)\\ncheck = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tcheck = False\\n\\t\\t\\tbreak\\n\\t\\tif not check:\\n\\t\\t\\tbreak\\nif(check):\\n\\tprint(\\\"possible\\\")\\nelse:\\n\\tprint(\\\"impossible\\\")\\n\\n\", \"import math\\nimport re\\nimport sys\\nfrom collections import defaultdict\\nfrom heapq import heappush, heappop\\nfrom fractions import gcd\\n\\ndef read(type = int):\\n  return type(input())\\n  \\ndef read_list(type = int, split = ' ', F = None):\\n  if F:\\n    return map(lambda x: F(type(x)), raw_input().split(split))\\n  return list(map(type, input().split(split)))\\n\\ndef read_list_of_list(N, type = int, split = ' ', F = None):\\n  return [read_list(type, F = F) for _ in range(N)]\\n\\n\\nm, n = read_list()\\nB = read_list_of_list(m)\\nL = []\\nfor b in B:\\n  b = set(b[1:])\\n  for l in L:\\n    if l.isdisjoint(b):\\n      print('impossible')\\n      return\\n  L += [b]\\n  \\nprint('possible')\", \"m, n = list(map(int, input().split()))\\ns = [set([int(x) for x in input().split()][1:]) for _ in range(m)]\\nok = True\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not s[i] & s[j]:\\n            ok = False\\n            break\\n    if not ok:\\n        break\\nprint((\\\"\\\" if ok else \\\"im\\\") + \\\"possible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\nl=[list(map(int,input().split())) for i in range(m)]\\n\\nl=[set(i[1:]) for i in l]\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\nprint('possible')\", \"m,n = map(int, input().split())\\nsets = []\\nfor i  in range(m):\\n    a = list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood = True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good = False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\nt = []\\nfor i in range(m):\\n    temp = list(map(int,input().split()))[1:]\\n    bit = 0\\n    for i in temp:\\n        bit ^= (1<<(i-1))\\n    t.append(bit)\\nans = True\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if t[i] & t[j] == 0:\\n            ans = False\\nprint('possible' if ans else 'impossible')\\n\", \"m,n = list(map(int,input().split()))\\nt  = [set([i for i in list(map(int,input().split()))[1:]]) for _ in range(m)]\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if len(t[i]&t[j]) == 0:\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m,n=list(map(int,input().split()))\\nL=[]\\nfor i in range(0,m):\\n    s=[int(x) for x in input().split()]\\n    s=s[1:]\\n    L.append(set(s))\\n\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if(len(L[i]&L[j])==0):\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m, n = list(map(int, input().split()))\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n         s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\\n\", \"m, n = map(int, input().split())\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n        s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\", \"m,n = [int(i) for i in input().split()]\\nmas = set(range(1,n+1))\\n\\nsetd = []\\nsets = []\\nfor i in range(m):\\n    s = set()\\n    [s.add(int(j)) for j in input().split()[1:]]\\n    setd.append(s)\\n    sets.append(mas.difference(s))\\n\\n\\n#print(setd)\\n#print(sets)\\n\\n\\nflag = True\\nfor i in range(m):\\n    for j in range(m):\\n        if sets[i].issuperset(setd[j]):\\n            flag = False\\n\\n            break\\n\\nif flag:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\n\\na = [0]*m\\n\\nfor i in range(m):\\n    k = list(map(int,input().split()))\\n    for j in range(k[0]):\\n        a[i] |= 1<<k[j+1]\\n\\nfor i in range(m):\\n    for j in range(m):\\n        if a[i]&a[j] == 0:\\n            print(\\\"impossible\\\")\\n            quit()\\nprint(\\\"possible\\\")\\n\", \"m, n = list(map(int,input().split()))\\nt = []\\n\\nfor i in range(m):\\n\\ttemp = list(map(int,input().split()))\\n\\tbit = 0\\n\\tfor i in temp[1:]:\\n\\t\\tbit ^= (1 << (i - 1))\\n\\tt.append(bit)\\n\\nans = True\\n\\nfor i in range(m - 1):\\n\\tfor j in range(i + 1, m):\\n\\t\\tif t[i] & t[j] == 0:\\n\\t\\t\\tans = False\\n\\nprint('possible' if ans else 'impossible')\\n\", \"m,n=list(map(int,input().split()))\\ns=set(range(1,n+1))\\nd=[[None,None]for i in range(m)]\\nfor i in range(m):\\n    x=list(map(int,input().split()))[1:]\\n    x=set(x)\\n    d[i][0]=x\\n    d[i][1]=s-x\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        bi,si=d[i]\\n        bj,sj=d[j]\\n        if sj.issuperset(bi) and bj.issubset(si):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nt = [set([int(i) for i in input().split()][1:]) for j in range(m)]\\nfor i in range(m - 1):\\n    for j in range(1, m):\\n        if not (t[i] & t[j]):\\n            print('impossible')\\n            return\\nprint('possible')\\n\"]",
        "difficulty": "interview",
        "input": "2 5\n3 1 2 3\n3 3 4 5\n",
        "output": "possible\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1166/E"
    },
    {
        "id": 244,
        "task_id": 2293,
        "test_case_id": 2,
        "question": "Dora the explorer has decided to use her money after several years of juicy royalties to go shopping. What better place to shop than Nlogonia?\n\nThere are $n$ stores numbered from $1$ to $n$ in Nlogonia. The $i$-th of these stores offers a positive integer $a_i$.\n\nEach day among the last $m$ days Dora bought a single integer from some of the stores. The same day, Swiper the fox bought a single integer from all the stores that Dora did not buy an integer from on that day.\n\nDora considers Swiper to be her rival, and she considers that she beat Swiper on day $i$ if and only if the least common multiple of the numbers she bought on day $i$ is strictly greater than the least common multiple of the numbers that Swiper bought on day $i$.\n\nThe least common multiple (LCM) of a collection of integers is the smallest positive integer that is divisible by all the integers in the collection.\n\nHowever, Dora forgot the values of $a_i$. Help Dora find out if there are positive integer values of $a_i$ such that she beat Swiper on every day. You don't need to find what are the possible values of $a_i$ though.\n\nNote that it is possible for some values of $a_i$ to coincide in a solution.\n\n\n-----Input-----\n\nThe first line contains integers $m$ and $n$ ($1\\leq m \\leq 50$, $1\\leq n \\leq 10^4$) — the number of days and the number of stores.\n\nAfter this $m$ lines follow, the $i$-th line starts with an integer $s_i$ ($1\\leq s_i \\leq n-1$), the number of integers Dora bought on day $i$, followed by $s_i$ distinct integers, the indices of the stores where Dora bought an integer on the $i$-th day. The indices are between $1$ and $n$.\n\n\n-----Output-----\n\nOutput must consist of a single line containing \"possible\" if there exist positive integers $a_i$ such that for each day the least common multiple of the integers bought by Dora is strictly greater than the least common multiple of the integers bought by Swiper on that day. Otherwise, print \"impossible\".\n\nNote that you don't have to restore the integers themselves.\n\n\n-----Examples-----\nInput\n2 5\n3 1 2 3\n3 3 4 5\n\nOutput\npossible\n\nInput\n10 10\n1 1\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n\nOutput\nimpossible\n\n\n\n-----Note-----\n\nIn the first sample, a possible choice for the values of the $a_i$ is $3, 4, 3, 5, 2$. On the first day, Dora buys the integers $3, 4$ and $3$, whose LCM is $12$, while Swiper buys integers $5$ and $2$, whose LCM is $10$. On the second day, Dora buys $3, 5$ and $2$, whose LCM is $30$, and Swiper buys integers $3$ and $4$, whose LCM is $12$.",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\n\\nm, n = list(map(int, input().split()))\\nDora = []\\nSwiper = []\\nall = set([i for i in range(1, n+1)])\\nfor _ in range(m):\\n    a = set(list(map(int, input().split()))[1:])\\n    Dora.append(a)\\n    Swiper.append(all.difference(a))\\n\\nflag = 1\\nfor i in range(m):\\n    for j in range(m):\\n        if Dora[i] | Swiper[j] == Swiper[j]:\\n            flag = 0\\n            break\\n    if flag == 0:\\n        break\\n\\nif flag == 1:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"# stdin=open('input.txt')\\nfrom sys import stdin, stdout\\ndef input():\\n\\treturn stdin.readline()[:-1]\\n\\n\\n# stdout=open('output.txt',mode='w+')\\n\\n# def print(x, end='\\\\n'):\\n# \\tstdout.write(str(x) +end)\\n\\n\\n# a, b = map(int, input().split())\\n\\n# l = list(map(int, input().split()))\\n\\n# n = int(input())\\n\\n\\n\\n\\n\\n# CODE BEGINS HERE.................\\n\\n# import copy\\nimport math\\n# import sys\\n# sys.setrecursionlimit(10**7)\\n\\nm, n = list(map(int, input().split()))\\n\\ndays = []\\nfor i in range(m):\\n\\tdays.append(set(list(map(int, input().split()))[1:]))\\npossible = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tpossible = False\\n\\t\\t\\tbreak\\n\\tif not possible:\\n\\t\\tbreak\\n\\nif possible:\\n\\tprint('possible')\\nelse:\\n\\tprint('impossible')\\n\\n#CODE ENDS HERE....................\\n\\n\\n#stdout.close()\\n\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nm,n=list(map(int,input().split()))\\n\\nD=[set(list(map(int,input().split()))[1:]) for i in range(m)]\\n\\n\\nfor i in range(m-1):\\n    for j in range(1,m):\\n        if D[i] & D[j]== set():\\n            print(\\\"impossible\\\")\\n            return\\nelse:\\n    print(\\\"possible\\\")\\n\\n\", \"def check(arr1, arr2):\\n    i1 = 0\\n    i2 = 0\\n    while True:\\n        if i1 == len(arr1) or i2 == len(arr2):\\n            return False\\n        elif arr1[i1] == arr2[i2]:\\n            return True\\n        elif arr1[i1] < arr2[i2]:\\n            i1 += 1\\n        else:\\n            i2 += 1\\n\\n\\nm, n = (int(x) for x in input().split())\\n\\nday___set = []\\nfor i in range(m):\\n    x = sorted([int(x) for x in input().split()][1:])\\n    day___set.append(x)\\n\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not check(day___set[i], day___set[j]):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nkok = {i for i in range(1, n + 1)}\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"inp = lambda cast=int: list(map(cast, input().split()))\\nprintf = lambda s='', *args, **kwargs: print(str(s).format(*args), flush=True, **kwargs)\\nm, n = inp()\\nA = []\\nfor _ in range(m ):\\n    l = inp()\\n    A.append(set(l[1:]))\\nfor i in range(m):\\n    for j in range(m):\\n        if i == j: continue\\n        if not A[i].intersection(A[j]):\\n            print('impossible')\\n            return\\nprint('possible')\", \"M, N = list(map(int, input().split()))\\nX = []\\nfor i in range(M):\\n    X.append(set(list(map(int, input().split()))[1:]))\\n\\nflg = 1\\nfor i in range(M):\\n    for j in range(i):\\n        if len(X[i] & X[j]) == 0:\\n            flg = 0\\n            break\\n    if flg == 0:\\n        break\\n\\nif flg:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\n#print(m,n)\\nfor i in range(m):\\n\\tl+=[list(map(int,input().split()))]\\nl=[set(i[1:]) for i in l]\\n#k=0\\n#print(n,m)\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\t#print(a,b,a.intersection(b))\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\n\\t\\\"\\\"\\\"count=0\\n\\t\\t\\t\\tfor j in range(m):\\n\\t\\t\\t\\t\\tif i in l[j]:\\n\\t\\t\\t\\t\\t\\tcount+=1\\n\\t\\t\\t\\tif count==m:\\n\\t\\t\\t\\t\\tprint('possible')\\n\\t\\t\\t\\t\\treturn\\\"\\\"\\\"\\nprint('possible')\", \"m,n=map(int,input().split())\\nsets=[]\\nfor i in range(m):\\n    a=list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood=True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good=False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"import math\\nm,n = list(map(int,input().split()))\\ndays = []\\nfor z in range(m):\\n\\tt = set(list(map(int,input().split()))[1:])\\n\\tdays.append(t)\\ncheck = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tcheck = False\\n\\t\\t\\tbreak\\n\\t\\tif not check:\\n\\t\\t\\tbreak\\nif(check):\\n\\tprint(\\\"possible\\\")\\nelse:\\n\\tprint(\\\"impossible\\\")\\n\\n\", \"import math\\nimport re\\nimport sys\\nfrom collections import defaultdict\\nfrom heapq import heappush, heappop\\nfrom fractions import gcd\\n\\ndef read(type = int):\\n  return type(input())\\n  \\ndef read_list(type = int, split = ' ', F = None):\\n  if F:\\n    return map(lambda x: F(type(x)), raw_input().split(split))\\n  return list(map(type, input().split(split)))\\n\\ndef read_list_of_list(N, type = int, split = ' ', F = None):\\n  return [read_list(type, F = F) for _ in range(N)]\\n\\n\\nm, n = read_list()\\nB = read_list_of_list(m)\\nL = []\\nfor b in B:\\n  b = set(b[1:])\\n  for l in L:\\n    if l.isdisjoint(b):\\n      print('impossible')\\n      return\\n  L += [b]\\n  \\nprint('possible')\", \"m, n = list(map(int, input().split()))\\ns = [set([int(x) for x in input().split()][1:]) for _ in range(m)]\\nok = True\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not s[i] & s[j]:\\n            ok = False\\n            break\\n    if not ok:\\n        break\\nprint((\\\"\\\" if ok else \\\"im\\\") + \\\"possible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\nl=[list(map(int,input().split())) for i in range(m)]\\n\\nl=[set(i[1:]) for i in l]\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\nprint('possible')\", \"m,n = map(int, input().split())\\nsets = []\\nfor i  in range(m):\\n    a = list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood = True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good = False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\nt = []\\nfor i in range(m):\\n    temp = list(map(int,input().split()))[1:]\\n    bit = 0\\n    for i in temp:\\n        bit ^= (1<<(i-1))\\n    t.append(bit)\\nans = True\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if t[i] & t[j] == 0:\\n            ans = False\\nprint('possible' if ans else 'impossible')\\n\", \"m,n = list(map(int,input().split()))\\nt  = [set([i for i in list(map(int,input().split()))[1:]]) for _ in range(m)]\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if len(t[i]&t[j]) == 0:\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m,n=list(map(int,input().split()))\\nL=[]\\nfor i in range(0,m):\\n    s=[int(x) for x in input().split()]\\n    s=s[1:]\\n    L.append(set(s))\\n\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if(len(L[i]&L[j])==0):\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m, n = list(map(int, input().split()))\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n         s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\\n\", \"m, n = map(int, input().split())\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n        s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\", \"m,n = [int(i) for i in input().split()]\\nmas = set(range(1,n+1))\\n\\nsetd = []\\nsets = []\\nfor i in range(m):\\n    s = set()\\n    [s.add(int(j)) for j in input().split()[1:]]\\n    setd.append(s)\\n    sets.append(mas.difference(s))\\n\\n\\n#print(setd)\\n#print(sets)\\n\\n\\nflag = True\\nfor i in range(m):\\n    for j in range(m):\\n        if sets[i].issuperset(setd[j]):\\n            flag = False\\n\\n            break\\n\\nif flag:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\n\\na = [0]*m\\n\\nfor i in range(m):\\n    k = list(map(int,input().split()))\\n    for j in range(k[0]):\\n        a[i] |= 1<<k[j+1]\\n\\nfor i in range(m):\\n    for j in range(m):\\n        if a[i]&a[j] == 0:\\n            print(\\\"impossible\\\")\\n            quit()\\nprint(\\\"possible\\\")\\n\", \"m, n = list(map(int,input().split()))\\nt = []\\n\\nfor i in range(m):\\n\\ttemp = list(map(int,input().split()))\\n\\tbit = 0\\n\\tfor i in temp[1:]:\\n\\t\\tbit ^= (1 << (i - 1))\\n\\tt.append(bit)\\n\\nans = True\\n\\nfor i in range(m - 1):\\n\\tfor j in range(i + 1, m):\\n\\t\\tif t[i] & t[j] == 0:\\n\\t\\t\\tans = False\\n\\nprint('possible' if ans else 'impossible')\\n\", \"m,n=list(map(int,input().split()))\\ns=set(range(1,n+1))\\nd=[[None,None]for i in range(m)]\\nfor i in range(m):\\n    x=list(map(int,input().split()))[1:]\\n    x=set(x)\\n    d[i][0]=x\\n    d[i][1]=s-x\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        bi,si=d[i]\\n        bj,sj=d[j]\\n        if sj.issuperset(bi) and bj.issubset(si):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nt = [set([int(i) for i in input().split()][1:]) for j in range(m)]\\nfor i in range(m - 1):\\n    for j in range(1, m):\\n        if not (t[i] & t[j]):\\n            print('impossible')\\n            return\\nprint('possible')\\n\"]",
        "difficulty": "interview",
        "input": "10 10\n1 1\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n",
        "output": "impossible\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1166/E"
    },
    {
        "id": 245,
        "task_id": 2293,
        "test_case_id": 3,
        "question": "Dora the explorer has decided to use her money after several years of juicy royalties to go shopping. What better place to shop than Nlogonia?\n\nThere are $n$ stores numbered from $1$ to $n$ in Nlogonia. The $i$-th of these stores offers a positive integer $a_i$.\n\nEach day among the last $m$ days Dora bought a single integer from some of the stores. The same day, Swiper the fox bought a single integer from all the stores that Dora did not buy an integer from on that day.\n\nDora considers Swiper to be her rival, and she considers that she beat Swiper on day $i$ if and only if the least common multiple of the numbers she bought on day $i$ is strictly greater than the least common multiple of the numbers that Swiper bought on day $i$.\n\nThe least common multiple (LCM) of a collection of integers is the smallest positive integer that is divisible by all the integers in the collection.\n\nHowever, Dora forgot the values of $a_i$. Help Dora find out if there are positive integer values of $a_i$ such that she beat Swiper on every day. You don't need to find what are the possible values of $a_i$ though.\n\nNote that it is possible for some values of $a_i$ to coincide in a solution.\n\n\n-----Input-----\n\nThe first line contains integers $m$ and $n$ ($1\\leq m \\leq 50$, $1\\leq n \\leq 10^4$) — the number of days and the number of stores.\n\nAfter this $m$ lines follow, the $i$-th line starts with an integer $s_i$ ($1\\leq s_i \\leq n-1$), the number of integers Dora bought on day $i$, followed by $s_i$ distinct integers, the indices of the stores where Dora bought an integer on the $i$-th day. The indices are between $1$ and $n$.\n\n\n-----Output-----\n\nOutput must consist of a single line containing \"possible\" if there exist positive integers $a_i$ such that for each day the least common multiple of the integers bought by Dora is strictly greater than the least common multiple of the integers bought by Swiper on that day. Otherwise, print \"impossible\".\n\nNote that you don't have to restore the integers themselves.\n\n\n-----Examples-----\nInput\n2 5\n3 1 2 3\n3 3 4 5\n\nOutput\npossible\n\nInput\n10 10\n1 1\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n\nOutput\nimpossible\n\n\n\n-----Note-----\n\nIn the first sample, a possible choice for the values of the $a_i$ is $3, 4, 3, 5, 2$. On the first day, Dora buys the integers $3, 4$ and $3$, whose LCM is $12$, while Swiper buys integers $5$ and $2$, whose LCM is $10$. On the second day, Dora buys $3, 5$ and $2$, whose LCM is $30$, and Swiper buys integers $3$ and $4$, whose LCM is $12$.",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\n\\nm, n = list(map(int, input().split()))\\nDora = []\\nSwiper = []\\nall = set([i for i in range(1, n+1)])\\nfor _ in range(m):\\n    a = set(list(map(int, input().split()))[1:])\\n    Dora.append(a)\\n    Swiper.append(all.difference(a))\\n\\nflag = 1\\nfor i in range(m):\\n    for j in range(m):\\n        if Dora[i] | Swiper[j] == Swiper[j]:\\n            flag = 0\\n            break\\n    if flag == 0:\\n        break\\n\\nif flag == 1:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"# stdin=open('input.txt')\\nfrom sys import stdin, stdout\\ndef input():\\n\\treturn stdin.readline()[:-1]\\n\\n\\n# stdout=open('output.txt',mode='w+')\\n\\n# def print(x, end='\\\\n'):\\n# \\tstdout.write(str(x) +end)\\n\\n\\n# a, b = map(int, input().split())\\n\\n# l = list(map(int, input().split()))\\n\\n# n = int(input())\\n\\n\\n\\n\\n\\n# CODE BEGINS HERE.................\\n\\n# import copy\\nimport math\\n# import sys\\n# sys.setrecursionlimit(10**7)\\n\\nm, n = list(map(int, input().split()))\\n\\ndays = []\\nfor i in range(m):\\n\\tdays.append(set(list(map(int, input().split()))[1:]))\\npossible = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tpossible = False\\n\\t\\t\\tbreak\\n\\tif not possible:\\n\\t\\tbreak\\n\\nif possible:\\n\\tprint('possible')\\nelse:\\n\\tprint('impossible')\\n\\n#CODE ENDS HERE....................\\n\\n\\n#stdout.close()\\n\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nm,n=list(map(int,input().split()))\\n\\nD=[set(list(map(int,input().split()))[1:]) for i in range(m)]\\n\\n\\nfor i in range(m-1):\\n    for j in range(1,m):\\n        if D[i] & D[j]== set():\\n            print(\\\"impossible\\\")\\n            return\\nelse:\\n    print(\\\"possible\\\")\\n\\n\", \"def check(arr1, arr2):\\n    i1 = 0\\n    i2 = 0\\n    while True:\\n        if i1 == len(arr1) or i2 == len(arr2):\\n            return False\\n        elif arr1[i1] == arr2[i2]:\\n            return True\\n        elif arr1[i1] < arr2[i2]:\\n            i1 += 1\\n        else:\\n            i2 += 1\\n\\n\\nm, n = (int(x) for x in input().split())\\n\\nday___set = []\\nfor i in range(m):\\n    x = sorted([int(x) for x in input().split()][1:])\\n    day___set.append(x)\\n\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not check(day___set[i], day___set[j]):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nkok = {i for i in range(1, n + 1)}\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"inp = lambda cast=int: list(map(cast, input().split()))\\nprintf = lambda s='', *args, **kwargs: print(str(s).format(*args), flush=True, **kwargs)\\nm, n = inp()\\nA = []\\nfor _ in range(m ):\\n    l = inp()\\n    A.append(set(l[1:]))\\nfor i in range(m):\\n    for j in range(m):\\n        if i == j: continue\\n        if not A[i].intersection(A[j]):\\n            print('impossible')\\n            return\\nprint('possible')\", \"M, N = list(map(int, input().split()))\\nX = []\\nfor i in range(M):\\n    X.append(set(list(map(int, input().split()))[1:]))\\n\\nflg = 1\\nfor i in range(M):\\n    for j in range(i):\\n        if len(X[i] & X[j]) == 0:\\n            flg = 0\\n            break\\n    if flg == 0:\\n        break\\n\\nif flg:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\n#print(m,n)\\nfor i in range(m):\\n\\tl+=[list(map(int,input().split()))]\\nl=[set(i[1:]) for i in l]\\n#k=0\\n#print(n,m)\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\t#print(a,b,a.intersection(b))\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\n\\t\\\"\\\"\\\"count=0\\n\\t\\t\\t\\tfor j in range(m):\\n\\t\\t\\t\\t\\tif i in l[j]:\\n\\t\\t\\t\\t\\t\\tcount+=1\\n\\t\\t\\t\\tif count==m:\\n\\t\\t\\t\\t\\tprint('possible')\\n\\t\\t\\t\\t\\treturn\\\"\\\"\\\"\\nprint('possible')\", \"m,n=map(int,input().split())\\nsets=[]\\nfor i in range(m):\\n    a=list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood=True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good=False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"import math\\nm,n = list(map(int,input().split()))\\ndays = []\\nfor z in range(m):\\n\\tt = set(list(map(int,input().split()))[1:])\\n\\tdays.append(t)\\ncheck = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tcheck = False\\n\\t\\t\\tbreak\\n\\t\\tif not check:\\n\\t\\t\\tbreak\\nif(check):\\n\\tprint(\\\"possible\\\")\\nelse:\\n\\tprint(\\\"impossible\\\")\\n\\n\", \"import math\\nimport re\\nimport sys\\nfrom collections import defaultdict\\nfrom heapq import heappush, heappop\\nfrom fractions import gcd\\n\\ndef read(type = int):\\n  return type(input())\\n  \\ndef read_list(type = int, split = ' ', F = None):\\n  if F:\\n    return map(lambda x: F(type(x)), raw_input().split(split))\\n  return list(map(type, input().split(split)))\\n\\ndef read_list_of_list(N, type = int, split = ' ', F = None):\\n  return [read_list(type, F = F) for _ in range(N)]\\n\\n\\nm, n = read_list()\\nB = read_list_of_list(m)\\nL = []\\nfor b in B:\\n  b = set(b[1:])\\n  for l in L:\\n    if l.isdisjoint(b):\\n      print('impossible')\\n      return\\n  L += [b]\\n  \\nprint('possible')\", \"m, n = list(map(int, input().split()))\\ns = [set([int(x) for x in input().split()][1:]) for _ in range(m)]\\nok = True\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not s[i] & s[j]:\\n            ok = False\\n            break\\n    if not ok:\\n        break\\nprint((\\\"\\\" if ok else \\\"im\\\") + \\\"possible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\nl=[list(map(int,input().split())) for i in range(m)]\\n\\nl=[set(i[1:]) for i in l]\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\nprint('possible')\", \"m,n = map(int, input().split())\\nsets = []\\nfor i  in range(m):\\n    a = list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood = True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good = False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\nt = []\\nfor i in range(m):\\n    temp = list(map(int,input().split()))[1:]\\n    bit = 0\\n    for i in temp:\\n        bit ^= (1<<(i-1))\\n    t.append(bit)\\nans = True\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if t[i] & t[j] == 0:\\n            ans = False\\nprint('possible' if ans else 'impossible')\\n\", \"m,n = list(map(int,input().split()))\\nt  = [set([i for i in list(map(int,input().split()))[1:]]) for _ in range(m)]\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if len(t[i]&t[j]) == 0:\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m,n=list(map(int,input().split()))\\nL=[]\\nfor i in range(0,m):\\n    s=[int(x) for x in input().split()]\\n    s=s[1:]\\n    L.append(set(s))\\n\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if(len(L[i]&L[j])==0):\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m, n = list(map(int, input().split()))\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n         s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\\n\", \"m, n = map(int, input().split())\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n        s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\", \"m,n = [int(i) for i in input().split()]\\nmas = set(range(1,n+1))\\n\\nsetd = []\\nsets = []\\nfor i in range(m):\\n    s = set()\\n    [s.add(int(j)) for j in input().split()[1:]]\\n    setd.append(s)\\n    sets.append(mas.difference(s))\\n\\n\\n#print(setd)\\n#print(sets)\\n\\n\\nflag = True\\nfor i in range(m):\\n    for j in range(m):\\n        if sets[i].issuperset(setd[j]):\\n            flag = False\\n\\n            break\\n\\nif flag:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\n\\na = [0]*m\\n\\nfor i in range(m):\\n    k = list(map(int,input().split()))\\n    for j in range(k[0]):\\n        a[i] |= 1<<k[j+1]\\n\\nfor i in range(m):\\n    for j in range(m):\\n        if a[i]&a[j] == 0:\\n            print(\\\"impossible\\\")\\n            quit()\\nprint(\\\"possible\\\")\\n\", \"m, n = list(map(int,input().split()))\\nt = []\\n\\nfor i in range(m):\\n\\ttemp = list(map(int,input().split()))\\n\\tbit = 0\\n\\tfor i in temp[1:]:\\n\\t\\tbit ^= (1 << (i - 1))\\n\\tt.append(bit)\\n\\nans = True\\n\\nfor i in range(m - 1):\\n\\tfor j in range(i + 1, m):\\n\\t\\tif t[i] & t[j] == 0:\\n\\t\\t\\tans = False\\n\\nprint('possible' if ans else 'impossible')\\n\", \"m,n=list(map(int,input().split()))\\ns=set(range(1,n+1))\\nd=[[None,None]for i in range(m)]\\nfor i in range(m):\\n    x=list(map(int,input().split()))[1:]\\n    x=set(x)\\n    d[i][0]=x\\n    d[i][1]=s-x\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        bi,si=d[i]\\n        bj,sj=d[j]\\n        if sj.issuperset(bi) and bj.issubset(si):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nt = [set([int(i) for i in input().split()][1:]) for j in range(m)]\\nfor i in range(m - 1):\\n    for j in range(1, m):\\n        if not (t[i] & t[j]):\\n            print('impossible')\\n            return\\nprint('possible')\\n\"]",
        "difficulty": "interview",
        "input": "3 10\n4 6 10 1 9\n9 6 1 8 10 4 9 5 7 2\n8 3 10 6 8 2 4 5 1\n",
        "output": "possible\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1166/E"
    },
    {
        "id": 246,
        "task_id": 2293,
        "test_case_id": 4,
        "question": "Dora the explorer has decided to use her money after several years of juicy royalties to go shopping. What better place to shop than Nlogonia?\n\nThere are $n$ stores numbered from $1$ to $n$ in Nlogonia. The $i$-th of these stores offers a positive integer $a_i$.\n\nEach day among the last $m$ days Dora bought a single integer from some of the stores. The same day, Swiper the fox bought a single integer from all the stores that Dora did not buy an integer from on that day.\n\nDora considers Swiper to be her rival, and she considers that she beat Swiper on day $i$ if and only if the least common multiple of the numbers she bought on day $i$ is strictly greater than the least common multiple of the numbers that Swiper bought on day $i$.\n\nThe least common multiple (LCM) of a collection of integers is the smallest positive integer that is divisible by all the integers in the collection.\n\nHowever, Dora forgot the values of $a_i$. Help Dora find out if there are positive integer values of $a_i$ such that she beat Swiper on every day. You don't need to find what are the possible values of $a_i$ though.\n\nNote that it is possible for some values of $a_i$ to coincide in a solution.\n\n\n-----Input-----\n\nThe first line contains integers $m$ and $n$ ($1\\leq m \\leq 50$, $1\\leq n \\leq 10^4$) — the number of days and the number of stores.\n\nAfter this $m$ lines follow, the $i$-th line starts with an integer $s_i$ ($1\\leq s_i \\leq n-1$), the number of integers Dora bought on day $i$, followed by $s_i$ distinct integers, the indices of the stores where Dora bought an integer on the $i$-th day. The indices are between $1$ and $n$.\n\n\n-----Output-----\n\nOutput must consist of a single line containing \"possible\" if there exist positive integers $a_i$ such that for each day the least common multiple of the integers bought by Dora is strictly greater than the least common multiple of the integers bought by Swiper on that day. Otherwise, print \"impossible\".\n\nNote that you don't have to restore the integers themselves.\n\n\n-----Examples-----\nInput\n2 5\n3 1 2 3\n3 3 4 5\n\nOutput\npossible\n\nInput\n10 10\n1 1\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n\nOutput\nimpossible\n\n\n\n-----Note-----\n\nIn the first sample, a possible choice for the values of the $a_i$ is $3, 4, 3, 5, 2$. On the first day, Dora buys the integers $3, 4$ and $3$, whose LCM is $12$, while Swiper buys integers $5$ and $2$, whose LCM is $10$. On the second day, Dora buys $3, 5$ and $2$, whose LCM is $30$, and Swiper buys integers $3$ and $4$, whose LCM is $12$.",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\n\\nm, n = list(map(int, input().split()))\\nDora = []\\nSwiper = []\\nall = set([i for i in range(1, n+1)])\\nfor _ in range(m):\\n    a = set(list(map(int, input().split()))[1:])\\n    Dora.append(a)\\n    Swiper.append(all.difference(a))\\n\\nflag = 1\\nfor i in range(m):\\n    for j in range(m):\\n        if Dora[i] | Swiper[j] == Swiper[j]:\\n            flag = 0\\n            break\\n    if flag == 0:\\n        break\\n\\nif flag == 1:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"# stdin=open('input.txt')\\nfrom sys import stdin, stdout\\ndef input():\\n\\treturn stdin.readline()[:-1]\\n\\n\\n# stdout=open('output.txt',mode='w+')\\n\\n# def print(x, end='\\\\n'):\\n# \\tstdout.write(str(x) +end)\\n\\n\\n# a, b = map(int, input().split())\\n\\n# l = list(map(int, input().split()))\\n\\n# n = int(input())\\n\\n\\n\\n\\n\\n# CODE BEGINS HERE.................\\n\\n# import copy\\nimport math\\n# import sys\\n# sys.setrecursionlimit(10**7)\\n\\nm, n = list(map(int, input().split()))\\n\\ndays = []\\nfor i in range(m):\\n\\tdays.append(set(list(map(int, input().split()))[1:]))\\npossible = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tpossible = False\\n\\t\\t\\tbreak\\n\\tif not possible:\\n\\t\\tbreak\\n\\nif possible:\\n\\tprint('possible')\\nelse:\\n\\tprint('impossible')\\n\\n#CODE ENDS HERE....................\\n\\n\\n#stdout.close()\\n\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nm,n=list(map(int,input().split()))\\n\\nD=[set(list(map(int,input().split()))[1:]) for i in range(m)]\\n\\n\\nfor i in range(m-1):\\n    for j in range(1,m):\\n        if D[i] & D[j]== set():\\n            print(\\\"impossible\\\")\\n            return\\nelse:\\n    print(\\\"possible\\\")\\n\\n\", \"def check(arr1, arr2):\\n    i1 = 0\\n    i2 = 0\\n    while True:\\n        if i1 == len(arr1) or i2 == len(arr2):\\n            return False\\n        elif arr1[i1] == arr2[i2]:\\n            return True\\n        elif arr1[i1] < arr2[i2]:\\n            i1 += 1\\n        else:\\n            i2 += 1\\n\\n\\nm, n = (int(x) for x in input().split())\\n\\nday___set = []\\nfor i in range(m):\\n    x = sorted([int(x) for x in input().split()][1:])\\n    day___set.append(x)\\n\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not check(day___set[i], day___set[j]):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nkok = {i for i in range(1, n + 1)}\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"inp = lambda cast=int: list(map(cast, input().split()))\\nprintf = lambda s='', *args, **kwargs: print(str(s).format(*args), flush=True, **kwargs)\\nm, n = inp()\\nA = []\\nfor _ in range(m ):\\n    l = inp()\\n    A.append(set(l[1:]))\\nfor i in range(m):\\n    for j in range(m):\\n        if i == j: continue\\n        if not A[i].intersection(A[j]):\\n            print('impossible')\\n            return\\nprint('possible')\", \"M, N = list(map(int, input().split()))\\nX = []\\nfor i in range(M):\\n    X.append(set(list(map(int, input().split()))[1:]))\\n\\nflg = 1\\nfor i in range(M):\\n    for j in range(i):\\n        if len(X[i] & X[j]) == 0:\\n            flg = 0\\n            break\\n    if flg == 0:\\n        break\\n\\nif flg:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\n#print(m,n)\\nfor i in range(m):\\n\\tl+=[list(map(int,input().split()))]\\nl=[set(i[1:]) for i in l]\\n#k=0\\n#print(n,m)\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\t#print(a,b,a.intersection(b))\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\n\\t\\\"\\\"\\\"count=0\\n\\t\\t\\t\\tfor j in range(m):\\n\\t\\t\\t\\t\\tif i in l[j]:\\n\\t\\t\\t\\t\\t\\tcount+=1\\n\\t\\t\\t\\tif count==m:\\n\\t\\t\\t\\t\\tprint('possible')\\n\\t\\t\\t\\t\\treturn\\\"\\\"\\\"\\nprint('possible')\", \"m,n=map(int,input().split())\\nsets=[]\\nfor i in range(m):\\n    a=list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood=True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good=False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"import math\\nm,n = list(map(int,input().split()))\\ndays = []\\nfor z in range(m):\\n\\tt = set(list(map(int,input().split()))[1:])\\n\\tdays.append(t)\\ncheck = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tcheck = False\\n\\t\\t\\tbreak\\n\\t\\tif not check:\\n\\t\\t\\tbreak\\nif(check):\\n\\tprint(\\\"possible\\\")\\nelse:\\n\\tprint(\\\"impossible\\\")\\n\\n\", \"import math\\nimport re\\nimport sys\\nfrom collections import defaultdict\\nfrom heapq import heappush, heappop\\nfrom fractions import gcd\\n\\ndef read(type = int):\\n  return type(input())\\n  \\ndef read_list(type = int, split = ' ', F = None):\\n  if F:\\n    return map(lambda x: F(type(x)), raw_input().split(split))\\n  return list(map(type, input().split(split)))\\n\\ndef read_list_of_list(N, type = int, split = ' ', F = None):\\n  return [read_list(type, F = F) for _ in range(N)]\\n\\n\\nm, n = read_list()\\nB = read_list_of_list(m)\\nL = []\\nfor b in B:\\n  b = set(b[1:])\\n  for l in L:\\n    if l.isdisjoint(b):\\n      print('impossible')\\n      return\\n  L += [b]\\n  \\nprint('possible')\", \"m, n = list(map(int, input().split()))\\ns = [set([int(x) for x in input().split()][1:]) for _ in range(m)]\\nok = True\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not s[i] & s[j]:\\n            ok = False\\n            break\\n    if not ok:\\n        break\\nprint((\\\"\\\" if ok else \\\"im\\\") + \\\"possible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\nl=[list(map(int,input().split())) for i in range(m)]\\n\\nl=[set(i[1:]) for i in l]\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\nprint('possible')\", \"m,n = map(int, input().split())\\nsets = []\\nfor i  in range(m):\\n    a = list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood = True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good = False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\nt = []\\nfor i in range(m):\\n    temp = list(map(int,input().split()))[1:]\\n    bit = 0\\n    for i in temp:\\n        bit ^= (1<<(i-1))\\n    t.append(bit)\\nans = True\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if t[i] & t[j] == 0:\\n            ans = False\\nprint('possible' if ans else 'impossible')\\n\", \"m,n = list(map(int,input().split()))\\nt  = [set([i for i in list(map(int,input().split()))[1:]]) for _ in range(m)]\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if len(t[i]&t[j]) == 0:\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m,n=list(map(int,input().split()))\\nL=[]\\nfor i in range(0,m):\\n    s=[int(x) for x in input().split()]\\n    s=s[1:]\\n    L.append(set(s))\\n\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if(len(L[i]&L[j])==0):\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m, n = list(map(int, input().split()))\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n         s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\\n\", \"m, n = map(int, input().split())\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n        s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\", \"m,n = [int(i) for i in input().split()]\\nmas = set(range(1,n+1))\\n\\nsetd = []\\nsets = []\\nfor i in range(m):\\n    s = set()\\n    [s.add(int(j)) for j in input().split()[1:]]\\n    setd.append(s)\\n    sets.append(mas.difference(s))\\n\\n\\n#print(setd)\\n#print(sets)\\n\\n\\nflag = True\\nfor i in range(m):\\n    for j in range(m):\\n        if sets[i].issuperset(setd[j]):\\n            flag = False\\n\\n            break\\n\\nif flag:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\n\\na = [0]*m\\n\\nfor i in range(m):\\n    k = list(map(int,input().split()))\\n    for j in range(k[0]):\\n        a[i] |= 1<<k[j+1]\\n\\nfor i in range(m):\\n    for j in range(m):\\n        if a[i]&a[j] == 0:\\n            print(\\\"impossible\\\")\\n            quit()\\nprint(\\\"possible\\\")\\n\", \"m, n = list(map(int,input().split()))\\nt = []\\n\\nfor i in range(m):\\n\\ttemp = list(map(int,input().split()))\\n\\tbit = 0\\n\\tfor i in temp[1:]:\\n\\t\\tbit ^= (1 << (i - 1))\\n\\tt.append(bit)\\n\\nans = True\\n\\nfor i in range(m - 1):\\n\\tfor j in range(i + 1, m):\\n\\t\\tif t[i] & t[j] == 0:\\n\\t\\t\\tans = False\\n\\nprint('possible' if ans else 'impossible')\\n\", \"m,n=list(map(int,input().split()))\\ns=set(range(1,n+1))\\nd=[[None,None]for i in range(m)]\\nfor i in range(m):\\n    x=list(map(int,input().split()))[1:]\\n    x=set(x)\\n    d[i][0]=x\\n    d[i][1]=s-x\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        bi,si=d[i]\\n        bj,sj=d[j]\\n        if sj.issuperset(bi) and bj.issubset(si):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nt = [set([int(i) for i in input().split()][1:]) for j in range(m)]\\nfor i in range(m - 1):\\n    for j in range(1, m):\\n        if not (t[i] & t[j]):\\n            print('impossible')\\n            return\\nprint('possible')\\n\"]",
        "difficulty": "interview",
        "input": "10 100\n4 51 22 73 78\n1 52\n5 49 74 100 14 80\n1 6\n2 98 65\n5 79 13 47 24 77\n6 47 57 35 24 59 94\n9 89 11 3 67 80 70 44 75 6\n7 12 9 92 30 10 29 70\n8 99 34 89 87 63 2 96 25\n",
        "output": "impossible\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1166/E"
    },
    {
        "id": 247,
        "task_id": 2293,
        "test_case_id": 5,
        "question": "Dora the explorer has decided to use her money after several years of juicy royalties to go shopping. What better place to shop than Nlogonia?\n\nThere are $n$ stores numbered from $1$ to $n$ in Nlogonia. The $i$-th of these stores offers a positive integer $a_i$.\n\nEach day among the last $m$ days Dora bought a single integer from some of the stores. The same day, Swiper the fox bought a single integer from all the stores that Dora did not buy an integer from on that day.\n\nDora considers Swiper to be her rival, and she considers that she beat Swiper on day $i$ if and only if the least common multiple of the numbers she bought on day $i$ is strictly greater than the least common multiple of the numbers that Swiper bought on day $i$.\n\nThe least common multiple (LCM) of a collection of integers is the smallest positive integer that is divisible by all the integers in the collection.\n\nHowever, Dora forgot the values of $a_i$. Help Dora find out if there are positive integer values of $a_i$ such that she beat Swiper on every day. You don't need to find what are the possible values of $a_i$ though.\n\nNote that it is possible for some values of $a_i$ to coincide in a solution.\n\n\n-----Input-----\n\nThe first line contains integers $m$ and $n$ ($1\\leq m \\leq 50$, $1\\leq n \\leq 10^4$) — the number of days and the number of stores.\n\nAfter this $m$ lines follow, the $i$-th line starts with an integer $s_i$ ($1\\leq s_i \\leq n-1$), the number of integers Dora bought on day $i$, followed by $s_i$ distinct integers, the indices of the stores where Dora bought an integer on the $i$-th day. The indices are between $1$ and $n$.\n\n\n-----Output-----\n\nOutput must consist of a single line containing \"possible\" if there exist positive integers $a_i$ such that for each day the least common multiple of the integers bought by Dora is strictly greater than the least common multiple of the integers bought by Swiper on that day. Otherwise, print \"impossible\".\n\nNote that you don't have to restore the integers themselves.\n\n\n-----Examples-----\nInput\n2 5\n3 1 2 3\n3 3 4 5\n\nOutput\npossible\n\nInput\n10 10\n1 1\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n\nOutput\nimpossible\n\n\n\n-----Note-----\n\nIn the first sample, a possible choice for the values of the $a_i$ is $3, 4, 3, 5, 2$. On the first day, Dora buys the integers $3, 4$ and $3$, whose LCM is $12$, while Swiper buys integers $5$ and $2$, whose LCM is $10$. On the second day, Dora buys $3, 5$ and $2$, whose LCM is $30$, and Swiper buys integers $3$ and $4$, whose LCM is $12$.",
        "solutions": "[\"import sys\\ninput = sys.stdin.readline\\n\\nm, n = list(map(int, input().split()))\\nDora = []\\nSwiper = []\\nall = set([i for i in range(1, n+1)])\\nfor _ in range(m):\\n    a = set(list(map(int, input().split()))[1:])\\n    Dora.append(a)\\n    Swiper.append(all.difference(a))\\n\\nflag = 1\\nfor i in range(m):\\n    for j in range(m):\\n        if Dora[i] | Swiper[j] == Swiper[j]:\\n            flag = 0\\n            break\\n    if flag == 0:\\n        break\\n\\nif flag == 1:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"# stdin=open('input.txt')\\nfrom sys import stdin, stdout\\ndef input():\\n\\treturn stdin.readline()[:-1]\\n\\n\\n# stdout=open('output.txt',mode='w+')\\n\\n# def print(x, end='\\\\n'):\\n# \\tstdout.write(str(x) +end)\\n\\n\\n# a, b = map(int, input().split())\\n\\n# l = list(map(int, input().split()))\\n\\n# n = int(input())\\n\\n\\n\\n\\n\\n# CODE BEGINS HERE.................\\n\\n# import copy\\nimport math\\n# import sys\\n# sys.setrecursionlimit(10**7)\\n\\nm, n = list(map(int, input().split()))\\n\\ndays = []\\nfor i in range(m):\\n\\tdays.append(set(list(map(int, input().split()))[1:]))\\npossible = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tpossible = False\\n\\t\\t\\tbreak\\n\\tif not possible:\\n\\t\\tbreak\\n\\nif possible:\\n\\tprint('possible')\\nelse:\\n\\tprint('impossible')\\n\\n#CODE ENDS HERE....................\\n\\n\\n#stdout.close()\\n\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nm,n=list(map(int,input().split()))\\n\\nD=[set(list(map(int,input().split()))[1:]) for i in range(m)]\\n\\n\\nfor i in range(m-1):\\n    for j in range(1,m):\\n        if D[i] & D[j]== set():\\n            print(\\\"impossible\\\")\\n            return\\nelse:\\n    print(\\\"possible\\\")\\n\\n\", \"def check(arr1, arr2):\\n    i1 = 0\\n    i2 = 0\\n    while True:\\n        if i1 == len(arr1) or i2 == len(arr2):\\n            return False\\n        elif arr1[i1] == arr2[i2]:\\n            return True\\n        elif arr1[i1] < arr2[i2]:\\n            i1 += 1\\n        else:\\n            i2 += 1\\n\\n\\nm, n = (int(x) for x in input().split())\\n\\nday___set = []\\nfor i in range(m):\\n    x = sorted([int(x) for x in input().split()][1:])\\n    day___set.append(x)\\n\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not check(day___set[i], day___set[j]):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nkok = {i for i in range(1, n + 1)}\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nD = []\\nfor i in range(m):\\n    A = list(map(int, input().split()))\\n    D.append(set(A[1:]))\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if D[i].intersection(D[j]) == set():\\n            print('impossible')\\n            return\\nprint('possible')\\n\", \"inp = lambda cast=int: list(map(cast, input().split()))\\nprintf = lambda s='', *args, **kwargs: print(str(s).format(*args), flush=True, **kwargs)\\nm, n = inp()\\nA = []\\nfor _ in range(m ):\\n    l = inp()\\n    A.append(set(l[1:]))\\nfor i in range(m):\\n    for j in range(m):\\n        if i == j: continue\\n        if not A[i].intersection(A[j]):\\n            print('impossible')\\n            return\\nprint('possible')\", \"M, N = list(map(int, input().split()))\\nX = []\\nfor i in range(M):\\n    X.append(set(list(map(int, input().split()))[1:]))\\n\\nflg = 1\\nfor i in range(M):\\n    for j in range(i):\\n        if len(X[i] & X[j]) == 0:\\n            flg = 0\\n            break\\n    if flg == 0:\\n        break\\n\\nif flg:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\n#print(m,n)\\nfor i in range(m):\\n\\tl+=[list(map(int,input().split()))]\\nl=[set(i[1:]) for i in l]\\n#k=0\\n#print(n,m)\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\t#print(a,b,a.intersection(b))\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\n\\t\\\"\\\"\\\"count=0\\n\\t\\t\\t\\tfor j in range(m):\\n\\t\\t\\t\\t\\tif i in l[j]:\\n\\t\\t\\t\\t\\t\\tcount+=1\\n\\t\\t\\t\\tif count==m:\\n\\t\\t\\t\\t\\tprint('possible')\\n\\t\\t\\t\\t\\treturn\\\"\\\"\\\"\\nprint('possible')\", \"m,n=map(int,input().split())\\nsets=[]\\nfor i in range(m):\\n    a=list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood=True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good=False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"import math\\nm,n = list(map(int,input().split()))\\ndays = []\\nfor z in range(m):\\n\\tt = set(list(map(int,input().split()))[1:])\\n\\tdays.append(t)\\ncheck = True\\nfor i in range(m):\\n\\tfor j in range(i):\\n\\t\\tif not days[i].intersection(days[j]):\\n\\t\\t\\tcheck = False\\n\\t\\t\\tbreak\\n\\t\\tif not check:\\n\\t\\t\\tbreak\\nif(check):\\n\\tprint(\\\"possible\\\")\\nelse:\\n\\tprint(\\\"impossible\\\")\\n\\n\", \"import math\\nimport re\\nimport sys\\nfrom collections import defaultdict\\nfrom heapq import heappush, heappop\\nfrom fractions import gcd\\n\\ndef read(type = int):\\n  return type(input())\\n  \\ndef read_list(type = int, split = ' ', F = None):\\n  if F:\\n    return map(lambda x: F(type(x)), raw_input().split(split))\\n  return list(map(type, input().split(split)))\\n\\ndef read_list_of_list(N, type = int, split = ' ', F = None):\\n  return [read_list(type, F = F) for _ in range(N)]\\n\\n\\nm, n = read_list()\\nB = read_list_of_list(m)\\nL = []\\nfor b in B:\\n  b = set(b[1:])\\n  for l in L:\\n    if l.isdisjoint(b):\\n      print('impossible')\\n      return\\n  L += [b]\\n  \\nprint('possible')\", \"m, n = list(map(int, input().split()))\\ns = [set([int(x) for x in input().split()][1:]) for _ in range(m)]\\nok = True\\nfor i in range(m):\\n    for j in range(i + 1, m):\\n        if not s[i] & s[j]:\\n            ok = False\\n            break\\n    if not ok:\\n        break\\nprint((\\\"\\\" if ok else \\\"im\\\") + \\\"possible\\\")\\n\", \"m,n=map(int,input().split())\\nl=[]\\nl=[list(map(int,input().split())) for i in range(m)]\\n\\nl=[set(i[1:]) for i in l]\\nfor i in range(m):\\n\\tfor j in range(i+1,m):\\n\\t\\tif len(l[i].intersection(l[j]))==0:\\n\\t\\t\\tprint('impossible')\\n\\t\\t\\treturn\\nprint('possible')\", \"m,n = map(int, input().split())\\nsets = []\\nfor i  in range(m):\\n    a = list(map(int,input().split()))\\n    sets.append(set(a[1:]))\\ngood = True\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        if len(sets[i]&sets[j])==0:\\n            good = False\\nif good:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\nt = []\\nfor i in range(m):\\n    temp = list(map(int,input().split()))[1:]\\n    bit = 0\\n    for i in temp:\\n        bit ^= (1<<(i-1))\\n    t.append(bit)\\nans = True\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if t[i] & t[j] == 0:\\n            ans = False\\nprint('possible' if ans else 'impossible')\\n\", \"m,n = list(map(int,input().split()))\\nt  = [set([i for i in list(map(int,input().split()))[1:]]) for _ in range(m)]\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if len(t[i]&t[j]) == 0:\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m,n=list(map(int,input().split()))\\nL=[]\\nfor i in range(0,m):\\n    s=[int(x) for x in input().split()]\\n    s=s[1:]\\n    L.append(set(s))\\n\\nfor i in range(m-1):\\n    for j in range(i+1,m):\\n        if(len(L[i]&L[j])==0):\\n            print('impossible')\\n            break\\n    else:\\n        continue\\n    break\\nelse:\\n    print('possible')\\n\", \"m, n = list(map(int, input().split()))\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n         s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\\n\", \"m, n = map(int, input().split())\\n\\ns = [0] * m\\n\\nfor w in range(m):\\n    for i in list(map(int, input().split()))[1:]:\\n        s[w] |= 1 << i\\n\\nfor i in s:\\n    for j in s:\\n        if not (i & j):\\n            print('impossible')\\n            return\\n\\nprint('possible')\", \"m,n = [int(i) for i in input().split()]\\nmas = set(range(1,n+1))\\n\\nsetd = []\\nsets = []\\nfor i in range(m):\\n    s = set()\\n    [s.add(int(j)) for j in input().split()[1:]]\\n    setd.append(s)\\n    sets.append(mas.difference(s))\\n\\n\\n#print(setd)\\n#print(sets)\\n\\n\\nflag = True\\nfor i in range(m):\\n    for j in range(m):\\n        if sets[i].issuperset(setd[j]):\\n            flag = False\\n\\n            break\\n\\nif flag:\\n    print(\\\"possible\\\")\\nelse:\\n    print(\\\"impossible\\\")\", \"m,n = list(map(int,input().split()))\\n\\na = [0]*m\\n\\nfor i in range(m):\\n    k = list(map(int,input().split()))\\n    for j in range(k[0]):\\n        a[i] |= 1<<k[j+1]\\n\\nfor i in range(m):\\n    for j in range(m):\\n        if a[i]&a[j] == 0:\\n            print(\\\"impossible\\\")\\n            quit()\\nprint(\\\"possible\\\")\\n\", \"m, n = list(map(int,input().split()))\\nt = []\\n\\nfor i in range(m):\\n\\ttemp = list(map(int,input().split()))\\n\\tbit = 0\\n\\tfor i in temp[1:]:\\n\\t\\tbit ^= (1 << (i - 1))\\n\\tt.append(bit)\\n\\nans = True\\n\\nfor i in range(m - 1):\\n\\tfor j in range(i + 1, m):\\n\\t\\tif t[i] & t[j] == 0:\\n\\t\\t\\tans = False\\n\\nprint('possible' if ans else 'impossible')\\n\", \"m,n=list(map(int,input().split()))\\ns=set(range(1,n+1))\\nd=[[None,None]for i in range(m)]\\nfor i in range(m):\\n    x=list(map(int,input().split()))[1:]\\n    x=set(x)\\n    d[i][0]=x\\n    d[i][1]=s-x\\nfor i in range(m):\\n    for j in range(i+1,m):\\n        bi,si=d[i]\\n        bj,sj=d[j]\\n        if sj.issuperset(bi) and bj.issubset(si):\\n            print('impossible')\\n            quit()\\nprint('possible')\\n\", \"m, n = list(map(int, input().split()))\\nt = [set([int(i) for i in input().split()][1:]) for j in range(m)]\\nfor i in range(m - 1):\\n    for j in range(1, m):\\n        if not (t[i] & t[j]):\\n            print('impossible')\\n            return\\nprint('possible')\\n\"]",
        "difficulty": "interview",
        "input": "4 4\n2 1 2\n2 2 3\n2 3 4\n2 4 1\n",
        "output": "impossible\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1166/E"
    },
    {
        "id": 248,
        "task_id": 2349,
        "test_case_id": 1,
        "question": "On the well-known testing system MathForces, a draw of $n$ rating units is arranged. The rating will be distributed according to the following algorithm: if $k$ participants take part in this event, then the $n$ rating is evenly distributed between them and rounded to the nearest lower integer, At the end of the drawing, an unused rating may remain — it is not given to any of the participants.\n\nFor example, if $n = 5$ and $k = 3$, then each participant will recieve an $1$ rating unit, and also $2$ rating units will remain unused. If $n = 5$, and $k = 6$, then none of the participants will increase their rating.\n\nVasya participates in this rating draw but does not have information on the total number of participants in this event. Therefore, he wants to know what different values of the rating increment are possible to get as a result of this draw and asks you for help.\n\nFor example, if $n=5$, then the answer is equal to the sequence $0, 1, 2, 5$. Each of the sequence values (and only them) can be obtained as $\\lfloor n/k \\rfloor$ for some positive integer $k$ (where $\\lfloor x \\rfloor$ is the value of $x$ rounded down): $0 = \\lfloor 5/7 \\rfloor$, $1 = \\lfloor 5/5 \\rfloor$, $2 = \\lfloor 5/2 \\rfloor$, $5 = \\lfloor 5/1 \\rfloor$.\n\nWrite a program that, for a given $n$, finds a sequence of all possible rating increments.\n\n\n-----Input-----\n\nThe first line contains integer number $t$ ($1 \\le t \\le 10$) — the number of test cases in the input. Then $t$ test cases follow.\n\nEach line contains an integer $n$ ($1 \\le n \\le 10^9$) — the total number of the rating units being drawn.\n\n\n-----Output-----\n\nOutput the answers for each of $t$ test cases. Each answer should be contained in two lines.\n\nIn the first line print a single integer $m$ — the number of different rating increment values that Vasya can get.\n\nIn the following line print $m$ integers in ascending order — the values of possible rating increments.\n\n\n-----Example-----\nInput\n4\n5\n11\n1\n3\n\nOutput\n4\n0 1 2 5 \n6\n0 1 2 3 5 11 \n2\n0 1 \n3\n0 1 3",
        "solutions": "[\"tst = int(input())\\nfor i in range(0, tst):\\n    n = int(input())\\n    ans = 1\\n    l = 1\\n    p = []\\n    while l <= n:\\n        ans += 1\\n        l = n // (n // l)\\n        p.append(n // l)\\n        l += 1\\n    p.append(0)\\n    p.reverse()\\n    print(len(p))\\n    print(\\\" \\\".join(str(x) for x in p))\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n\\n    l = [n]\\n    test = 2\\n    while n//test != l[-1]:\\n        l.append(n//test)\\n        test += 1\\n\\n    while l[-1] != 0:\\n        l.append(l[-1] - 1)\\n        \\n    print(len(l))\\n    print(' '.join(map(str,l[::-1])))\\n\", \"for _ in range(int(input())):\\n    n = int(input())\\n    d = 1\\n    res = [0]\\n    while d <= n:\\n        e = n // d\\n        res.append(e)\\n        d = (n // e) + 1\\n    print(len(res))\\n    print(*sorted(res))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    set_ = set()\\n    for i in range(1, int(n**0.5)+10):\\n        set_.add(n // i)\\n    li = sorted(list(set_))\\n    num = li[0]\\n    li2 = [i for i in range(num)]\\n    print(len(li2) + len(li))\\n    print(*li2 + li)\", \"t=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    aa=[]\\n    ind=1\\n    while True:\\n        aa.append(n//ind)\\n        if len(aa)>=2:\\n            if aa[-1]==aa[-2]:\\n                for i in range(aa[-1],-1,-1):\\n                    aa.append(i)\\n                break\\n        ind+=1\\n    print(len(set(aa)))\\n    print(*sorted(list(set(aa))))\\n    \\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor testcases in range(t):\\n    n=int(input())\\n\\n    ANS=[n//1]\\n\\n    for i in range(2,n):\\n        ANS.append(n//i)\\n\\n        if n/(i-1)-n/i<1:\\n            break\\n\\n    A=list(range(0,ANS[-1]))+sorted(set(ANS))\\n\\n    print(len(A))\\n    print(*A)\\n\", \"def kek(n):\\n\\tl = [0]\\n\\tl2 = []\\n\\ti = 1\\n\\twhile i * i < n:\\n\\t\\tl.append(i)\\n\\t\\tif n // i != i:\\n\\t\\t\\tl2.append(n // i)\\n\\t\\ti += 1\\n\\tif i * i == n:\\n\\t\\tl.append(i)\\n\\tl2.reverse()\\n\\tl += l2\\n\\treturn l\\n\\ndef main():\\n\\tfor _ in range(int(input())):\\n\\t\\tn = int(input())\\n\\t\\tl = kek(n)\\n\\t\\tprint(len(l))\\n\\t\\tfor i in l:\\n\\t\\t\\tprint(i, end=' ')\\n\\t\\tprint()\\nmain()\", \"for _ in range(int(input())):\\n\\tn=int(input())\\n\\tif n<=1000005:\\n\\t\\tl=[0,1]\\n\\t\\tfor k in range(n-1,0,-1):\\n\\t\\t\\ta=n//k\\n\\t\\t\\tif a>l[-1]:\\n\\t\\t\\t\\tl.append(a)\\n\\t\\tprint(len(l))\\n\\t\\tprint(*l)\\n\\telse:\\n\\t\\tl=[x for x in range(1001)]\\n\\t\\tfor k in range(1000000,0,-1):\\n\\t\\t\\ta=n//k\\n\\t\\t\\tif a>l[-1]:\\n\\t\\t\\t\\tl.append(a)\\n\\t\\tprint(len(l))\\n\\t\\tprint(*l)\", \"q = int(input())\\nfor ifwfwe in range(q):\\n\\tn = int(input())\\n\\ti = 1\\n\\todp = [0]\\n\\twhile i*i <= n:\\n\\t\\todp.append(i)\\n\\t\\ti += 1\\n\\twhile i > 0:\\n\\t\\tif n // i > odp[-1]:\\n\\t\\t\\todp.append(n//i)\\n\\t\\ti -= 1\\n\\tprint(len(odp))\\n\\tprint(*odp)\", \"def solve():\\n    n = int(input())\\n    s = set()\\n    s.add(0)\\n    for i in range(1, int(n**0.5)+1):\\n        k = n//i\\n        s.add(k)\\n        s.add(i)\\n    ans = sorted(s)\\n    print(len(ans))\\n    print(*ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\", \"#603_C\\n\\nt = int(input())\\n\\nfor i in range(0, t):\\n    n = int(input())\\n    ln = [0]\\n    oned = False\\n    sqt = n // int(n ** 0.5)\\n    on = -1\\n    for j in range(1, max(2, int(n ** 0.5) + 1)):\\n        if n // j != on:\\n            ln.append(n // j)\\n            if n // j == 1:\\n                oned = True\\n        on = n // j\\n    for j in range(len(ln) - 1, 0, -1):\\n        if n // ln[j] == sqt:\\n            continue\\n        ln.append(n // ln[j])\\n        if n // ln[j] == 1:\\n            oned = True\\n    if not oned:\\n        ln.append(1)\\n    print(len(ln))\\n    print(\\\" \\\".join([str(j) for j in sorted(ln)]))\\n\", \"import sys\\ndef I():\\n        return sys.stdin.readline().rstrip()\\n\\nfor _ in range( int(I()) ):\\n    n = int(I())\\n    a = [ 0, 1 ]\\n    i = n\\n    while i > 0:\\n        if n // i > a[ -1 ]:\\n            a.append( n // i )\\n        i = n // ( a[ -1 ] + 1 )\\n    print( len( a ) )\\n    print( *a )\\n\", \"import math\\nt = int(input())\\nfor i in range (t):\\n    n = int(input())\\n    m = math.floor(math.sqrt(n))\\n    ans = [j for j in range (m + 1)]\\n    left = m\\n    while m > 0:\\n        k = n//m\\n        if left == k:\\n            m -= 1\\n            continue\\n        ans.append(k)\\n        left = k\\n        m -= 1\\n    print(len(ans))\\n    print(*ans, sep = \\\" \\\")\", \"t = int(input())\\n\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ts = set.union({0}, *({i, n//i} for i in range(1, int(n**.5)+1)))\\n\\tprint(len(s))\\n\\tfor v in sorted(s):\\n\\t\\tprint(v, end=\\\" \\\")\\n\\tprint()\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\n\\tans = {0}\\n\\n\\tfor i in range(1, int(n ** 0.5 + 1)):\\n\\t\\tans.add(n // i)\\n\\t\\tans.add(n // (n // i))\\n\\n\\tprint(len(ans))\\n\\tprint(*sorted(ans))\", \"from math import sqrt\\nt=int(input())\\nfor _ in range(t):\\n\\tn=int(input())\\n\\tans=set()\\n\\tans.add(0)\\n\\troot=int(sqrt(n))\\n\\tfor x in range(1,root+1):\\n\\t\\tans.add(x)\\n\\t\\tans.add(n//x)\\n\\tprint(len(ans))\\n\\tans=sorted(ans)\\n\\tfor x in ans:\\n\\t\\tprint(x,end=' ')\\n\\tprint()\", \"# from fractions import gcd\\n# from datetime import date, timedelta\\n# from heapq import*\\n# import math\\n# from collections import defaultdict, Counter, deque\\n# import sys\\n# from bisect import *\\n# import itertools\\n# import copy\\n# sys.setrecursionlimit(10 ** 7)\\n# MOD = 10 ** 9 + 7\\n\\n\\n\\n\\n\\ndef main():\\n    t = int(input())\\n    for _ in range(t):\\n        n = int(input())\\n        prev = -1\\n        ans = []\\n        for i in range(1,40000):\\n            v = n//i\\n            if v == prev:\\n                break\\n            ans.append(v)\\n            prev = v\\n        for i in range(v-1, -1, -1):\\n            ans.append(i)\\n        print(len(ans))\\n        print(*ans[::-1])\\n\\n\\n\\n\\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"3\\n\\nimport os\\nimport sys\\n\\n\\ndef main():\\n    T = read_int()\\n    for _ in range(T):\\n        ans = solve(read_int())\\n        print(len(ans))\\n        print(*ans)\\n\\n\\ndef solve(N):\\n    ans = [N]\\n    i = 2\\n    while i * (i - 1) <= N:\\n        v = N // i\\n        if ans[-1] != v:\\n            ans.append(v)\\n        i += 1\\n\\n    v = ans[-1]\\n    for i in range(v - 1, -1, -1):\\n        ans.append(i)\\n    ans.reverse()\\n    return ans\\n\\n\\n###############################################################################\\n\\nDEBUG = 'DEBUG' in os.environ\\n\\n\\ndef inp():\\n    return sys.stdin.readline().rstrip()\\n\\n\\ndef read_int():\\n    return int(inp())\\n\\n\\ndef read_ints():\\n    return [int(e) for e in inp().split()]\\n\\n\\ndef dprint(*value, sep=' ', end='\\\\n'):\\n    if DEBUG:\\n        print(*value, sep=sep, end=end)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# from sys import stdin\\n# def rl():\\n#     return [int(w) for w in stdin.readline().split()]\\nfrom bisect import bisect_right\\nfrom bisect import bisect_left\\nfrom collections import defaultdict\\nfrom math import sqrt,factorial,gcd,log2,inf,ceil\\n# map(int,input().split())\\n# # l = list(map(int,input().split()))\\n# from itertools import permutations\\nimport sys\\n# input = sys.stdin.readline\\n\\n# t = int(input())\\n#\\n# for _ in range(t):\\n#     a,b,c = map(int,input().split())\\n#     a,b,c = sorted([a,b,c])\\n#     ans = 0\\n#     ans+=b\\n#     c-=b\\n#\\n#     a,c = sorted([a,c])\\n#     ans+=a\\n#     print(ans)\\n\\n\\n# print(ans)\\n\\n\\n\\n\\nt = int(input())\\n\\nfor _ in range(t):\\n\\n    n = int(input())\\n\\n    ans = [1,0]\\n\\n    for i in range(1,int(sqrt(n)+1)):\\n        ans.append(n//i)\\n        ans.append(n//(n//i))\\n\\n    ans = list(set(ans))\\n    print(len(ans))\\n    ans.sort()\\n    print(*ans)\\n\\n\\n\\n\\n\", \"import sys\\n\\n\\n# inf = open('input.txt', 'r')\\n# reader = (int(line.rstrip()) for line in inf)\\nreader = (int(s.rstrip()) for s in sys.stdin)\\n\\ndef rating(n):\\n    m = n\\n    ans = [0, 1]\\n    ndiv = 2\\n    while True:\\n        brick = n // ndiv\\n        if not brick:\\n            break\\n        ndiv = n // brick\\n        ans.append(ndiv)\\n        ndiv += 1\\n    return ans\\n\\nt = next(reader)\\nfor _ in range(t):\\n    n = next(reader)\\n    ans = rating(n)\\n    sys.stdout.write(str(len(ans)) + '\\\\n')\\n    sys.stdout.write(' '.join(map(str, ans)) + '\\\\n')\\n    \\n# inf.close()\\n\", \"import math\\nt = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    divisors = set(n // i for i in range(1, int(math.sqrt(n))+1))\\n    for d in divisors.copy():\\n        divisors.add(n // d)\\n    divisors.add(0)\\n\\n    print(len(divisors))\\n    print(*sorted(divisors))\\n\", \"'''input\\n4\\n5\\n11\\n1\\n3\\n'''\\nfrom sys import stdin, stdout\\n\\n\\nfrom collections import defaultdict, deque\\n\\n# main starts \\nt = int(stdin.readline().strip())\\nfor _ in range(t):\\n\\tn = int(stdin.readline().strip())\\n\\tans = set()\\n\\tfor i in range(1, int(n ** 0.5) + 1):\\n\\t\\tans.add(i)\\n\\t\\tans.add(n//i)\\n\\n\\tans.add(0)\\n\\tans.add(1)\\n\\tans.add(n)\\n\\tans = list(ans)\\n\\tans.sort()\\n\\tprint(len(ans))\\n\\tprint(*ans)\\n\", \"sp = lambda: list(map(int, input().split()))\\nsi = lambda: int(input())\\n\\nTESTCASES = int(input())\\nfor tc in range(TESTCASES):\\n    n=si()\\n    ints = set(range(int(n**0.5)+1))\\n    for i in range(int(n**0.5)+1,0,-1):\\n        ints.add(n//i)\\n    ints=sorted(list(ints))\\n    print(len(ints))\\n    print(\\\" \\\".join(map(str,ints)))\\n\", \"for i in range(int(input())):\\n\\tn = int(input())\\n\\tb = [i for i in range(1, int(n**(1/2) + 1))]\\n\\tr = [str(m) for m in sorted(list(set(b + [n//i for i in b])))]\\n\\tprint(len(r) + 1)\\n\\tprint(0, ' '.join([str(m) for m in sorted(list(set(b + [n//i for i in b])))]))\"]",
        "difficulty": "interview",
        "input": "4\n5\n11\n1\n3\n",
        "output": "4\n0 1 2 5 \n6\n0 1 2 3 5 11 \n2\n0 1 \n3\n0 1 3 \n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1263/C"
    },
    {
        "id": 249,
        "task_id": 2349,
        "test_case_id": 2,
        "question": "On the well-known testing system MathForces, a draw of $n$ rating units is arranged. The rating will be distributed according to the following algorithm: if $k$ participants take part in this event, then the $n$ rating is evenly distributed between them and rounded to the nearest lower integer, At the end of the drawing, an unused rating may remain — it is not given to any of the participants.\n\nFor example, if $n = 5$ and $k = 3$, then each participant will recieve an $1$ rating unit, and also $2$ rating units will remain unused. If $n = 5$, and $k = 6$, then none of the participants will increase their rating.\n\nVasya participates in this rating draw but does not have information on the total number of participants in this event. Therefore, he wants to know what different values of the rating increment are possible to get as a result of this draw and asks you for help.\n\nFor example, if $n=5$, then the answer is equal to the sequence $0, 1, 2, 5$. Each of the sequence values (and only them) can be obtained as $\\lfloor n/k \\rfloor$ for some positive integer $k$ (where $\\lfloor x \\rfloor$ is the value of $x$ rounded down): $0 = \\lfloor 5/7 \\rfloor$, $1 = \\lfloor 5/5 \\rfloor$, $2 = \\lfloor 5/2 \\rfloor$, $5 = \\lfloor 5/1 \\rfloor$.\n\nWrite a program that, for a given $n$, finds a sequence of all possible rating increments.\n\n\n-----Input-----\n\nThe first line contains integer number $t$ ($1 \\le t \\le 10$) — the number of test cases in the input. Then $t$ test cases follow.\n\nEach line contains an integer $n$ ($1 \\le n \\le 10^9$) — the total number of the rating units being drawn.\n\n\n-----Output-----\n\nOutput the answers for each of $t$ test cases. Each answer should be contained in two lines.\n\nIn the first line print a single integer $m$ — the number of different rating increment values that Vasya can get.\n\nIn the following line print $m$ integers in ascending order — the values of possible rating increments.\n\n\n-----Example-----\nInput\n4\n5\n11\n1\n3\n\nOutput\n4\n0 1 2 5 \n6\n0 1 2 3 5 11 \n2\n0 1 \n3\n0 1 3",
        "solutions": "[\"tst = int(input())\\nfor i in range(0, tst):\\n    n = int(input())\\n    ans = 1\\n    l = 1\\n    p = []\\n    while l <= n:\\n        ans += 1\\n        l = n // (n // l)\\n        p.append(n // l)\\n        l += 1\\n    p.append(0)\\n    p.reverse()\\n    print(len(p))\\n    print(\\\" \\\".join(str(x) for x in p))\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n\\n    l = [n]\\n    test = 2\\n    while n//test != l[-1]:\\n        l.append(n//test)\\n        test += 1\\n\\n    while l[-1] != 0:\\n        l.append(l[-1] - 1)\\n        \\n    print(len(l))\\n    print(' '.join(map(str,l[::-1])))\\n\", \"for _ in range(int(input())):\\n    n = int(input())\\n    d = 1\\n    res = [0]\\n    while d <= n:\\n        e = n // d\\n        res.append(e)\\n        d = (n // e) + 1\\n    print(len(res))\\n    print(*sorted(res))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    set_ = set()\\n    for i in range(1, int(n**0.5)+10):\\n        set_.add(n // i)\\n    li = sorted(list(set_))\\n    num = li[0]\\n    li2 = [i for i in range(num)]\\n    print(len(li2) + len(li))\\n    print(*li2 + li)\", \"t=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    aa=[]\\n    ind=1\\n    while True:\\n        aa.append(n//ind)\\n        if len(aa)>=2:\\n            if aa[-1]==aa[-2]:\\n                for i in range(aa[-1],-1,-1):\\n                    aa.append(i)\\n                break\\n        ind+=1\\n    print(len(set(aa)))\\n    print(*sorted(list(set(aa))))\\n    \\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor testcases in range(t):\\n    n=int(input())\\n\\n    ANS=[n//1]\\n\\n    for i in range(2,n):\\n        ANS.append(n//i)\\n\\n        if n/(i-1)-n/i<1:\\n            break\\n\\n    A=list(range(0,ANS[-1]))+sorted(set(ANS))\\n\\n    print(len(A))\\n    print(*A)\\n\", \"def kek(n):\\n\\tl = [0]\\n\\tl2 = []\\n\\ti = 1\\n\\twhile i * i < n:\\n\\t\\tl.append(i)\\n\\t\\tif n // i != i:\\n\\t\\t\\tl2.append(n // i)\\n\\t\\ti += 1\\n\\tif i * i == n:\\n\\t\\tl.append(i)\\n\\tl2.reverse()\\n\\tl += l2\\n\\treturn l\\n\\ndef main():\\n\\tfor _ in range(int(input())):\\n\\t\\tn = int(input())\\n\\t\\tl = kek(n)\\n\\t\\tprint(len(l))\\n\\t\\tfor i in l:\\n\\t\\t\\tprint(i, end=' ')\\n\\t\\tprint()\\nmain()\", \"for _ in range(int(input())):\\n\\tn=int(input())\\n\\tif n<=1000005:\\n\\t\\tl=[0,1]\\n\\t\\tfor k in range(n-1,0,-1):\\n\\t\\t\\ta=n//k\\n\\t\\t\\tif a>l[-1]:\\n\\t\\t\\t\\tl.append(a)\\n\\t\\tprint(len(l))\\n\\t\\tprint(*l)\\n\\telse:\\n\\t\\tl=[x for x in range(1001)]\\n\\t\\tfor k in range(1000000,0,-1):\\n\\t\\t\\ta=n//k\\n\\t\\t\\tif a>l[-1]:\\n\\t\\t\\t\\tl.append(a)\\n\\t\\tprint(len(l))\\n\\t\\tprint(*l)\", \"q = int(input())\\nfor ifwfwe in range(q):\\n\\tn = int(input())\\n\\ti = 1\\n\\todp = [0]\\n\\twhile i*i <= n:\\n\\t\\todp.append(i)\\n\\t\\ti += 1\\n\\twhile i > 0:\\n\\t\\tif n // i > odp[-1]:\\n\\t\\t\\todp.append(n//i)\\n\\t\\ti -= 1\\n\\tprint(len(odp))\\n\\tprint(*odp)\", \"def solve():\\n    n = int(input())\\n    s = set()\\n    s.add(0)\\n    for i in range(1, int(n**0.5)+1):\\n        k = n//i\\n        s.add(k)\\n        s.add(i)\\n    ans = sorted(s)\\n    print(len(ans))\\n    print(*ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\", \"#603_C\\n\\nt = int(input())\\n\\nfor i in range(0, t):\\n    n = int(input())\\n    ln = [0]\\n    oned = False\\n    sqt = n // int(n ** 0.5)\\n    on = -1\\n    for j in range(1, max(2, int(n ** 0.5) + 1)):\\n        if n // j != on:\\n            ln.append(n // j)\\n            if n // j == 1:\\n                oned = True\\n        on = n // j\\n    for j in range(len(ln) - 1, 0, -1):\\n        if n // ln[j] == sqt:\\n            continue\\n        ln.append(n // ln[j])\\n        if n // ln[j] == 1:\\n            oned = True\\n    if not oned:\\n        ln.append(1)\\n    print(len(ln))\\n    print(\\\" \\\".join([str(j) for j in sorted(ln)]))\\n\", \"import sys\\ndef I():\\n        return sys.stdin.readline().rstrip()\\n\\nfor _ in range( int(I()) ):\\n    n = int(I())\\n    a = [ 0, 1 ]\\n    i = n\\n    while i > 0:\\n        if n // i > a[ -1 ]:\\n            a.append( n // i )\\n        i = n // ( a[ -1 ] + 1 )\\n    print( len( a ) )\\n    print( *a )\\n\", \"import math\\nt = int(input())\\nfor i in range (t):\\n    n = int(input())\\n    m = math.floor(math.sqrt(n))\\n    ans = [j for j in range (m + 1)]\\n    left = m\\n    while m > 0:\\n        k = n//m\\n        if left == k:\\n            m -= 1\\n            continue\\n        ans.append(k)\\n        left = k\\n        m -= 1\\n    print(len(ans))\\n    print(*ans, sep = \\\" \\\")\", \"t = int(input())\\n\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ts = set.union({0}, *({i, n//i} for i in range(1, int(n**.5)+1)))\\n\\tprint(len(s))\\n\\tfor v in sorted(s):\\n\\t\\tprint(v, end=\\\" \\\")\\n\\tprint()\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\n\\tans = {0}\\n\\n\\tfor i in range(1, int(n ** 0.5 + 1)):\\n\\t\\tans.add(n // i)\\n\\t\\tans.add(n // (n // i))\\n\\n\\tprint(len(ans))\\n\\tprint(*sorted(ans))\", \"from math import sqrt\\nt=int(input())\\nfor _ in range(t):\\n\\tn=int(input())\\n\\tans=set()\\n\\tans.add(0)\\n\\troot=int(sqrt(n))\\n\\tfor x in range(1,root+1):\\n\\t\\tans.add(x)\\n\\t\\tans.add(n//x)\\n\\tprint(len(ans))\\n\\tans=sorted(ans)\\n\\tfor x in ans:\\n\\t\\tprint(x,end=' ')\\n\\tprint()\", \"# from fractions import gcd\\n# from datetime import date, timedelta\\n# from heapq import*\\n# import math\\n# from collections import defaultdict, Counter, deque\\n# import sys\\n# from bisect import *\\n# import itertools\\n# import copy\\n# sys.setrecursionlimit(10 ** 7)\\n# MOD = 10 ** 9 + 7\\n\\n\\n\\n\\n\\ndef main():\\n    t = int(input())\\n    for _ in range(t):\\n        n = int(input())\\n        prev = -1\\n        ans = []\\n        for i in range(1,40000):\\n            v = n//i\\n            if v == prev:\\n                break\\n            ans.append(v)\\n            prev = v\\n        for i in range(v-1, -1, -1):\\n            ans.append(i)\\n        print(len(ans))\\n        print(*ans[::-1])\\n\\n\\n\\n\\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"3\\n\\nimport os\\nimport sys\\n\\n\\ndef main():\\n    T = read_int()\\n    for _ in range(T):\\n        ans = solve(read_int())\\n        print(len(ans))\\n        print(*ans)\\n\\n\\ndef solve(N):\\n    ans = [N]\\n    i = 2\\n    while i * (i - 1) <= N:\\n        v = N // i\\n        if ans[-1] != v:\\n            ans.append(v)\\n        i += 1\\n\\n    v = ans[-1]\\n    for i in range(v - 1, -1, -1):\\n        ans.append(i)\\n    ans.reverse()\\n    return ans\\n\\n\\n###############################################################################\\n\\nDEBUG = 'DEBUG' in os.environ\\n\\n\\ndef inp():\\n    return sys.stdin.readline().rstrip()\\n\\n\\ndef read_int():\\n    return int(inp())\\n\\n\\ndef read_ints():\\n    return [int(e) for e in inp().split()]\\n\\n\\ndef dprint(*value, sep=' ', end='\\\\n'):\\n    if DEBUG:\\n        print(*value, sep=sep, end=end)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# from sys import stdin\\n# def rl():\\n#     return [int(w) for w in stdin.readline().split()]\\nfrom bisect import bisect_right\\nfrom bisect import bisect_left\\nfrom collections import defaultdict\\nfrom math import sqrt,factorial,gcd,log2,inf,ceil\\n# map(int,input().split())\\n# # l = list(map(int,input().split()))\\n# from itertools import permutations\\nimport sys\\n# input = sys.stdin.readline\\n\\n# t = int(input())\\n#\\n# for _ in range(t):\\n#     a,b,c = map(int,input().split())\\n#     a,b,c = sorted([a,b,c])\\n#     ans = 0\\n#     ans+=b\\n#     c-=b\\n#\\n#     a,c = sorted([a,c])\\n#     ans+=a\\n#     print(ans)\\n\\n\\n# print(ans)\\n\\n\\n\\n\\nt = int(input())\\n\\nfor _ in range(t):\\n\\n    n = int(input())\\n\\n    ans = [1,0]\\n\\n    for i in range(1,int(sqrt(n)+1)):\\n        ans.append(n//i)\\n        ans.append(n//(n//i))\\n\\n    ans = list(set(ans))\\n    print(len(ans))\\n    ans.sort()\\n    print(*ans)\\n\\n\\n\\n\\n\", \"import sys\\n\\n\\n# inf = open('input.txt', 'r')\\n# reader = (int(line.rstrip()) for line in inf)\\nreader = (int(s.rstrip()) for s in sys.stdin)\\n\\ndef rating(n):\\n    m = n\\n    ans = [0, 1]\\n    ndiv = 2\\n    while True:\\n        brick = n // ndiv\\n        if not brick:\\n            break\\n        ndiv = n // brick\\n        ans.append(ndiv)\\n        ndiv += 1\\n    return ans\\n\\nt = next(reader)\\nfor _ in range(t):\\n    n = next(reader)\\n    ans = rating(n)\\n    sys.stdout.write(str(len(ans)) + '\\\\n')\\n    sys.stdout.write(' '.join(map(str, ans)) + '\\\\n')\\n    \\n# inf.close()\\n\", \"import math\\nt = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    divisors = set(n // i for i in range(1, int(math.sqrt(n))+1))\\n    for d in divisors.copy():\\n        divisors.add(n // d)\\n    divisors.add(0)\\n\\n    print(len(divisors))\\n    print(*sorted(divisors))\\n\", \"'''input\\n4\\n5\\n11\\n1\\n3\\n'''\\nfrom sys import stdin, stdout\\n\\n\\nfrom collections import defaultdict, deque\\n\\n# main starts \\nt = int(stdin.readline().strip())\\nfor _ in range(t):\\n\\tn = int(stdin.readline().strip())\\n\\tans = set()\\n\\tfor i in range(1, int(n ** 0.5) + 1):\\n\\t\\tans.add(i)\\n\\t\\tans.add(n//i)\\n\\n\\tans.add(0)\\n\\tans.add(1)\\n\\tans.add(n)\\n\\tans = list(ans)\\n\\tans.sort()\\n\\tprint(len(ans))\\n\\tprint(*ans)\\n\", \"sp = lambda: list(map(int, input().split()))\\nsi = lambda: int(input())\\n\\nTESTCASES = int(input())\\nfor tc in range(TESTCASES):\\n    n=si()\\n    ints = set(range(int(n**0.5)+1))\\n    for i in range(int(n**0.5)+1,0,-1):\\n        ints.add(n//i)\\n    ints=sorted(list(ints))\\n    print(len(ints))\\n    print(\\\" \\\".join(map(str,ints)))\\n\", \"for i in range(int(input())):\\n\\tn = int(input())\\n\\tb = [i for i in range(1, int(n**(1/2) + 1))]\\n\\tr = [str(m) for m in sorted(list(set(b + [n//i for i in b])))]\\n\\tprint(len(r) + 1)\\n\\tprint(0, ' '.join([str(m) for m in sorted(list(set(b + [n//i for i in b])))]))\"]",
        "difficulty": "interview",
        "input": "10\n2\n4\n6\n7\n8\n9\n10\n12\n13\n14\n",
        "output": "3\n0 1 2 \n4\n0 1 2 4 \n5\n0 1 2 3 6 \n5\n0 1 2 3 7 \n5\n0 1 2 4 8 \n6\n0 1 2 3 4 9 \n6\n0 1 2 3 5 10 \n7\n0 1 2 3 4 6 12 \n7\n0 1 2 3 4 6 13 \n7\n0 1 2 3 4 7 14 \n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1263/C"
    },
    {
        "id": 250,
        "task_id": 2349,
        "test_case_id": 3,
        "question": "On the well-known testing system MathForces, a draw of $n$ rating units is arranged. The rating will be distributed according to the following algorithm: if $k$ participants take part in this event, then the $n$ rating is evenly distributed between them and rounded to the nearest lower integer, At the end of the drawing, an unused rating may remain — it is not given to any of the participants.\n\nFor example, if $n = 5$ and $k = 3$, then each participant will recieve an $1$ rating unit, and also $2$ rating units will remain unused. If $n = 5$, and $k = 6$, then none of the participants will increase their rating.\n\nVasya participates in this rating draw but does not have information on the total number of participants in this event. Therefore, he wants to know what different values of the rating increment are possible to get as a result of this draw and asks you for help.\n\nFor example, if $n=5$, then the answer is equal to the sequence $0, 1, 2, 5$. Each of the sequence values (and only them) can be obtained as $\\lfloor n/k \\rfloor$ for some positive integer $k$ (where $\\lfloor x \\rfloor$ is the value of $x$ rounded down): $0 = \\lfloor 5/7 \\rfloor$, $1 = \\lfloor 5/5 \\rfloor$, $2 = \\lfloor 5/2 \\rfloor$, $5 = \\lfloor 5/1 \\rfloor$.\n\nWrite a program that, for a given $n$, finds a sequence of all possible rating increments.\n\n\n-----Input-----\n\nThe first line contains integer number $t$ ($1 \\le t \\le 10$) — the number of test cases in the input. Then $t$ test cases follow.\n\nEach line contains an integer $n$ ($1 \\le n \\le 10^9$) — the total number of the rating units being drawn.\n\n\n-----Output-----\n\nOutput the answers for each of $t$ test cases. Each answer should be contained in two lines.\n\nIn the first line print a single integer $m$ — the number of different rating increment values that Vasya can get.\n\nIn the following line print $m$ integers in ascending order — the values of possible rating increments.\n\n\n-----Example-----\nInput\n4\n5\n11\n1\n3\n\nOutput\n4\n0 1 2 5 \n6\n0 1 2 3 5 11 \n2\n0 1 \n3\n0 1 3",
        "solutions": "[\"tst = int(input())\\nfor i in range(0, tst):\\n    n = int(input())\\n    ans = 1\\n    l = 1\\n    p = []\\n    while l <= n:\\n        ans += 1\\n        l = n // (n // l)\\n        p.append(n // l)\\n        l += 1\\n    p.append(0)\\n    p.reverse()\\n    print(len(p))\\n    print(\\\" \\\".join(str(x) for x in p))\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n\\n    l = [n]\\n    test = 2\\n    while n//test != l[-1]:\\n        l.append(n//test)\\n        test += 1\\n\\n    while l[-1] != 0:\\n        l.append(l[-1] - 1)\\n        \\n    print(len(l))\\n    print(' '.join(map(str,l[::-1])))\\n\", \"for _ in range(int(input())):\\n    n = int(input())\\n    d = 1\\n    res = [0]\\n    while d <= n:\\n        e = n // d\\n        res.append(e)\\n        d = (n // e) + 1\\n    print(len(res))\\n    print(*sorted(res))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    set_ = set()\\n    for i in range(1, int(n**0.5)+10):\\n        set_.add(n // i)\\n    li = sorted(list(set_))\\n    num = li[0]\\n    li2 = [i for i in range(num)]\\n    print(len(li2) + len(li))\\n    print(*li2 + li)\", \"t=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    aa=[]\\n    ind=1\\n    while True:\\n        aa.append(n//ind)\\n        if len(aa)>=2:\\n            if aa[-1]==aa[-2]:\\n                for i in range(aa[-1],-1,-1):\\n                    aa.append(i)\\n                break\\n        ind+=1\\n    print(len(set(aa)))\\n    print(*sorted(list(set(aa))))\\n    \\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor testcases in range(t):\\n    n=int(input())\\n\\n    ANS=[n//1]\\n\\n    for i in range(2,n):\\n        ANS.append(n//i)\\n\\n        if n/(i-1)-n/i<1:\\n            break\\n\\n    A=list(range(0,ANS[-1]))+sorted(set(ANS))\\n\\n    print(len(A))\\n    print(*A)\\n\", \"def kek(n):\\n\\tl = [0]\\n\\tl2 = []\\n\\ti = 1\\n\\twhile i * i < n:\\n\\t\\tl.append(i)\\n\\t\\tif n // i != i:\\n\\t\\t\\tl2.append(n // i)\\n\\t\\ti += 1\\n\\tif i * i == n:\\n\\t\\tl.append(i)\\n\\tl2.reverse()\\n\\tl += l2\\n\\treturn l\\n\\ndef main():\\n\\tfor _ in range(int(input())):\\n\\t\\tn = int(input())\\n\\t\\tl = kek(n)\\n\\t\\tprint(len(l))\\n\\t\\tfor i in l:\\n\\t\\t\\tprint(i, end=' ')\\n\\t\\tprint()\\nmain()\", \"for _ in range(int(input())):\\n\\tn=int(input())\\n\\tif n<=1000005:\\n\\t\\tl=[0,1]\\n\\t\\tfor k in range(n-1,0,-1):\\n\\t\\t\\ta=n//k\\n\\t\\t\\tif a>l[-1]:\\n\\t\\t\\t\\tl.append(a)\\n\\t\\tprint(len(l))\\n\\t\\tprint(*l)\\n\\telse:\\n\\t\\tl=[x for x in range(1001)]\\n\\t\\tfor k in range(1000000,0,-1):\\n\\t\\t\\ta=n//k\\n\\t\\t\\tif a>l[-1]:\\n\\t\\t\\t\\tl.append(a)\\n\\t\\tprint(len(l))\\n\\t\\tprint(*l)\", \"q = int(input())\\nfor ifwfwe in range(q):\\n\\tn = int(input())\\n\\ti = 1\\n\\todp = [0]\\n\\twhile i*i <= n:\\n\\t\\todp.append(i)\\n\\t\\ti += 1\\n\\twhile i > 0:\\n\\t\\tif n // i > odp[-1]:\\n\\t\\t\\todp.append(n//i)\\n\\t\\ti -= 1\\n\\tprint(len(odp))\\n\\tprint(*odp)\", \"def solve():\\n    n = int(input())\\n    s = set()\\n    s.add(0)\\n    for i in range(1, int(n**0.5)+1):\\n        k = n//i\\n        s.add(k)\\n        s.add(i)\\n    ans = sorted(s)\\n    print(len(ans))\\n    print(*ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\", \"#603_C\\n\\nt = int(input())\\n\\nfor i in range(0, t):\\n    n = int(input())\\n    ln = [0]\\n    oned = False\\n    sqt = n // int(n ** 0.5)\\n    on = -1\\n    for j in range(1, max(2, int(n ** 0.5) + 1)):\\n        if n // j != on:\\n            ln.append(n // j)\\n            if n // j == 1:\\n                oned = True\\n        on = n // j\\n    for j in range(len(ln) - 1, 0, -1):\\n        if n // ln[j] == sqt:\\n            continue\\n        ln.append(n // ln[j])\\n        if n // ln[j] == 1:\\n            oned = True\\n    if not oned:\\n        ln.append(1)\\n    print(len(ln))\\n    print(\\\" \\\".join([str(j) for j in sorted(ln)]))\\n\", \"import sys\\ndef I():\\n        return sys.stdin.readline().rstrip()\\n\\nfor _ in range( int(I()) ):\\n    n = int(I())\\n    a = [ 0, 1 ]\\n    i = n\\n    while i > 0:\\n        if n // i > a[ -1 ]:\\n            a.append( n // i )\\n        i = n // ( a[ -1 ] + 1 )\\n    print( len( a ) )\\n    print( *a )\\n\", \"import math\\nt = int(input())\\nfor i in range (t):\\n    n = int(input())\\n    m = math.floor(math.sqrt(n))\\n    ans = [j for j in range (m + 1)]\\n    left = m\\n    while m > 0:\\n        k = n//m\\n        if left == k:\\n            m -= 1\\n            continue\\n        ans.append(k)\\n        left = k\\n        m -= 1\\n    print(len(ans))\\n    print(*ans, sep = \\\" \\\")\", \"t = int(input())\\n\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ts = set.union({0}, *({i, n//i} for i in range(1, int(n**.5)+1)))\\n\\tprint(len(s))\\n\\tfor v in sorted(s):\\n\\t\\tprint(v, end=\\\" \\\")\\n\\tprint()\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\n\\tans = {0}\\n\\n\\tfor i in range(1, int(n ** 0.5 + 1)):\\n\\t\\tans.add(n // i)\\n\\t\\tans.add(n // (n // i))\\n\\n\\tprint(len(ans))\\n\\tprint(*sorted(ans))\", \"from math import sqrt\\nt=int(input())\\nfor _ in range(t):\\n\\tn=int(input())\\n\\tans=set()\\n\\tans.add(0)\\n\\troot=int(sqrt(n))\\n\\tfor x in range(1,root+1):\\n\\t\\tans.add(x)\\n\\t\\tans.add(n//x)\\n\\tprint(len(ans))\\n\\tans=sorted(ans)\\n\\tfor x in ans:\\n\\t\\tprint(x,end=' ')\\n\\tprint()\", \"# from fractions import gcd\\n# from datetime import date, timedelta\\n# from heapq import*\\n# import math\\n# from collections import defaultdict, Counter, deque\\n# import sys\\n# from bisect import *\\n# import itertools\\n# import copy\\n# sys.setrecursionlimit(10 ** 7)\\n# MOD = 10 ** 9 + 7\\n\\n\\n\\n\\n\\ndef main():\\n    t = int(input())\\n    for _ in range(t):\\n        n = int(input())\\n        prev = -1\\n        ans = []\\n        for i in range(1,40000):\\n            v = n//i\\n            if v == prev:\\n                break\\n            ans.append(v)\\n            prev = v\\n        for i in range(v-1, -1, -1):\\n            ans.append(i)\\n        print(len(ans))\\n        print(*ans[::-1])\\n\\n\\n\\n\\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"3\\n\\nimport os\\nimport sys\\n\\n\\ndef main():\\n    T = read_int()\\n    for _ in range(T):\\n        ans = solve(read_int())\\n        print(len(ans))\\n        print(*ans)\\n\\n\\ndef solve(N):\\n    ans = [N]\\n    i = 2\\n    while i * (i - 1) <= N:\\n        v = N // i\\n        if ans[-1] != v:\\n            ans.append(v)\\n        i += 1\\n\\n    v = ans[-1]\\n    for i in range(v - 1, -1, -1):\\n        ans.append(i)\\n    ans.reverse()\\n    return ans\\n\\n\\n###############################################################################\\n\\nDEBUG = 'DEBUG' in os.environ\\n\\n\\ndef inp():\\n    return sys.stdin.readline().rstrip()\\n\\n\\ndef read_int():\\n    return int(inp())\\n\\n\\ndef read_ints():\\n    return [int(e) for e in inp().split()]\\n\\n\\ndef dprint(*value, sep=' ', end='\\\\n'):\\n    if DEBUG:\\n        print(*value, sep=sep, end=end)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# from sys import stdin\\n# def rl():\\n#     return [int(w) for w in stdin.readline().split()]\\nfrom bisect import bisect_right\\nfrom bisect import bisect_left\\nfrom collections import defaultdict\\nfrom math import sqrt,factorial,gcd,log2,inf,ceil\\n# map(int,input().split())\\n# # l = list(map(int,input().split()))\\n# from itertools import permutations\\nimport sys\\n# input = sys.stdin.readline\\n\\n# t = int(input())\\n#\\n# for _ in range(t):\\n#     a,b,c = map(int,input().split())\\n#     a,b,c = sorted([a,b,c])\\n#     ans = 0\\n#     ans+=b\\n#     c-=b\\n#\\n#     a,c = sorted([a,c])\\n#     ans+=a\\n#     print(ans)\\n\\n\\n# print(ans)\\n\\n\\n\\n\\nt = int(input())\\n\\nfor _ in range(t):\\n\\n    n = int(input())\\n\\n    ans = [1,0]\\n\\n    for i in range(1,int(sqrt(n)+1)):\\n        ans.append(n//i)\\n        ans.append(n//(n//i))\\n\\n    ans = list(set(ans))\\n    print(len(ans))\\n    ans.sort()\\n    print(*ans)\\n\\n\\n\\n\\n\", \"import sys\\n\\n\\n# inf = open('input.txt', 'r')\\n# reader = (int(line.rstrip()) for line in inf)\\nreader = (int(s.rstrip()) for s in sys.stdin)\\n\\ndef rating(n):\\n    m = n\\n    ans = [0, 1]\\n    ndiv = 2\\n    while True:\\n        brick = n // ndiv\\n        if not brick:\\n            break\\n        ndiv = n // brick\\n        ans.append(ndiv)\\n        ndiv += 1\\n    return ans\\n\\nt = next(reader)\\nfor _ in range(t):\\n    n = next(reader)\\n    ans = rating(n)\\n    sys.stdout.write(str(len(ans)) + '\\\\n')\\n    sys.stdout.write(' '.join(map(str, ans)) + '\\\\n')\\n    \\n# inf.close()\\n\", \"import math\\nt = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    divisors = set(n // i for i in range(1, int(math.sqrt(n))+1))\\n    for d in divisors.copy():\\n        divisors.add(n // d)\\n    divisors.add(0)\\n\\n    print(len(divisors))\\n    print(*sorted(divisors))\\n\", \"'''input\\n4\\n5\\n11\\n1\\n3\\n'''\\nfrom sys import stdin, stdout\\n\\n\\nfrom collections import defaultdict, deque\\n\\n# main starts \\nt = int(stdin.readline().strip())\\nfor _ in range(t):\\n\\tn = int(stdin.readline().strip())\\n\\tans = set()\\n\\tfor i in range(1, int(n ** 0.5) + 1):\\n\\t\\tans.add(i)\\n\\t\\tans.add(n//i)\\n\\n\\tans.add(0)\\n\\tans.add(1)\\n\\tans.add(n)\\n\\tans = list(ans)\\n\\tans.sort()\\n\\tprint(len(ans))\\n\\tprint(*ans)\\n\", \"sp = lambda: list(map(int, input().split()))\\nsi = lambda: int(input())\\n\\nTESTCASES = int(input())\\nfor tc in range(TESTCASES):\\n    n=si()\\n    ints = set(range(int(n**0.5)+1))\\n    for i in range(int(n**0.5)+1,0,-1):\\n        ints.add(n//i)\\n    ints=sorted(list(ints))\\n    print(len(ints))\\n    print(\\\" \\\".join(map(str,ints)))\\n\", \"for i in range(int(input())):\\n\\tn = int(input())\\n\\tb = [i for i in range(1, int(n**(1/2) + 1))]\\n\\tr = [str(m) for m in sorted(list(set(b + [n//i for i in b])))]\\n\\tprint(len(r) + 1)\\n\\tprint(0, ' '.join([str(m) for m in sorted(list(set(b + [n//i for i in b])))]))\"]",
        "difficulty": "interview",
        "input": "3\n990\n94\n848\n",
        "output": "62\n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 38 39 41 43 45 47 49 52 55 58 61 66 70 76 82 90 99 110 123 141 165 198 247 330 495 990 \n19\n0 1 2 3 4 5 6 7 8 9 10 11 13 15 18 23 31 47 94 \n58\n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36 38 40 42 44 47 49 53 56 60 65 70 77 84 94 106 121 141 169 212 282 424 848 \n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1263/C"
    },
    {
        "id": 251,
        "task_id": 2349,
        "test_case_id": 4,
        "question": "On the well-known testing system MathForces, a draw of $n$ rating units is arranged. The rating will be distributed according to the following algorithm: if $k$ participants take part in this event, then the $n$ rating is evenly distributed between them and rounded to the nearest lower integer, At the end of the drawing, an unused rating may remain — it is not given to any of the participants.\n\nFor example, if $n = 5$ and $k = 3$, then each participant will recieve an $1$ rating unit, and also $2$ rating units will remain unused. If $n = 5$, and $k = 6$, then none of the participants will increase their rating.\n\nVasya participates in this rating draw but does not have information on the total number of participants in this event. Therefore, he wants to know what different values of the rating increment are possible to get as a result of this draw and asks you for help.\n\nFor example, if $n=5$, then the answer is equal to the sequence $0, 1, 2, 5$. Each of the sequence values (and only them) can be obtained as $\\lfloor n/k \\rfloor$ for some positive integer $k$ (where $\\lfloor x \\rfloor$ is the value of $x$ rounded down): $0 = \\lfloor 5/7 \\rfloor$, $1 = \\lfloor 5/5 \\rfloor$, $2 = \\lfloor 5/2 \\rfloor$, $5 = \\lfloor 5/1 \\rfloor$.\n\nWrite a program that, for a given $n$, finds a sequence of all possible rating increments.\n\n\n-----Input-----\n\nThe first line contains integer number $t$ ($1 \\le t \\le 10$) — the number of test cases in the input. Then $t$ test cases follow.\n\nEach line contains an integer $n$ ($1 \\le n \\le 10^9$) — the total number of the rating units being drawn.\n\n\n-----Output-----\n\nOutput the answers for each of $t$ test cases. Each answer should be contained in two lines.\n\nIn the first line print a single integer $m$ — the number of different rating increment values that Vasya can get.\n\nIn the following line print $m$ integers in ascending order — the values of possible rating increments.\n\n\n-----Example-----\nInput\n4\n5\n11\n1\n3\n\nOutput\n4\n0 1 2 5 \n6\n0 1 2 3 5 11 \n2\n0 1 \n3\n0 1 3",
        "solutions": "[\"tst = int(input())\\nfor i in range(0, tst):\\n    n = int(input())\\n    ans = 1\\n    l = 1\\n    p = []\\n    while l <= n:\\n        ans += 1\\n        l = n // (n // l)\\n        p.append(n // l)\\n        l += 1\\n    p.append(0)\\n    p.reverse()\\n    print(len(p))\\n    print(\\\" \\\".join(str(x) for x in p))\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n\\n    l = [n]\\n    test = 2\\n    while n//test != l[-1]:\\n        l.append(n//test)\\n        test += 1\\n\\n    while l[-1] != 0:\\n        l.append(l[-1] - 1)\\n        \\n    print(len(l))\\n    print(' '.join(map(str,l[::-1])))\\n\", \"for _ in range(int(input())):\\n    n = int(input())\\n    d = 1\\n    res = [0]\\n    while d <= n:\\n        e = n // d\\n        res.append(e)\\n        d = (n // e) + 1\\n    print(len(res))\\n    print(*sorted(res))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    set_ = set()\\n    for i in range(1, int(n**0.5)+10):\\n        set_.add(n // i)\\n    li = sorted(list(set_))\\n    num = li[0]\\n    li2 = [i for i in range(num)]\\n    print(len(li2) + len(li))\\n    print(*li2 + li)\", \"t=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    aa=[]\\n    ind=1\\n    while True:\\n        aa.append(n//ind)\\n        if len(aa)>=2:\\n            if aa[-1]==aa[-2]:\\n                for i in range(aa[-1],-1,-1):\\n                    aa.append(i)\\n                break\\n        ind+=1\\n    print(len(set(aa)))\\n    print(*sorted(list(set(aa))))\\n    \\n\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor testcases in range(t):\\n    n=int(input())\\n\\n    ANS=[n//1]\\n\\n    for i in range(2,n):\\n        ANS.append(n//i)\\n\\n        if n/(i-1)-n/i<1:\\n            break\\n\\n    A=list(range(0,ANS[-1]))+sorted(set(ANS))\\n\\n    print(len(A))\\n    print(*A)\\n\", \"def kek(n):\\n\\tl = [0]\\n\\tl2 = []\\n\\ti = 1\\n\\twhile i * i < n:\\n\\t\\tl.append(i)\\n\\t\\tif n // i != i:\\n\\t\\t\\tl2.append(n // i)\\n\\t\\ti += 1\\n\\tif i * i == n:\\n\\t\\tl.append(i)\\n\\tl2.reverse()\\n\\tl += l2\\n\\treturn l\\n\\ndef main():\\n\\tfor _ in range(int(input())):\\n\\t\\tn = int(input())\\n\\t\\tl = kek(n)\\n\\t\\tprint(len(l))\\n\\t\\tfor i in l:\\n\\t\\t\\tprint(i, end=' ')\\n\\t\\tprint()\\nmain()\", \"for _ in range(int(input())):\\n\\tn=int(input())\\n\\tif n<=1000005:\\n\\t\\tl=[0,1]\\n\\t\\tfor k in range(n-1,0,-1):\\n\\t\\t\\ta=n//k\\n\\t\\t\\tif a>l[-1]:\\n\\t\\t\\t\\tl.append(a)\\n\\t\\tprint(len(l))\\n\\t\\tprint(*l)\\n\\telse:\\n\\t\\tl=[x for x in range(1001)]\\n\\t\\tfor k in range(1000000,0,-1):\\n\\t\\t\\ta=n//k\\n\\t\\t\\tif a>l[-1]:\\n\\t\\t\\t\\tl.append(a)\\n\\t\\tprint(len(l))\\n\\t\\tprint(*l)\", \"q = int(input())\\nfor ifwfwe in range(q):\\n\\tn = int(input())\\n\\ti = 1\\n\\todp = [0]\\n\\twhile i*i <= n:\\n\\t\\todp.append(i)\\n\\t\\ti += 1\\n\\twhile i > 0:\\n\\t\\tif n // i > odp[-1]:\\n\\t\\t\\todp.append(n//i)\\n\\t\\ti -= 1\\n\\tprint(len(odp))\\n\\tprint(*odp)\", \"def solve():\\n    n = int(input())\\n    s = set()\\n    s.add(0)\\n    for i in range(1, int(n**0.5)+1):\\n        k = n//i\\n        s.add(k)\\n        s.add(i)\\n    ans = sorted(s)\\n    print(len(ans))\\n    print(*ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\", \"#603_C\\n\\nt = int(input())\\n\\nfor i in range(0, t):\\n    n = int(input())\\n    ln = [0]\\n    oned = False\\n    sqt = n // int(n ** 0.5)\\n    on = -1\\n    for j in range(1, max(2, int(n ** 0.5) + 1)):\\n        if n // j != on:\\n            ln.append(n // j)\\n            if n // j == 1:\\n                oned = True\\n        on = n // j\\n    for j in range(len(ln) - 1, 0, -1):\\n        if n // ln[j] == sqt:\\n            continue\\n        ln.append(n // ln[j])\\n        if n // ln[j] == 1:\\n            oned = True\\n    if not oned:\\n        ln.append(1)\\n    print(len(ln))\\n    print(\\\" \\\".join([str(j) for j in sorted(ln)]))\\n\", \"import sys\\ndef I():\\n        return sys.stdin.readline().rstrip()\\n\\nfor _ in range( int(I()) ):\\n    n = int(I())\\n    a = [ 0, 1 ]\\n    i = n\\n    while i > 0:\\n        if n // i > a[ -1 ]:\\n            a.append( n // i )\\n        i = n // ( a[ -1 ] + 1 )\\n    print( len( a ) )\\n    print( *a )\\n\", \"import math\\nt = int(input())\\nfor i in range (t):\\n    n = int(input())\\n    m = math.floor(math.sqrt(n))\\n    ans = [j for j in range (m + 1)]\\n    left = m\\n    while m > 0:\\n        k = n//m\\n        if left == k:\\n            m -= 1\\n            continue\\n        ans.append(k)\\n        left = k\\n        m -= 1\\n    print(len(ans))\\n    print(*ans, sep = \\\" \\\")\", \"t = int(input())\\n\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ts = set.union({0}, *({i, n//i} for i in range(1, int(n**.5)+1)))\\n\\tprint(len(s))\\n\\tfor v in sorted(s):\\n\\t\\tprint(v, end=\\\" \\\")\\n\\tprint()\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\n\\tans = {0}\\n\\n\\tfor i in range(1, int(n ** 0.5 + 1)):\\n\\t\\tans.add(n // i)\\n\\t\\tans.add(n // (n // i))\\n\\n\\tprint(len(ans))\\n\\tprint(*sorted(ans))\", \"from math import sqrt\\nt=int(input())\\nfor _ in range(t):\\n\\tn=int(input())\\n\\tans=set()\\n\\tans.add(0)\\n\\troot=int(sqrt(n))\\n\\tfor x in range(1,root+1):\\n\\t\\tans.add(x)\\n\\t\\tans.add(n//x)\\n\\tprint(len(ans))\\n\\tans=sorted(ans)\\n\\tfor x in ans:\\n\\t\\tprint(x,end=' ')\\n\\tprint()\", \"# from fractions import gcd\\n# from datetime import date, timedelta\\n# from heapq import*\\n# import math\\n# from collections import defaultdict, Counter, deque\\n# import sys\\n# from bisect import *\\n# import itertools\\n# import copy\\n# sys.setrecursionlimit(10 ** 7)\\n# MOD = 10 ** 9 + 7\\n\\n\\n\\n\\n\\ndef main():\\n    t = int(input())\\n    for _ in range(t):\\n        n = int(input())\\n        prev = -1\\n        ans = []\\n        for i in range(1,40000):\\n            v = n//i\\n            if v == prev:\\n                break\\n            ans.append(v)\\n            prev = v\\n        for i in range(v-1, -1, -1):\\n            ans.append(i)\\n        print(len(ans))\\n        print(*ans[::-1])\\n\\n\\n\\n\\n\\n    \\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"3\\n\\nimport os\\nimport sys\\n\\n\\ndef main():\\n    T = read_int()\\n    for _ in range(T):\\n        ans = solve(read_int())\\n        print(len(ans))\\n        print(*ans)\\n\\n\\ndef solve(N):\\n    ans = [N]\\n    i = 2\\n    while i * (i - 1) <= N:\\n        v = N // i\\n        if ans[-1] != v:\\n            ans.append(v)\\n        i += 1\\n\\n    v = ans[-1]\\n    for i in range(v - 1, -1, -1):\\n        ans.append(i)\\n    ans.reverse()\\n    return ans\\n\\n\\n###############################################################################\\n\\nDEBUG = 'DEBUG' in os.environ\\n\\n\\ndef inp():\\n    return sys.stdin.readline().rstrip()\\n\\n\\ndef read_int():\\n    return int(inp())\\n\\n\\ndef read_ints():\\n    return [int(e) for e in inp().split()]\\n\\n\\ndef dprint(*value, sep=' ', end='\\\\n'):\\n    if DEBUG:\\n        print(*value, sep=sep, end=end)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# from sys import stdin\\n# def rl():\\n#     return [int(w) for w in stdin.readline().split()]\\nfrom bisect import bisect_right\\nfrom bisect import bisect_left\\nfrom collections import defaultdict\\nfrom math import sqrt,factorial,gcd,log2,inf,ceil\\n# map(int,input().split())\\n# # l = list(map(int,input().split()))\\n# from itertools import permutations\\nimport sys\\n# input = sys.stdin.readline\\n\\n# t = int(input())\\n#\\n# for _ in range(t):\\n#     a,b,c = map(int,input().split())\\n#     a,b,c = sorted([a,b,c])\\n#     ans = 0\\n#     ans+=b\\n#     c-=b\\n#\\n#     a,c = sorted([a,c])\\n#     ans+=a\\n#     print(ans)\\n\\n\\n# print(ans)\\n\\n\\n\\n\\nt = int(input())\\n\\nfor _ in range(t):\\n\\n    n = int(input())\\n\\n    ans = [1,0]\\n\\n    for i in range(1,int(sqrt(n)+1)):\\n        ans.append(n//i)\\n        ans.append(n//(n//i))\\n\\n    ans = list(set(ans))\\n    print(len(ans))\\n    ans.sort()\\n    print(*ans)\\n\\n\\n\\n\\n\", \"import sys\\n\\n\\n# inf = open('input.txt', 'r')\\n# reader = (int(line.rstrip()) for line in inf)\\nreader = (int(s.rstrip()) for s in sys.stdin)\\n\\ndef rating(n):\\n    m = n\\n    ans = [0, 1]\\n    ndiv = 2\\n    while True:\\n        brick = n // ndiv\\n        if not brick:\\n            break\\n        ndiv = n // brick\\n        ans.append(ndiv)\\n        ndiv += 1\\n    return ans\\n\\nt = next(reader)\\nfor _ in range(t):\\n    n = next(reader)\\n    ans = rating(n)\\n    sys.stdout.write(str(len(ans)) + '\\\\n')\\n    sys.stdout.write(' '.join(map(str, ans)) + '\\\\n')\\n    \\n# inf.close()\\n\", \"import math\\nt = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    divisors = set(n // i for i in range(1, int(math.sqrt(n))+1))\\n    for d in divisors.copy():\\n        divisors.add(n // d)\\n    divisors.add(0)\\n\\n    print(len(divisors))\\n    print(*sorted(divisors))\\n\", \"'''input\\n4\\n5\\n11\\n1\\n3\\n'''\\nfrom sys import stdin, stdout\\n\\n\\nfrom collections import defaultdict, deque\\n\\n# main starts \\nt = int(stdin.readline().strip())\\nfor _ in range(t):\\n\\tn = int(stdin.readline().strip())\\n\\tans = set()\\n\\tfor i in range(1, int(n ** 0.5) + 1):\\n\\t\\tans.add(i)\\n\\t\\tans.add(n//i)\\n\\n\\tans.add(0)\\n\\tans.add(1)\\n\\tans.add(n)\\n\\tans = list(ans)\\n\\tans.sort()\\n\\tprint(len(ans))\\n\\tprint(*ans)\\n\", \"sp = lambda: list(map(int, input().split()))\\nsi = lambda: int(input())\\n\\nTESTCASES = int(input())\\nfor tc in range(TESTCASES):\\n    n=si()\\n    ints = set(range(int(n**0.5)+1))\\n    for i in range(int(n**0.5)+1,0,-1):\\n        ints.add(n//i)\\n    ints=sorted(list(ints))\\n    print(len(ints))\\n    print(\\\" \\\".join(map(str,ints)))\\n\", \"for i in range(int(input())):\\n\\tn = int(input())\\n\\tb = [i for i in range(1, int(n**(1/2) + 1))]\\n\\tr = [str(m) for m in sorted(list(set(b + [n//i for i in b])))]\\n\\tprint(len(r) + 1)\\n\\tprint(0, ' '.join([str(m) for m in sorted(list(set(b + [n//i for i in b])))]))\"]",
        "difficulty": "interview",
        "input": "2\n960\n961\n",
        "output": "61\n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 38 40 41 43 45 48 50 53 56 60 64 68 73 80 87 96 106 120 137 160 192 240 320 480 960 \n62\n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 40 41 43 45 48 50 53 56 60 64 68 73 80 87 96 106 120 137 160 192 240 320 480 961 \n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1263/C"
    },
    {
        "id": 252,
        "task_id": 2498,
        "test_case_id": 1,
        "question": "Given are a sequence A= {a_1,a_2,......a_N} of N positive even numbers, and an integer M.\nLet a semi-common multiple of A be a positive integer X that satisfies the following condition for every k (1 \\leq k \\leq N):\n - There exists a non-negative integer p such that X= a_k \\times (p+0.5).\nFind the number of semi-common multiples of A among the integers between 1 and M (inclusive).\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^9\n - 2 \\leq a_i \\leq 10^9\n - a_i is an even number.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 a_2 ... a_N\n\n-----Output-----\nPrint the number of semi-common multiples of A among the integers between 1 and M (inclusive).\n\n-----Sample Input-----\n2 50\n6 10\n\n-----Sample Output-----\n2\n\n - 15 = 6  \\times 2.5 \n - 15 = 10 \\times 1.5 \n - 45 = 6  \\times 7.5 \n - 45 = 10 \\times 4.5 \nThus, 15 and 45 are semi-common multiples of A. There are no other semi-common multiples of A between 1 and 50, so the answer is 2.",
        "solutions": "[\"n, m = map( int, input().split() )\\na = list( map( int, input().split() ) )\\n\\ndef f( a_k ): # 2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\n    count = 0\\n    while a_k % 2 == 0:\\n        count += 1\\n        a_k = a_k // 2\\n    return count\\n\\nb = []\\nf_0 = f( a[ 0 ] )\\nfor a_k in a:\\n    f_k = f( a_k )\\n    if f_k != f_0:\\n        print( 0 )\\n        return\\n    b.append( a_k // pow( 2, f_k ) )\\n\\nimport math\\ndef lcm( x, y ):\\n    return x * y // math.gcd( x, y )\\n\\nb_lcm = 1\\nfor b_k in b:\\n    b_lcm = lcm( b_lcm, b_k )\\n\\na_lcm = b_lcm * pow( 2, f_0 )\\n# print( b_lcm, f_0, b )\\nprint( ( m + a_lcm // 2 ) // a_lcm )\", \"from functools import reduce\\n\\nN, M = list(map(int, input().split()))\\nAs = list(map(int, input().split()))\\n\\nBs = [A//2 for A in As]\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a%b\\n    return a\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b\\n\\nnums = []\\nfor B in Bs:\\n    num = 0\\n    while B%2 == 0:\\n        B //= 2\\n        num += 1\\n    nums.append(num)\\n\\nif len(set(nums)) != 1:\\n    ans = 0\\nelse:\\n    L = reduce(lcm, Bs)\\n    ans = M//L - M//(2*L)\\n\\nprint(ans)\\n\", \"import math\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\nb = {}\\nfor i in range(n):\\n    count = 0\\n    temp = a[i]\\n    while temp % 2 == 0:\\n        count += 1\\n        temp //= 2\\n    b.setdefault(count, 0)\\n    b[count] += 1\\nif len(b.keys()) >= 2:\\n    ans = 0\\nelse:\\n    temp = 1\\n    for i in range(n):\\n        temp = temp * a[i] // math.gcd(temp, a[i])\\n    temp2 = temp // 2\\n    ans = m // temp2 - m // temp\\nprint(ans)\", \"import numpy as np\\nimport sys\\n\\ndef main():\\n    N,M=list(map(int,input().split()))\\n    A=list(map(int,input().split()))\\n    A_double=list([x//2 for x in A])\\n\\n    mini_multi=int(np.lcm.reduce(A_double))\\n\\n    res=M//mini_multi\\n    \\n    for i in A_double:\\n        if (mini_multi//i)%2==0:\\n            print((0))\\n            return\\n\\n    if res%2!=0:\\n        res+=1\\n\\n\\n    print((res//2))\\n\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# ABC150D\\n\\nimport sys\\ninput=sys.stdin.readline\\nfrom math import gcd,ceil\\n\\ndef main():\\n    N,M=list(map(int,input().split()))\\n    A=list([int(x)//2 for x in input().split()])\\n    lcm=A[0]\\n    for i in range(1,N):\\n        lcm=lcm*A[i]//gcd(lcm,A[i])\\n    allo=1\\n    for i in range(N):\\n        allo&=(lcm//A[i])%2\\n    if allo:\\n        print((ceil(int(M//lcm)/2)))\\n    else:\\n        print((0))\\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nfrom math import gcd\\nfrom copy import deepcopy\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\n\\ndef resolve():\\n    n, m = list(map(int, input().split()))\\n    A = list(map(int, input().split()))\\n\\n    A_ = deepcopy(A)\\n    cnt = [0] * n\\n    for i in range(n):\\n        while A_[i] % 2 == 0:\\n            A_[i] //= 2\\n            cnt[i] += 1\\n        if i != 0 and cnt[i] != cnt[i - 1]:\\n            print((0))\\n            return\\n\\n    L = 1\\n    for a in A:\\n        L = lcm(L, a // 2)\\n\\n    res = m // L - (m // (L * 2))\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from math import gcd\\ndef lcm(a,b):return (a*b)//(gcd(a,b))\\n\\ndef f(x):\\n    cnt=0\\n    while(x%2==0):\\n        cnt+=1\\n        x=x//2\\n    return cnt\\n\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(map(lambda x: x//2,a))\\n\\nt=f(a[0])\\nfor i in range(n):\\n    if(f(a[i])!=t):\\n        print(0)\\n        return\\n    a[i]=a[i]//(2**t)\\nm=m//(2**t)\\nl=1\\nfor i in range(n):\\n    l=lcm(l,a[i])\\n    if(l>m):\\n        print(0)\\n        return\\nm=m//l\\nprint((m+1)//2)\", \"import math\\n\\nn,m=list(map(int,input().split()))\\na=list(map(int,input().split()))\\n\\nif n==1:\\n  a1=a[0]//2\\n  ans_m=m//a1\\n  if ans_m==0:\\n    print((0))\\n  else:\\n    print(((ans_m-1)//2+1))\\n  \\nelse:\\n  x=a[0]\\n  ch=0\\n  ch1=0\\n  while x%2==0:\\n    x=x//2\\n    ch+=1\\n  dob=2**ch\\n  for i in a:\\n    if i%dob==0 and i%(dob*2)!=0:\\n      ch1+=1\\n  if ch1!=n:\\n    print((0))\\n  else:\\n    ans=a[0]//2\\n    for j in range(1,n):\\n      ans=(ans*(a[j]//2))//math.gcd(ans,a[j]//2)\\n    ans_m=m//ans\\n    if ans_m==0:\\n      print((0))\\n    else:\\n      print(((ans_m-1)//2+1))\\n    \\n      \\n\", \"from math import gcd, ceil\\nN,M = map(int,input().split())\\nA = list(map(int,input().split()))\\nA = [a//2 for a in A]\\nB = 1\\n\\nfor a in A:\\n  B*=a//gcd(B,a)\\n  \\nfor a in A:\\n  if B//a%2==0:\\n    print(0)\\n    return\\n\\nprint(ceil((M//B)/2))\", \"def solve():\\n    import math\\n    N,M = [int(i) for i in input().split()]\\n    A = list(map(int, input().split()))\\n\\n    lcm = A[0]\\n    for i in range(1, N):\\n        lcm = lcm * A[i] // math.gcd(lcm, A[i])\\n    first = lcm // 2\\n\\n    ans_exists = True\\n    for i in range(N):\\n        if first % A[i] == 0:\\n            ans_exists = False\\n\\n    if ans_exists:\\n        ans = int((M-first) // lcm + 1)\\n        print(ans)\\n    else:\\n        print('0')\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# -*- coding: utf-8 -*-\\n\\\"\\\"\\\"\\nCreated on Wed Sep  9 14:33:00 2020\\n\\n@author: liang\\n\\\"\\\"\\\"\\nfrom math import gcd\\n\\nN, M = map(int, input().split())\\nA = [int(i) for i in input().split()]\\n\\nflag = False\\nres = 1\\nfor a in A:\\n    a //= 2\\n    res *= a//gcd(res,a)\\n    if res > M:\\n        flag = True\\n        break\\n    #print(res)\\n\\\"\\\"\\\"\\n\\u5b58\\u5728\\u30c1\\u30a7\\u30c3\\u30af\\n\\uff12\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u500b\\u6570\\u540c\\u3058\\uff1f\\n\\\"\\\"\\\"\\n\\nfor a in A:\\n    if int(res/a) == res/a:\\n        flag = True\\n        \\nif flag:\\n    ans = 0\\n    print(ans)\\nelse:\\n    #ans = (M - res(A)//2)//res + 1\\n    #ans = (M-1)//res//2 + 1\\n    ans= (M//res + 1)//2\\n    print(ans)\", \"import math\\n\\nN, M = map(int,input().split())\\nA = list(map(int,input().split()))\\n\\npow2 = 0\\nwhile A[0] % 2 == 0:\\n    A[0] //= 2\\n    pow2 += 1\\n\\nfor i in range(1,N):\\n    cnt = 0\\n    while A[i] % 2 == 0:\\n        A[i] //= 2\\n        cnt += 1\\n    if cnt != pow2:\\n        print(0)\\n        return\\n\\nLCM = 2**max(0,pow2-1)\\nfor i in range(N):\\n    LCM = LCM * A[i] // math.gcd(LCM,A[i])\\n\\nans = M // LCM\\nprint((ans+1)//2)\", \"from math import gcd\\nfrom functools import reduce\\nimport sys\\ninput = sys.stdin.readline\\n\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a, b)\\n\\n\\ndef count_factor_2(num):\\n    count = 0\\n    while num % 2 == 0:\\n        num //= 2\\n        count += 1\\n    return count\\n\\n\\ndef main():\\n    n, m = list(map(int, input().split()))\\n    A = list([x//2 for x in set(map(int, input().split()))])\\n\\n    check = len(set(map(count_factor_2, A)))\\n    if check != 1:\\n        print((0))\\n        return\\n\\n    lcm_a = reduce(lcm, A)\\n    step = lcm_a * 2\\n    ans = (m + lcm_a) // step\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nA = list(map(lambda x: int(x)//2, input().split()))\\n\\nimport math\\n\\ndef lcm(x, y):\\n  return (x // math.gcd(x, y)) * y\\n\\ndef pow2(x):\\n  ret = 0\\n  while x%2 == 0:\\n    ret += 1\\n    x //= 2\\n  return ret\\n\\nP = []\\nfor a in A:\\n  P.append(pow2(a))\\n\\nif len(set(P)) != 1:\\n  print(0)\\nelse:\\n  m = 1\\n  for a in A:\\n    m = lcm(m, a)\\n  print(-(-(M//m)//2))\", \"def GCM(x, y):\\n  if x%y==0:\\n    return y\\n  else:\\n    return GCM(y, x%y)\\n\\nN, M = map(int, input().split())\\n\\nA = list(map(int, input().split()))\\n\\ncount2 = [0 for i in range(N)]\\nfor i in range(N):\\n  a = A[i]\\n  while a%2==0:\\n    count2[i] += 1\\n    a = a//2\\n  A[i] = a\\nif sum(count2) == count2[0]*N:\\n  count2 = count2[0]\\n  buf = 1\\n  for i in range(N):\\n    buf = A[i]*buf//GCM(buf, A[i])\\n  buf *= 2**(count2-1)\\n  #print(buf)\\n  n = M//buf\\n  print((n+1)//2)\\n  \\nelse:\\n  print(0)\", \"import fractions\\nimport math\\nfrom functools import reduce\\n\\ndef lcm_base(x, y):\\n    return (x * y) // fractions.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\nb=lcm_list(map(lambda x: x//2, a))\\nswt=0\\n\\nfor i in range(n):\\n  if 0==(b//(a[i]//2))%2:\\n    swt=1\\n    break\\n\\nif 0==swt:\\n  print(math.ceil((m//b)/2))\\nelse:\\n  print(0)\", \"import math\\nimport numpy as np\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nc=1\\ntest=A[0]\\nl=0\\n\\nwhile test%2 == 0:\\n  test=test//2\\n  c*=2\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n  \\nfor i in np.arange(N-1):\\n  if A[i+1]%c!=0:\\n    print(0)\\n    l=1\\n    break\\n  elif A[i+1]%(c*2)==0:\\n    print(0)\\n    l=1\\n    break\\n  else:\\n    k=A[i+1]//c\\n    test=lcm_base(test, k)\\nif l==0:\\n  k=test*c//2\\n  print(M//k//2 + M//k%2)\", \"from math import gcd\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nmemo = {}\\n\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\n\\nb = 1\\n\\nfor a in A:\\n    b = lcm(a//2, b)\\n    if b > M:\\n        break\\n\\nif any([2 * b // a % 2 == 0 for a in A]):\\n    print(0)\\nelse:\\n    ans = M // b\\n    print(ans - ans // 2)\", \"import copy\\n# from math import gcd\\n\\n\\ndef gcd(a, b):\\n    if b == 0:\\n        return a\\n    else:\\n        return gcd(b, a%b)\\n\\ndef lcm(a, b):\\n    return (a // gcd(a, b)) * b\\ndef main():\\n    n, m = map(int, input().split())\\n    A = set([int(x) for x in input().split()])\\n    a_lcm = 1\\n    for a in A:\\n        a_lcm = lcm(a_lcm, a)\\n        # m\\u304clcm\\u306e\\u534a\\u5206\\u3088\\u308a\\u3082\\u5c0f\\u3055\\u304b\\u3063\\u305f\\u30890\\n        if (a_lcm / 2) > m:\\n            print(0)\\n            return\\n    for a in A:\\n        if (a_lcm / 2) % a == 0:\\n            print(0)\\n            return\\n    # # \\u3042\\u3068\\u306f\\u5b9a\\u6570\\u500d\\u306e\\u6570\\u8abf\\u3079\\u3066\\u7d42\\u308f\\u308a\\n    ans = int((m - (a_lcm / 2)) // a_lcm) + 1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"from math import gcd\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\ndef lcm(ab):\\n    l=len(ab)\\n    ret=ab[0]\\n    for i in range(1,l):\\n        ret=ret//gcd(ab[i],ret)*ab[i]\\n    return ret\\ndef count2(a):\\n    ret=0\\n    while a%2==0:\\n        a//=2\\n        ret+=1\\n    return 2**ret\\nn,m=map(int,input().split())\\nA=list(map(int,input().split()))\\n#\\u3053\\u308c\\u306f\\u3044\\u3089\\u306a\\u3044\\u3067\\u3059\\nif any(i%2 for i in A):\\n    print(0);return\\nA=[i//2 for i in A]\\n#\\u5168\\u4f53\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\np=lcm(A)\\nc=count2(p)\\n#2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3082\\u306e\\u304c\\u3042\\u308b\\u5834\\u5408\\nif any(i%c for i in A):\\n    print(0);return\\nx=m//p\\n#print(p//c)\\nprint(-(-x//2))\", \"from math import gcd\\n\\nn, m = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = [a//2 for a in  A]\\nlcm = 1\\n\\nfor i in range(n):\\n    lcm = lcm * A[i] // gcd(lcm, A[i])\\n    if lcm > m:\\n        print((0))\\n        return\\n        \\nfor a in A:\\n    if lcm // a % 2 == 0:\\n        print((0))\\n        return\\n\\nprint(((m//lcm + 1) // 2))\\n\", \"from fractions import gcd\\n\\ndef lcm_base(x, y):\\n    return (x * y) // gcd(x, y)\\ndef lcm(numbers):\\n    x = numbers[0]\\n    for y in numbers:\\n        x = lcm_base(x, y)\\n    return x\\n\\nN, M = list(map(int, input().split()))\\naaa = list(map(int, input().split()))\\na = aaa[0]\\ncnt = 0\\nwhile a % 2 == 0:\\n    cnt += 1\\n    a //= 2\\nfor a in aaa:\\n    if a % 2 ** cnt != 0 or a % 2 ** (cnt + 1) == 0:\\n        print((0))\\n        return        \\nbbb = [a // 2 for a in aaa]\\nlc = lcm(bbb)\\nq, r = divmod(M // lc , 2)\\nprint((q + r))\\n\", \"N, M = map(int, input().split())\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print(0)\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7, 11]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print(0)\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\", \"import math\\nfrom functools import reduce\\nn, m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\na0 = A[0]\\ncnt = 0\\nwhile a0%2 == 0:\\n    a0 //= 2\\n    cnt += 1\\n\\na = []\\nfor aa in A:\\n    if cnt == 1:\\n        if aa%4 == 0:\\n            print(0)\\n            return\\n    else:\\n        if aa%(2**(cnt-1)) != 0 or aa%(2**cnt) != 0 or aa%(2**(cnt+1)) == 0:\\n            print(0)\\n            return\\n    a.append(aa//2)\\n\\n\\ndef lcm_base(p, q):\\n    return (p * q) // math.gcd(p, q)\\n\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\nlcm = lcm_list(a)\\nprint(m//lcm - m//(lcm*2))\", \"def main():\\n    import math\\n    n,m = list(map(int,input().split()))\\n    a = sorted(list(map(int,input().split())))\\n    for i in range(n):\\n        a[i] //= 2\\n    g=1\\n    for i in range(n):\\n        g = a[i] * g // math.gcd(g,a[i])\\n    for i in range(n):\\n        if g//a[i] % 2 == 0:\\n            print((0))\\n            return\\n    if g>m:\\n        print((0))\\n        return\\n    print((1 + (m-g)//(2*g)))\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nfrom functools import reduce\\nn, m = input().split()\\na = list(map(int, input().split()))\\nb =[0]*int(n)\\nfor i in range(len(a)):\\n  b[i] = a[i]//2\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\nc = 0\\n\\nx = lcm_list(b)\\nfor i in range(int(n)):\\n  if (x // b[i]) % 2 == 0:\\n    c = -1\\n    break\\n  else:\\n    continue\\n    \\nif c == -1:\\n  print((0))\\nelse:\\n  print((math.floor(((int(m)/x)+1)/2)))\\n\\n\", \"N, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\n\\nfrom fractions import gcd\\ndef two(n):\\n    ans = 0\\n    while n%2==0:\\n        n //= 2\\n        ans += 1\\n    return ans\\n\\ndef multi_lcm(A):\\n    ans = A[0]\\n    for a in A:\\n        ans *= a//gcd(ans,a)\\n    return ans\\n\\ndef solve(N,M,A):\\n    ans = 0\\n    num_two = len(set(map(two,A)))\\n    if num_two != 1:\\n        return 0\\n    l = multi_lcm(A)\\n    ans = (M+l//2)//l\\n    return ans\\nprint((solve(N,M,A)))\\n\", \"from math import gcd\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nf = lambda n: 0 if n%2 else f(n>>1)+1\\nx = f(A[0])\\n\\nif sum(x!=f(a) for a in A):\\n    print(0)\\n    return\\n\\nA = [a>>x for a in A]\\n\\ny = 1\\nfor a in A:\\n    y = y*a//gcd(y, a)\\n    if y<<(x-1) > M:\\n        print(0)\\n        return\\n\\nprint((M//(y<<(x-1))+1)//2)\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = [i // 2 for i in A]\\nlcd = 1\\nfor a in A:\\n    lcd *= a // gcd(lcd, a)\\nfor a in A:\\n    if lcd // a % 2 == 0:\\n        print((0))\\n        return\\nprint(((M//lcd+1)//2))\\n\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7, 11]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\ndef euclid(a, b):\\n  while b:\\n    a, b = b, a%b\\n  return a\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // euclid(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"N, M = map(int, input().split())\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print(0)\\n    return\\nans = 0\\n\\nimport math\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print(0)\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\", \"from math import gcd\\ndef readinput():\\n    n,m=list(map(int,input().split()))\\n    a=list(map(int,input().split()))\\n    return n,m,a\\n\\ndef lcm(a,b):\\n    return a*b//gcd(a,b)\\n\\ndef main(n,m,a):\\n    #s=set(a)\\n    #print(s)\\n    x=a[0]//2\\n    for i in range(1,n):\\n        x=lcm(x,a[i]//2)\\n    #print(x)\\n    gusubai=False\\n    kisubai=False\\n    for i in range(n):\\n        if x%a[i]!=0:\\n            gusubai=True\\n        else:\\n            kisubai=True\\n    \\n    y=m//x\\n    #print(y,x,m)\\n    if gusubai and not kisubai:\\n        ans=y//2+y%2\\n    elif gusubai and kisubai:\\n        ans=0\\n    else:\\n        ans=y\\n    return ans\\n\\ndef __starting_point():\\n    n,m,a=readinput()\\n    ans=main(n,m,a)\\n    print(ans)\\n\\n__starting_point()\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    N, M = MI()\\n    L = LI()\\n    L = [i//2 for i in L]\\n    \\n    past = L[0]\\n\\n    for i in L:\\n        past = (past // math.gcd(i, past)) * i\\n        if past > M or (past // i) % 2 == 0:\\n            print(0)\\n            return\\n    \\n    temp = M // past\\n    ans = (temp+1)//2\\n    print(ans)        \\n    \\n\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"from fractions import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(lambda x: int(x),input().split()))\\n\\ncnt = [0 for _ in range(N)]\\nfor i in range(N):\\n  a = A[i]\\n  while a%2 == 0:\\n    a = a // 2\\n    cnt[i] += 1\\n\\nif max(cnt) > min(cnt):\\n  print(0)\\n  return\\nC = max(cnt)\\n\\nA = list(map(lambda x: x // pow(2,C), A))\\ndef gcd(a,b):\\n  if a<b:\\n    a,b = b,a\\n  while a%b > 0:\\n    a,b = b,a%b\\n  return b\\n\\ndef lcm(a,b):\\n  return a*b//gcd(a,b)\\n\\nx = A[0]\\nfor a in A[1:]:\\n  x = lcm(x,a)\\nx = x * pow(2,C-1)\\n\\nprint((M // x + 1) // 2)\", \"from math import gcd\\nfrom functools import reduce\\n\\nn,m=map(int,input().split())\\nlst=list(map(lambda x : int(x)//2,input().split()))\\ndivi=0\\nx=lst[0]\\nwhile x%2==0:\\n    x//=2\\n    divi+=1\\n\\nfor i in range(1,n):\\n    divi2=0\\n    x=lst[i]\\n    while x%2==0:\\n        x//=2\\n        divi2+=1\\n    if divi!=divi2 :\\n        print(0)\\n        return\\n\\nwork=reduce(lambda x,y: x*y//gcd(x,y),lst)\\nprint((m//work+1)//2)\", \"n, m = map(int, input().split())\\naas = set(list(map(int, input().split())))\\na = [i//2 for i in aas]\\nimport math\\nN = len(a)\\ndef n_of_twos(x):\\n    res = 0\\n    while x%(2**(res+1))==0:\\n        res += 1\\n    return res\\nif N>=2:\\n    n_of_twos_0 = n_of_twos(a[0])\\n    for i in range(1,N):\\n        if n_of_twos(a[i]) != n_of_twos_0:\\n            print(0)\\n            return\\nans = a[0]\\nfor i in range(1, N):\\n    ans = ans * a[i] // math.gcd(ans, a[i])\\nif ans > m:\\n    print(0)\\n    return\\nprint(1 + (m//ans-1)//2)\", \"from math import gcd, ceil\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print(0)\\n        return\\nprint(ceil((m // l) / 2))\", \"import queue\\nimport numpy as np\\nimport math\\n\\nN, M = map(int, input().split())\\na2 = list(map(int, input().split()))\\na = []\\nfor i in a2:\\n    a.append(i//2)\\n\\nlcm = a[0]\\n\\nfor i in a:\\n    lcm *= i // math.gcd(lcm, i)\\n\\nhasAns = True\\nfor i in a:\\n    if (lcm // i) % 2 == 0:\\n        hasAns = False\\n        break\\n\\nans = 0\\n\\nif hasAns:\\n    ans = ((M // lcm) + 1 )// 2\\n\\nprint(ans)\", \"from math import gcd\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(set(a))\\na=list(map(lambda x: x//2, a))\\n\\ndef lcm(q):\\n  x = q[0]\\n  for i in range(1, len(q)):\\n    x = (x * q[i]) // gcd(x, q[i])\\n  return x\\n\\nlcma=lcm(a)\\nfor i in range(len(a)):\\n  if (lcma//a[i])%2==0:\\n    print(0)\\n    return\\ntemp=m//lcma\\nprint(-(-temp//2))\", \"import sys\\nimport math\\n# import bisect\\n# import numpy as np\\n# from decimal import Decimal\\n# from numba import njit, i8, u1, b1 #JIT compiler\\n# from itertools import combinations, product\\n# from collections import Counter, deque, defaultdict\\n\\n# sys.setrecursionlimit(10 ** 6)\\nMOD = 10 ** 9 + 7\\nINF = 10 ** 9\\nPI = 3.14159265358979323846\\n\\ndef read_str():      return sys.stdin.readline().strip()\\ndef read_int():      return int(sys.stdin.readline().strip())\\ndef read_ints():     return map(int, sys.stdin.readline().strip().split())\\ndef read_ints2(x):   return map(lambda num: int(num) - x, sys.stdin.readline().strip().split())\\ndef read_str_list(): return list(sys.stdin.readline().strip().split())\\ndef read_int_list(): return list(map(int, sys.stdin.readline().strip().split()))\\ndef GCD(a: int, b: int) -> int: return b if a%b==0 else GCD(b, a%b)\\ndef LCM(a: int, b: int) -> int: return (a * b) // GCD(a, b)\\n\\ndef Main():\\n    n, m = read_ints()\\n    a = read_int_list()\\n    a = [x // 2 for x in a]\\n    lcm = 1\\n    for x in a:\\n        lcm *= x // math.gcd(lcm, x)\\n    for x in a:\\n        if lcm // x % 2 == 0:\\n            print(0)\\n            return\\n    print(math.ceil((m // lcm) / 2))\\n\\ndef __starting_point():\\n    Main()\\n__starting_point()\", \"import sys\\ninput=sys.stdin.readline\\nimport math\\n\\nN,M=(int(x) for x in input().rstrip('\\\\n').split())\\nAs=[int(x) for x in input().rstrip('\\\\n').split()]\\nn = 1\\nuse2 = 0\\ncheck = 0\\nfor i in range(N):\\n  x = As[i]\\n  if i==0:\\n    while x % 2==0:\\n      use2+=1 \\n      x = x//2\\n    lcm=x\\n  else:\\n    use=0\\n    while x%2==0:\\n      x = x//2\\n      use += 1\\n    if use2 != use:\\n      check += 1\\n      break\\n    lcm=lcm*x//(math.gcd(lcm,x))\\nif check > 0:\\n  print(0)\\nelse:\\n  LCM=2**(use2-1)\\n  LCM=LCM*lcm\\n  print(((M//LCM)+1)//2)\", \"def lcm(a, b):\\n  return a // gcd(a, b) * b\\n\\ndef gcd(a, b):\\n  if(b == 0): return a\\n  else: return gcd(b, a % b)\\n\\ndef cnt(a):\\n  res = 0\\n  while(a and a % 2 == 0):\\n    a //= 2\\n    res += 1\\n  return res\\n\\nn, m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nl = 1\\nc = cnt(A[0])\\nfor a in A:\\n  if cnt(a) != c or c == 0:\\n    print(0)\\n    return\\n  else:\\n    l = lcm(l, a // 2)\\nd = m // l\\nprint((d + 1) // 2)\", \"from math import gcd\\nfrom functools import reduce\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a,b)\\n\\na = [i//2 for i in a]\\n\\nl = reduce(lcm, a)\\n\\nif any((l//i) % 2 == 0 for i in a):\\n    print(0)\\n    return\\n\\nprint(-(-(m//l)//2))\", \"import math\\nn,m= list(map(int,input().split()))\\nal= list(map(int,input().split()))\\ntwos = set()\\nfor c in al:\\n    temp,tempc=0,c\\n    while tempc%2==0:\\n        tempc//=2\\n        temp+=1\\n    twos.add(temp)\\nif len(twos)>1:print((0))\\nelse:\\n    lcmv=al[0]\\n    for i in range(1,n):lcmv = lcmv*al[i] // math.gcd(lcmv,al[i])\\n    print((max(0,1 + (m-lcmv//2)//lcmv)))\\n\", \"from functools import reduce\\n\\ndef main():\\n  N,M=map(int,input().split())\\n  *A,=map(int,input().split())\\n\\n  A = list(set(A))\\n  N = len(A)\\n\\n  B = [A[i]//2 for i in range(N)]\\n\\n  def factorize(n):\\n      out=[]\\n      i = 2\\n      while i==2:\\n          if n%i==0:\\n              out.append(i)\\n              n //= i\\n          else:\\n              i += 1\\n          if n == 1:break\\n          if i > int(n**.5+3):\\n              out.append(n)\\n              break\\n      return out\\n\\n  ord_list=[len(factorize(B[i])) for i in range(N)]\\n\\n  if len(set(ord_list)) != 1:\\n    print(0)\\n    return\\n\\n  def gcd(a,b):\\n    if b == 0: return a\\n    return gcd(b,a%b)\\n\\n  def lcm(a,b):\\n    return a*b//gcd(a,b)\\n\\n  LCM = reduce(lcm,B)\\n  print((M//LCM+1)//2)\\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"from math import gcd\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\ndef lcm_g(A):\\n    ret = 1\\n    for a in A:\\n        ret = lcm(ret, a)\\n    return ret\\n\\ndef is_hcm(x, A):\\n    for i in range(N):\\n        if x % A[i] != A[i] // 2:\\n            return False\\n    return True\\n\\nN, M = [int(x) for x in input().split()]\\nA = [int(x) for x in input().split()]\\n\\nl = lcm_g(A)\\nif is_hcm(l // 2, A):\\n    ans = (2 * M + l) // (2 * l)\\nelse:\\n    ans = 0\\n\\nprint(ans)\", \"import math\\nimport fractions\\nfrom functools import reduce\\n \\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na=[t//2 for t in a] # \\u30ea\\u30b9\\u30c8\\u306e\\u8981\\u7d20\\u3092\\u5168\\u30662\\u3067\\u5272\\u308b\\n \\ndef lcm_base(x, y):\\n    return (x * y) // fractions.gcd(x, y)\\n \\ndef lcm_list(numbers): # \\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3092\\u6c42\\u3081\\u308b\\n    return reduce(lcm_base, numbers, 1)\\n \\ndef num_dev2(x): # 2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n    return format(x, 'b')[::-1].find('1')\\n \\nlcm = lcm_list(a)\\nq = m // lcm # m\\u306f\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3067\\u4f55\\u56de\\u5272\\u308c\\u308b\\u304b\\n \\ncount = 0\\ndev2 = num_dev2(a[0])\\nfor i in range(1, n):\\n    if dev2 != num_dev2(a[i]): # \\u30ea\\u30b9\\u30c8\\u306e\\u5168\\u3066\\u306e\\u8981\\u7d20\\u306e\\u30012\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u306f\\u7b49\\u3057\\u3044\\u304b\\uff1f\\n        count += 1\\n        break\\nif count != 0:\\n    print(0)\\nelse:\\n    print(math.ceil(q/2))\", \"import sys, re\\nfrom collections import deque, defaultdict, Counter\\nfrom math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd\\nfrom itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby\\nfrom operator import itemgetter, mul\\nfrom copy import deepcopy\\nfrom string import ascii_lowercase, ascii_uppercase, digits\\nfrom bisect import bisect, bisect_left, insort, insort_left\\nfrom heapq import heappush, heappop\\nfrom functools import reduce, lru_cache\\ndef input(): return sys.stdin.readline().strip()\\ndef INT(): return int(input())\\ndef MAP(): return map(int, input().split())\\ndef LIST(): return list(map(int, input().split()))\\ndef TUPLE(): return tuple(map(int, input().split()))\\ndef ZIP(n): return zip(*(MAP() for _ in range(n)))\\nsys.setrecursionlimit(10 ** 9)\\nINF = 10**6#float('inf')\\n#mod = 10 ** 9 + 7 \\nmod = 998244353\\n#from decimal import *\\n#import numpy as np\\n#decimal.getcontext().prec = 10\\n\\nN, M = MAP()\\na = LIST()\\n\\nA = sorted([x//2 for x in a], reverse=True)\\n\\nb = A[0]\\ncnt = 0\\nwhile b%2 == 0:\\n\\tb //= 2\\n\\tcnt += 1\\n\\nfor x in A:\\n\\tif x%pow(2, cnt) or (x//pow(2, cnt))%2 == 0:\\n\\t\\tprint(0)\\n\\t\\treturn\\n\\nlcm = A[-1]\\nfor x in A:\\n\\tlcm = lcm*x//gcd(lcm, x)\\n\\nr = lcm//A[0]\\nn = M//A[0]\\n\\n#2p+1\\u304c1<=2p+1<=n \\u306e\\u7bc4\\u56f2\\u3067 r\\u306e\\u500d\\u6570\\u3068\\u306a\\u308bp\\u306e\\u500b\\u6570\\nif r%2 == 0:\\n\\tprint(0)\\nelse:\\n\\tprint(n//r - n//(2*r))\", \"from math import gcd, ceil\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print((0))\\n        return\\nprint((ceil((m // l) / 2)))\\n\", \"from functools import reduce\\nimport math\\ndef lcm_base(x, y):\\n  return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n  return reduce(lcm_base, numbers, 1)\\n\\ndef lcm_list(numbers):\\n  return reduce(lcm_base, numbers, 1)\\n\\nn,m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i//2 for i in list(set(a))]\\nnothing = False\\ncnt_common = -1\\nfor i in a:\\n  cnt = 0\\n  while i % 2 == 0:\\n    i = i//2\\n    cnt += 1\\n  if cnt_common == -1:\\n    cnt_common = cnt\\n    continue\\n  if cnt_common != cnt:\\n    nothing = True\\n    break\\n\\nb=lcm_list(a)\\nif nothing:\\n  print(0)\\nelse:\\n  ans = (m-b)//(2*b) + 1\\n  print(max(ans,0))\", \"from fractions import gcd\\ndef lcm(a,b):\\n    return (a*b)//gcd(a,b)\\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\nans = 1\\nfor i in a:\\n    ans = lcm(ans,i)\\nfor i in a:\\n    if (ans//i) % 2 == 0:\\n        print(0)\\n        return\\nprint(((m//(ans//2))+1)//2)\", \"import math\\nN, M = map(int, input().split())\\nB = tuple(int(a) // 2 for a in input().split())\\n\\nx = B[0]\\nfor i in range(1, N):\\n    x = (x * B[i]) // math.gcd(x, B[i])\\n\\nfor b in B:\\n    if (x // b) % 2 == 0:\\n        print(0)\\n        break\\nelse:\\n    ans = (M // x) - (M // (2 * x))\\n    print(ans)\", \"import math\\nfrom functools import reduce\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef div2_n(x):\\n    n = 0\\n    while x % 2 == 0:\\n      if x % 2 == 0:\\n          n += 1\\n          x >>= 1\\n    return n\\n  \\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\n\\na2 = [i//2 for i in a]\\nn0 = div2_n(a2[0])\\nfor i in range(1,n):\\n    if div2_n(a2[i]) != n0:\\n        print((0))\\n        return\\n\\na2_l = lcm(*a2)\\nprint((m//a2_l - m//(a2_l*2)))\\n\", \"N, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\ndef gcd(a,b):\\n    while b > 0:\\n        a, b = b, a % b\\n    return a\\n\\n\\nG = A[0]/2\\nfor a in A[1:]:\\n    G *= (a/2)/gcd(G,a//2)\\nfor a in A:\\n    if G % a == 0:\\n        print(0)\\n        return\\nprint(int(M//G - M//G//2))\", \"n , m = list(map(int, input().split()))\\na = list(map(int,input().split()))\\n\\ndef gcd(num1,num2):\\n    r=1\\n    while r>0:\\n        r=num1%num2\\n        num1=num2\\n        num2=r\\n    return num1\\n\\ndef lcm(num1,num2):\\n    gcd1=gcd(num1,num2)\\n    return num1*num2//gcd1\\n\\nlcm1=a[0]//2\\nlcm2=a[0]\\n\\nfor i in range(1,n):\\n    t=a[i]\\n    lcm1=lcm(lcm1,t//2)\\n    lcm2=lcm(lcm2,t)\\n    ta=max(t//2,lcm1)\\n    tb=min(t//2,lcm1)\\n    if ta!=tb and ta//tb%2==0:\\n        lcm1=0\\n        lcm2=0\\n        break\\n\\nif lcm1!=0:\\n    ans1=m//lcm1\\n    ans2=m//lcm2\\n    ans=ans1-ans2\\nelse:\\n    ans=0\\n\\nprint(ans)\\n\", \"import sys, re\\nfrom collections import deque, defaultdict, Counter\\nfrom math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd\\nfrom itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby\\nfrom operator import itemgetter, mul\\nfrom copy import deepcopy\\nfrom string import ascii_lowercase, ascii_uppercase, digits\\nfrom bisect import bisect, bisect_left, insort, insort_left\\nfrom heapq import heappush, heappop\\nfrom functools import reduce, lru_cache\\ndef input(): return sys.stdin.readline().strip()\\ndef INT(): return int(input())\\ndef MAP(): return map(int, input().split())\\ndef LIST(): return list(map(int, input().split()))\\ndef TUPLE(): return tuple(map(int, input().split()))\\ndef ZIP(n): return zip(*(MAP() for _ in range(n)))\\nsys.setrecursionlimit(10 ** 9)\\nINF = 10**6#float('inf')\\n#mod = 10 ** 9 + 7 \\nmod = 998244353\\n#from decimal import *\\n#import numpy as np\\n#decimal.getcontext().prec = 10\\n\\nN, M = MAP()\\na = LIST()\\n\\nA = sorted([x//2 for x in a], reverse=True)\\n\\nlcm = A[-1]\\nfor x in A:\\n\\tlcm = lcm*x//gcd(lcm, x)\\n\\nr = lcm//A[0]\\nn = M//A[0]\\n\\n\\nfor x in A:\\n\\tif lcm//x%2 == 0:\\n\\t\\tprint(0)\\n\\t\\treturn\\n#2p+1\\u304c1<=2p+1<=n \\u306e\\u7bc4\\u56f2\\u3067 r\\u306e\\u500d\\u6570\\u3068\\u306a\\u308bp\\u306e\\u500b\\u6570\\nif r%2 == 0:\\n\\tprint(0)\\nelse:\\n\\tprint(n//r - n//(2*r))\", \"import math\\nfrom functools import reduce\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nN,M = map(int,input().split())\\na = list(map(lambda a: int(a)//2, input().split()))\\ng = lcm(*a)\\nif any([g // item % 2 == 0 for item in a]):\\n    print(0)\\nelse:\\n    ans = M//g\\n    ans = max(math.ceil(ans/2),0)   \\n    print(ans)\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = [a//2 for a in map(int, input().split())]\\n\\nlcm = 1\\nfor a in A:\\n    lcm = lcm*a//gcd(lcm, a)\\n    if lcm > M:\\n        print((0))\\n        return\\n\\nfor a in A:\\n    div = lcm//a\\n    if div % 2 == 0:\\n        print((0))\\n        return\\n\\nans = (M//lcm+1)//2\\nprint(ans)\\n\", \"import math\\ndef LCM(a, b):\\n    g = math.gcd(a, b)\\n    return a * b // g\\n\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = list(set(A))\\nN = len(A)\\na0 = A[0]\\ndiv = 1\\nwhile a0 % 2 == 0:\\n    div *= 2\\n    a0 //= 2\\n\\nfor i in range(1, N):\\n    a = A[i] % div\\n    b = A[i] // div\\n    if (b % 2 == 0) or (a != 0):\\n        print((0))\\n        return\\n\\nfor i in range(N):\\n    A[i] //= 2\\n\\nif N > 1:\\n    lcm = LCM(A[0], A[1])\\n    for i in range(2, N):\\n        lcm = LCM(lcm, A[i])\\n\\nif N == 1:\\n    lcm = A[0]\\n\\nans = M // lcm\\nif ans % 2 == 1:\\n    print((ans // 2 + 1))\\nelse:\\n    print((ans // 2))\\n\", \"import math\\ndef lcm(x,y):\\n    return(x*y)//math.gcd(x,y)\\nn,m=map(int,input().split())\\nl=list(map(int,input().split()))\\na=l[0]//2\\nfor i in range(n-1):\\n    a=lcm(a,l[i+1]//2)\\n \\nok = True\\nfor i in range(n):\\n  if (a//(l[i]//2))%2!=1:\\n    ok=False\\n    break\\nans = 0\\nif ok:\\n    ans = ((m//a)+1)//2\\nprint(ans)\", \"import sys\\nN,M = list(map(int,input().split()))\\nA = list(map(int,input().split()))\\na = []\\nfor i in A:\\n  i = i//2\\n  a.append(i)\\ndef gcd(p,q):\\n  p,q = max(p,q),min(p,q)\\n  while q!=0:\\n    p,q = q,p%q\\n  return p\\ndef lcm(p,q):\\n  return(p*q//gcd(p,q))\\ndef aaa(i):\\n  count = 0\\n  while i%2==0:\\n    i = i//2\\n    count+=1\\n  return count\\nmax_num = a[0]\\naa = aaa(a[0])\\nfor i in a:\\n  max_num = lcm(i,max_num)\\n  if aa != aaa(i):\\n    print((0))\\n    return\\nprint((((M//max_num)+1)//2))\\n\", \"import math\\ndef lcm(a,b):\\n  return (a*b)//math.gcd(a,b)\\ndef co(num):\\n  return format(num, 'b')[::-1].find('1')\\nN,M=map(int,input().split())\\nL=list(map(int,input().split()))\\nL2=[co(i) for i in L]\\nif len(set(L2))!=1:\\n  print(0)\\n  return\\nL=[i//2 for i in L]\\ns=L[0]\\nfor i in range(N):\\n  s=lcm(s,L[i])\\nc=M//s\\nprint((c+1)//2)\", \"import math\\nfrom functools import reduce\\n\\nN,M=list(map(int,input().split()))\\nA=[int(x)//2 for x in input().split()]\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nLCM=lcm(*A)\\nfor a in A:\\n  if LCM//a%2==0:\\n    print((0))\\n    break\\nelse:\\n  print(((M//LCM+1)//2))\\n\", \"import numpy as np\\nfrom math import ceil\\n\\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\na = [x//2 for x in a]\\nlcm = np.lcm.reduce(a)\\nans = 0\\n\\nfor i in a:\\n    if lcm // i % 2 == 0:\\n        break\\nelse:\\n    ans = ceil((m//lcm)/2)\\n\\nprint(ans)\", \"import math\\n\\ndef n_2(n):\\n  c=0\\n  while n%2==0:\\n    c+=1\\n    n>>=1\\n  return (n,c)\\n\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nA[0],a=n_2(A[0])\\np=False\\nfor i in range(1,N):\\n  A[i],b=n_2(A[i])\\n  if a!=b:\\n    p=True\\n    break\\nif p:\\n  print(0)\\n  return\\nn=1\\nfor _ in range(a-1):\\n  n*=2\\nl=n\\nfor a in A:\\n  l=l*a//math.gcd(l,a)\\nans=M//l-M//(2*l)\\nprint(ans)\", \"def abc150_d():\\n    n, m = (int(x) for x in input().split())\\n    A = [int(x) // 2 for x in input().split()]\\n\\n    from math import gcd\\n    def lcm(a, b):\\n        return a * b // gcd(a, b)\\n\\n    x = 1\\n    for a in A:\\n        x = lcm(x, a)\\n\\n    valid = True\\n    for a in A:\\n        if (x // a) % 2 == 0:\\n            valid = False\\n            break\\n\\n    if valid: ans = (m // x + 1) // 2\\n    else: ans = 0\\n    print(ans)\\n\\ndef __starting_point():\\n    abc150_d()\\n__starting_point()\", \"from math import gcd\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(set(a))\\na=list(map(lambda x: x//2, a))\\n\\ndef lcm(q):\\n  x = q[0]\\n  for i in range(1, len(q)):\\n    x = (x * q[i]) // gcd(x, q[i])\\n  return x\\n\\nlcma=lcm(a)\\nfor i in range(len(a)):\\n  if (lcma//a[i])%2==0:\\n    print(0)\\n    return\\ntemp=m//lcma\\nprint(temp//2 if temp%2==0 else temp//2+1)\", \"from math import gcd, ceil\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print(0)\\n        return\\nprint(ceil((m // l) / 2))\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ndef lcm(a, b):\\n    \\\"\\\"\\\"\\u6700\\u5c0f\\u516c\\u500d\\u6570\\\"\\\"\\\"\\n    from math import gcd\\n    return (a * b) // gcd(a, b)\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, M, As):\\n    if sum([a % 2 for a in As]) > 0:\\n        print((0))\\n        return\\n\\n    As = [a // 2 for a in As]\\n    all_lcm = 1\\n    for a in As:\\n        all_lcm = lcm(all_lcm, a)\\n        if all_lcm > M:\\n            print((0))\\n            return\\n\\n    for a in As:\\n        if (all_lcm // a) % 2 == 0:\\n            print((0))\\n            return\\n    from math import ceil\\n    print((ceil(M // all_lcm / 2)))\\n\\n\\ndef __starting_point():\\n    N, M = list(map(int, input().split()))\\n    As = [int(i) for i in input().split()]\\n\\n    # import random\\n    # N, M = 10 ** 5, 10 ** 9\\n    # As = [random.randint(5, 5) * 2 for _ in range(N)]\\n    solve(N, M, As)\\n\\n__starting_point()\", \"import sys,math\\nr=sys.stdin.readline\\ndef gcd(a,b):\\n    a,b=max(a,b),min(a,b)\\n    while b>0:\\n        a,b=b,a%b\\n    return a\\ndef lcm(arr):\\n    while len(arr)!=1:\\n        a=arr.pop()\\n        b=arr.pop()\\n        c=gcd(a,b)\\n        arr.insert(0,int(a*b/c))\\n    return arr[0]\\ndef cnt2(num):\\n    cnt=0\\n    while num%2==0:\\n        num/=2\\n        cnt+=1\\n    return cnt\\nN,M=list(map(int,r().split()))\\nseq=list(map(int,r().split()))\\nseq=list(set(seq))\\ntmp=cnt2(seq[0])\\nfor num in seq:\\n    if tmp!=cnt2(num):\\n        print((0))\\n        return\\nT=lcm(list([x//2 for x in seq]))\\nif T>M:\\n    print((0))\\n    return\\nprint((math.floor(M//T/2+0.5)))\\n\\n\\n\\n\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"from math import gcd\\n\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nl = [0] * n\\nfor i in range(n):\\n    tmp = a[i]\\n    while tmp % 2 == 0:\\n        tmp //= 2\\n        l[i] += 1\\n    if i > 0 and l[i] != l[i - 1]:\\n        print((0))\\n        return\\nres = 1\\nfor i in range(n):\\n    res = lcm(res, a[i] // 2)\\nprint((m // res - m // (res * 2)))\\n\", \"def main():\\n    N, M = map(int, input().split())\\n    A = tuple(map(int,input().split()))\\n    ans = count(A, N, M)\\n    print(ans)\\ndef count(A, N, M):\\n    t = hMt(A[0])\\n    B = [A[0]//(2**t)]\\n    for val in A[1:]:\\n        if hMt(val) != t:\\n            ans = 0\\n            return ans\\n        B.append(val//(2**t))\\n    T = nlcm(B)\\n    MdivT = (M//(2**(t-1)))//T\\n    ans = countodd(MdivT)\\n    return ans\\ndef countodd(num):\\n    if num%2 == 0:\\n        ans = num//2\\n    else:\\n        ans = num//2 + num%2\\n    return ans\\ndef nlcm(A):\\n    LCM = A[0]\\n    for val in A[1:]:\\n        #print(\\\"%d %d gcm:%d LCM:%d\\\"%(LCM,val,gcm(LCM,val),lcm(LCM,val)))\\n        LCM = lcm(LCM,val)\\n    return LCM\\n    \\ndef gcm(a, b):\\n    abtuple = (a,b)\\n    abmin = min([0,1], key=lambda x:abtuple[x])\\n    remainder = abtuple[1-abmin]%abtuple[abmin]\\n    if remainder == 0:\\n        return abtuple[abmin]\\n    return gcm(abtuple[abmin], remainder)\\ndef lcm(a,b):\\n    prod = a*b\\n    ans = prod//gcm(a,b)\\n    return ans\\ndef hMt(num):\\n    ans = 0\\n    tmp = num\\n    while tmp%2 == 0:\\n        tmp = tmp//2\\n        ans += 1\\n    return ans\\nmain()\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"from math import gcd\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\ndef lcm(ab):\\n    l=len(ab)\\n    ret=ab[0]\\n    for i in range(1,l):\\n        ret=ret//gcd(ab[i],ret)*ab[i]\\n    return ret\\ndef count2(a):\\n    ret=0\\n    while a%2==0:\\n        a//=2\\n        ret+=1\\n    return 2**ret\\nn,m=map(int,input().split())\\nA=list(map(int,input().split()))\\nif any(i%2 for i in A):\\n    print(0);return\\nA=[i//2 for i in A]\\n#\\u5168\\u4f53\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\np=lcm(A)\\nc=count2(p)\\n#2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3082\\u306e\\u304c\\u3042\\u308b\\u5834\\u5408\\n#\\u9055\\u3046\\u3058\\u3083\\u3093\\nif any(i%c for i in A):\\n    print(0);return\\nx=m//p\\n#print(p//c)\\nif x%2==0:\\n    print(x//2)\\nelse:\\n    print(x//2+1)\", \"def gcd(a, b):\\n    if b == 0:\\n        return a\\n    r = a % b   \\n    return gcd(b, r)\\n\\ndef lcm(a, b):\\n    x = gcd(a, b)\\n    return a * b // x\\n\\ndef gcdN(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = gcd(x, a[i])\\n    return x\\n\\ndef lcmN(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = lcm(x, a[i])\\n    return x\\n\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))  #;print(a)\\n\\ng = gcdN(a)\\nfor i in a:\\n    if (i//g) % 2 == 0:\\n        print((0))\\n        break\\nelse:\\n    l = lcmN(a) \\n    k = 2*m // l\\n    print(((k+1)//2))\\n\", \"from math import gcd, ceil\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print((0))\\n        return\\n#print(ceil((m // l) / 2))\\nprint(((m//l+1)//2))\\n\", \"n,m=list(map(int,input().split()))\\na=list(map(int,input().split()))\\n\\nfor i in range(n):\\n  a[i]=a[i]//2\\n  \\ndef gcd(a,b):\\n  if b==0:\\n    return a\\n  else:\\n    return gcd(b,a%b)\\n  \\ndef lcm(a,b):\\n  return a*b//gcd(a,b)\\n\\ndef check(x):\\n  cnt=0\\n  while(1):\\n    if x%2==0:\\n      x=x//2\\n      cnt+=1\\n    else:\\n      break\\n  return cnt\\n\\ncnt=a[0]\\nfor i in range(n):\\n  cnt=lcm(cnt,a[i])\\n\\n\\nl=check(a[0])\\nfor i in range(1,n):\\n  x=check(a[i])\\n  if x!=l:\\n    print((0))\\n    return\\n\\n\\ns=m//cnt\\nif s%2==0:\\n  print((s//2))\\nelse:\\n  print((s//2+1))\\n\\n  \\n\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nlcm = 1\\nfor a in A:\\n    lcm = lcm * a // gcd(lcm, a)\\n    if lcm > M*2:\\n        print((0))\\n        return\\nfor a in A:\\n    if lcm // a % 2 == 0:\\n        print((0))\\n        return\\nans = M // (lcm//2) - M // lcm\\nprint(ans)\\n\", \"from math import gcd\\ndef lcm(x,y):\\n    return x*y//gcd(x,y)\\ndef cnt(x):\\n    i = 0\\n    while x%2 == 0:\\n        x = x//2\\n        i += 1\\n    return i \\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\nmemo = cnt(a[0])\\nfor i in range(n):\\n    if cnt(a[i]) != memo:\\n        print(0)\\n        return\\n    a[i] = a[i]//2\\n\\nt = 1\\nfor i in range(n):\\n    t = lcm(t,a[i])\\nprint(m//t-m//(2*t))\", \"import math\\nimport numpy as np\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nc=1\\ntest=A[0]\\nl=0\\n\\nwhile test%2 == 0:\\n  test=test//2\\n  c*=2\\n  \\nfor i in np.arange(N-1):\\n  if A[i+1]%c!=0:\\n    print(0)\\n    l=1\\n    break\\n  elif A[i+1]%(c*2)==0:\\n    print(0)\\n    l=1\\n    break\\n  else:\\n    k=A[i+1]//c\\n    test=test*k//math.gcd(test,k)\\nif l==0:\\n  k=test*c//2\\n  print(M//k//2+M//k%2)\", \"# \\u53c2\\u8003 : https://at274.hatenablog.com/entry/2020/01/15/060000\\nfrom functools import reduce\\nimport math\\n\\n\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\ndef lcm_list(numbers):  # \\u30ea\\u30b9\\u30c8\\u3092\\u6295\\u3052\\u308b\\u3068\\u5168\\u8981\\u7d20\\u306elcm\\u304c\\u8fd4\\u3063\\u3066\\u304f\\u308b\\n    return reduce(lcm, numbers, 1)\\n\\n\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\n\\n# \\u6700\\u521d\\u3001A\\u306e\\u8981\\u7d20\\u306f\\u5168\\u3066\\u5076\\u6570\\u30022\\u3067\\u5272\\u3063\\u305f\\u3082\\u306e\\u306b\\u7f6e\\u304d\\u63db\\u3048\\nA = [a // 2 for a in A]\\n\\n# \\u5168\\u3066\\u306e\\u8981\\u7d20\\u306b\\u3064\\u3044\\u3066\\u3001\\uff12\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3068\\u984c\\u610f\\u306f\\u6e80\\u305f\\u305b\\u306a\\u3044\\ncount_div_2 = None\\nfor a in A:\\n    cnt = 0\\n    while a % 2 == 0:\\n        a //= 2\\n        cnt += 1\\n    # 1\\u500b\\u76ee\\u306f\\u7121\\u6761\\u4ef6\\u3067\\u4fdd\\u5b58\\n    if count_div_2 is None:\\n        count_div_2 = cnt\\n    # 2\\u500b\\u76ee\\u304b\\u3089\\u30c1\\u30a7\\u30c3\\u30af\\n    elif cnt != count_div_2:\\n        print((0))\\n        return\\n\\n# my_lcm = A\\u306e\\u5168\\u8981\\u7d20\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3002\\u3000\\u3053\\u306e\\u5947\\u6570\\u500d\\u304c\\u984c\\u610f\\u3092\\u6e80\\u305f\\u3059\\u3002\\n# my_lcm\\u304cM\\u3092\\u8d85\\u3048\\u3066\\u3044\\u305f\\u30891\\u3064\\u3082\\u4f5c\\u308c\\u306a\\u3044\\nmy_lcm = lcm_list(A)\\nif my_lcm > M:\\n    print((0))\\n    return\\n\\ntmp = M // my_lcm\\n# my_lcm\\u306e1,2,...M\\u500d\\u307e\\u3067\\u4f7f\\u3048\\u308b\\u304c\\u3001\\u5076\\u6570\\u306f\\u4f7f\\u3048\\u306a\\u3044\\n# tmp=1or2\\u306a\\u30891\\u500b, 3or4\\u306a\\u30892\\u500b, 5or6\\u306a\\u30893\\u500b,...\\nans = (tmp + 1) // 2\\nprint(ans)\\n\", \"import math\\nimport collections\\nimport sys\\n\\ninput = sys.stdin.readline\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\n\\nn,m=MI()\\nA=LI()\\ndef num2(x):\\n    ans=0\\n    while x%2==0:\\n        x=x//2\\n        ans+=1\\n    return ans\\nmod=2**(num2(A[0]))\\nfor i in range(1,n):\\n    if A[i]%mod!=0:\\n        print((0))\\n        return\\n    if A[i]%mod==0 and (A[i]//mod)%2==0:\\n        print((0))\\n        return\\n#print(A)\\nfor i in range(n):\\n    A[i]//=2\\n#print(A)\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b\\n\\nL=A[0]   \\nfor i in range(1,n):\\n    L=lcm(L,A[i])\\n#print(L)\\nif L>m:\\n    an=0\\nelse:\\n    an=int(((m/L)-1)/2)+1\\nprint(an)\\n\", \"import math\\n\\ndef lcm(a, b):\\n  return a*b//math.gcd(a, b)\\n\\ndef f(num):\\n  cnt = 0\\n  while num % 2 == 0:\\n    num = num // 2\\n    cnt += 1\\n  return cnt\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\n\\nfor i in range(n):\\n  a[i] = a[i] // 2\\n\\nt = f(a[0])\\nfor i in range(n):\\n  if f(a[i]) != t:\\n    print(0)\\n    return\\n  a[i] = a[i] >> t\\nm = m >> t\\nl = 1\\nfor i in range(n):\\n  l = lcm(l, a[i])\\n  if l > m:\\n    print(0)\\n    return\\n\\nm = m // l\\nprint((m+1)//2)\", \"import math\\nfrom functools import reduce\\n\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\ndef my_round(val, digit=0):\\n    p = 10 ** digit\\n    return (val * p * 2 + 1) // 2 / p\\n\\n\\nn, m = list(map(int, input().split()))\\na_pr = [i // 2 for i in list(map(int, input().split()))]\\nlcm_ = lcm_list(a_pr)\\nres, div2 = 0, None\\nfor ai in a_pr:\\n    cnt = 0\\n    while ai % 2 == 0:\\n        ai //= 2\\n        cnt += 1\\n    if div2 is None:\\n        div2 = cnt\\n    elif cnt != div2:\\n        print((0))\\n        return\\n\\nprint((int(my_round(m // lcm_ / 2))))\\n\", \"from math import gcd, ceil\\nfrom functools import reduce\\nimport sys\\n\\ndef lcm_base(x, y):\\n    return (x * y) // gcd(x, y)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nN, M = map(int, input().split())\\na = [int(i)//2 for i in input().split()]\\n\\ns = set()\\nfor x in a:\\n    cur = 0\\n    y = x\\n    while y%2 == 0:\\n        cur += 1\\n        y //= 2\\n    s.add(cur)\\n    if len(s) >= 2:\\n        print(0)\\n        return\\nlcm = lcm_list(a)\\nprint((M//lcm+1)//2)\", \"from math import gcd, ceil\\n\\n\\ndef lcm(a, b):\\n    return (a*b)//gcd(a, b)\\n\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    a[i] = a[i]//2\\n\\nlcm_v = a[0]\\nfor i in range(1, n):\\n    lcm_v = lcm(lcm_v, a[i])\\n\\nok = True\\nfor aa in a:\\n    if (lcm_v//aa) % 2 != 1:\\n        ok = False\\n        break\\nans = 0\\nif ok:\\n    ans = ((m//lcm_v)+1)//2\\nprint(ans)\\n\", \"from collections import deque,defaultdict\\ndef gcd(a,b):\\n    return b if not a%b else gcd(b,a%b)\\ndef lcm(a,b):\\n    return (a*b)//gcd(a,b)\\nn,m=list(map(int, input().split()))\\nA=[int(i) for i in input().split()]\\ntmp = A[0]\\nfor i in range(1,n):\\n    tmp = lcm(tmp,A[i])\\nans = m//tmp\\nlis = set()\\nfor i in A:\\n    r = i\\n    k=0\\n    while(r%2==0):\\n        k+=1\\n        r//=2\\n    lis.add(k)\\nif(m//(tmp)*tmp+tmp//2<=m):\\n    ans += 1\\nif(len(lis)!=1):\\n    ans=0\\n\\nprint(ans)\\n\\n\", \"import math\\nfrom decimal import Decimal, ROUND_HALF_UP\\ndef lcm(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = (x * a[i]) // math.gcd(x, a[i])\\n    return x\\ndef gcd(a):\\n  temp = math.gcd(a[0], a[1])\\n  for i in a:\\n    temp = math.gcd(temp,  i)\\n  return temp\\nn,m = map(int, input().split(\\\" \\\"))\\na = list(map(int, input().split(\\\" \\\")))\\nzero = False\\ncount = 0\\n#a = list(map(lambda x: x // 2, na))\\nmini = lcm(a)\\nif len(a) != 1:\\n  maxi = gcd(a)\\nelse:\\n  maxi = a[0]\\nmaxi2 = maxi\\nnibai = 1\\nwhile(True):\\n  if maxi2 % 2 == 0:\\n    nibai *= 2\\n    maxi2 //= 2\\n  else:\\n    break\\nfor i in a:\\n  if i % (2 * nibai) == 0:\\n    zero = True\\n    break\\n#print(nibai, maxi, mini)\\nif not zero:\\n  t = Decimal(str((m * 2 // mini) / 2))\\n  #print(t)\\n  print(t.quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nelse:\\n  print(0)\", \"from math import gcd\\nimport sys\\n\\ndef lcm(x,y):\\n    return x*y//gcd(x,y)\\n\\ndef count(x):\\n    res=0\\n    while True:\\n        if x%2==0:\\n            res+=1\\n            x//=2\\n        else:\\n            break\\n    return res\\n\\nn,m=list(map(int,input().split()))\\nA=list(map(int,input().split()))\\nA=list(set(A))\\nn=len(A)\\n\\nA.sort(reverse=True)\\n\\ntemp=A[0]\\nfor i in range(1,n):\\n    if count(A[i])!=count(temp):\\n        print((0))\\n        return\\n    else:\\n        temp=lcm(temp,A[i])\\n\\nans=m//(temp//2)-m//temp\\nprint(ans)\\n\", \"import math\\nimport fractions\\nfrom functools import reduce\\n\\nn, m = map(int,input().split())\\na = list(map(int,input().split()))\\na = [t // 2 for t in a]#\\u30ea\\u30b9\\u30c8\\u306e\\u8981\\u7d20\\u3059\\u3079\\u3066\\u30922\\u3067\\u5272\\u308b\\n\\ndef lcm_base(x, y):\\n    return (x * y)//fractions.gcd(x,y)\\n\\ndef lcm_list(numbers): #\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3092\\u6c42\\u3081\\u308b\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef num_dev2(x):\\n    return bin(x)[::-1].find(\\\"1\\\") #\\uff12\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u3092\\u78ba\\u8a8d\\n\\nlcm = lcm_list(a)\\nq = m//lcm #m\\u306f\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3067\\u4f55\\u56de\\u5272\\u308c\\u308b\\u304b\\n\\ncount = 0\\ndev2 = num_dev2(a[0])\\nfor i in range(1,n):\\n    if dev2 != num_dev2(a[i]):#\\u30ea\\u30b9\\u30c8\\u306e\\u3059\\u3079\\u3066\\u306e\\u8981\\u7d20\\u306e\\uff12\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u306f\\u7b49\\u3057\\u3044\\u304b\\n        count += 1\\n        break\\nif count != 0:\\n    print(0)\\nelse:\\n    print(math.ceil(q/2))\", \"from math import gcd\\n\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b \\n\\nN, M = map(int, input().split())\\nAs = list(map(int, input().split()))\\n\\nrightmostbit = As[0] & -As[0]\\nfor A in As[1:]:\\n    if rightmostbit != A & -A:\\n        print(0)\\n        return \\n\\n\\nlcm_of_half_As = 1\\nfor A in As:\\n    lcm_of_half_As = lcm(lcm_of_half_As, A //  2)\\n    if lcm_of_half_As > M:\\n        break\\n\\nprint((M // lcm_of_half_As + 1) // 2)\", \"import sys\\nimport numpy as np\\ndef input(): return sys.stdin.readline().rstrip()\\n\\ndef kosuu(x):\\n    re = [0,0]\\n    while x % 2 == 0:\\n        x = x//2\\n        re[1]+=1\\n    re[0]=x\\n    return re\\n\\n        \\n \\ndef main():\\n    n,m=map(int, input().split())\\n    a=list(map(int, input().split()))\\n    li = [kosuu(a[0])[0]]\\n    hantei = kosuu(a[0])[1]\\n    for i in a[1:]:\\n        hantei2 = kosuu(i)\\n        if hantei2[1] != hantei:\\n            print(0)\\n            break\\n        else:\\n            li.append(hantei2[0])\\n    else:\\n        lc = np.lcm.reduce(li)\\n        print(((m//(lc*2**(hantei-1)))+1)//2)\\n            \\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nimport sys\\nfrom functools import reduce\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nfor i in range(N):\\n  A[i] = A[i] // 2\\n  \\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n  \\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nC = lcm_list(A)\\nB = [0 for _ in range(N)]\\n\\nfor i in range(N):\\n  B[i] = C // A[i]\\n  if B[i] % 2 == 0:\\n    print(0)\\n    return\\n\\nprint( (M // C + 1) // 2)\", \"import math\\nfrom functools import reduce\\n\\nn,m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\ndef lcm_base(x,y):\\n  return x*y//math.gcd(x,y)\\n\\ndef lcm(target_list):\\n  return reduce(lcm_base, target_list)\\n\\nA_gcd = reduce(math.gcd, A)\\nflg = True\\n\\nfor a in A:\\n  if a//A_gcd%2==0:\\n    flg = False\\n    break\\n    \\nif flg:\\n  min_x = int(lcm(A))//2\\n  ans = m//min_x - m//(2*min_x)\\n  print(ans)\\nelse:\\n  print(0)\", \"from math import gcd\\nfrom functools import reduce\\nimport sys\\ninput = sys.stdin.readline\\n\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a, b)\\n\\n\\ndef count_factor_2(num):\\n    count = 0\\n    while num % 2 == 0:\\n        num //= 2\\n        count += 1\\n    return count\\n\\n\\ndef main():\\n    n, m = list(map(int, input().split()))\\n    A = list([int(x)//2 for x in input().split()])\\n\\n    check = len(set(map(count_factor_2, A)))\\n    if check != 1:\\n        print((0))\\n        return\\n\\n    lcm_a = reduce(lcm, A)\\n    step = lcm_a * 2\\n    ans = (m + lcm_a) // step\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\"]",
        "difficulty": "interview",
        "input": "2 50\n6 10\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc150/tasks/abc150_d"
    },
    {
        "id": 253,
        "task_id": 2498,
        "test_case_id": 2,
        "question": "Given are a sequence A= {a_1,a_2,......a_N} of N positive even numbers, and an integer M.\nLet a semi-common multiple of A be a positive integer X that satisfies the following condition for every k (1 \\leq k \\leq N):\n - There exists a non-negative integer p such that X= a_k \\times (p+0.5).\nFind the number of semi-common multiples of A among the integers between 1 and M (inclusive).\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^9\n - 2 \\leq a_i \\leq 10^9\n - a_i is an even number.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 a_2 ... a_N\n\n-----Output-----\nPrint the number of semi-common multiples of A among the integers between 1 and M (inclusive).\n\n-----Sample Input-----\n2 50\n6 10\n\n-----Sample Output-----\n2\n\n - 15 = 6  \\times 2.5 \n - 15 = 10 \\times 1.5 \n - 45 = 6  \\times 7.5 \n - 45 = 10 \\times 4.5 \nThus, 15 and 45 are semi-common multiples of A. There are no other semi-common multiples of A between 1 and 50, so the answer is 2.",
        "solutions": "[\"n, m = map( int, input().split() )\\na = list( map( int, input().split() ) )\\n\\ndef f( a_k ): # 2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\n    count = 0\\n    while a_k % 2 == 0:\\n        count += 1\\n        a_k = a_k // 2\\n    return count\\n\\nb = []\\nf_0 = f( a[ 0 ] )\\nfor a_k in a:\\n    f_k = f( a_k )\\n    if f_k != f_0:\\n        print( 0 )\\n        return\\n    b.append( a_k // pow( 2, f_k ) )\\n\\nimport math\\ndef lcm( x, y ):\\n    return x * y // math.gcd( x, y )\\n\\nb_lcm = 1\\nfor b_k in b:\\n    b_lcm = lcm( b_lcm, b_k )\\n\\na_lcm = b_lcm * pow( 2, f_0 )\\n# print( b_lcm, f_0, b )\\nprint( ( m + a_lcm // 2 ) // a_lcm )\", \"from functools import reduce\\n\\nN, M = list(map(int, input().split()))\\nAs = list(map(int, input().split()))\\n\\nBs = [A//2 for A in As]\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a%b\\n    return a\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b\\n\\nnums = []\\nfor B in Bs:\\n    num = 0\\n    while B%2 == 0:\\n        B //= 2\\n        num += 1\\n    nums.append(num)\\n\\nif len(set(nums)) != 1:\\n    ans = 0\\nelse:\\n    L = reduce(lcm, Bs)\\n    ans = M//L - M//(2*L)\\n\\nprint(ans)\\n\", \"import math\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\nb = {}\\nfor i in range(n):\\n    count = 0\\n    temp = a[i]\\n    while temp % 2 == 0:\\n        count += 1\\n        temp //= 2\\n    b.setdefault(count, 0)\\n    b[count] += 1\\nif len(b.keys()) >= 2:\\n    ans = 0\\nelse:\\n    temp = 1\\n    for i in range(n):\\n        temp = temp * a[i] // math.gcd(temp, a[i])\\n    temp2 = temp // 2\\n    ans = m // temp2 - m // temp\\nprint(ans)\", \"import numpy as np\\nimport sys\\n\\ndef main():\\n    N,M=list(map(int,input().split()))\\n    A=list(map(int,input().split()))\\n    A_double=list([x//2 for x in A])\\n\\n    mini_multi=int(np.lcm.reduce(A_double))\\n\\n    res=M//mini_multi\\n    \\n    for i in A_double:\\n        if (mini_multi//i)%2==0:\\n            print((0))\\n            return\\n\\n    if res%2!=0:\\n        res+=1\\n\\n\\n    print((res//2))\\n\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# ABC150D\\n\\nimport sys\\ninput=sys.stdin.readline\\nfrom math import gcd,ceil\\n\\ndef main():\\n    N,M=list(map(int,input().split()))\\n    A=list([int(x)//2 for x in input().split()])\\n    lcm=A[0]\\n    for i in range(1,N):\\n        lcm=lcm*A[i]//gcd(lcm,A[i])\\n    allo=1\\n    for i in range(N):\\n        allo&=(lcm//A[i])%2\\n    if allo:\\n        print((ceil(int(M//lcm)/2)))\\n    else:\\n        print((0))\\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nfrom math import gcd\\nfrom copy import deepcopy\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\n\\ndef resolve():\\n    n, m = list(map(int, input().split()))\\n    A = list(map(int, input().split()))\\n\\n    A_ = deepcopy(A)\\n    cnt = [0] * n\\n    for i in range(n):\\n        while A_[i] % 2 == 0:\\n            A_[i] //= 2\\n            cnt[i] += 1\\n        if i != 0 and cnt[i] != cnt[i - 1]:\\n            print((0))\\n            return\\n\\n    L = 1\\n    for a in A:\\n        L = lcm(L, a // 2)\\n\\n    res = m // L - (m // (L * 2))\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from math import gcd\\ndef lcm(a,b):return (a*b)//(gcd(a,b))\\n\\ndef f(x):\\n    cnt=0\\n    while(x%2==0):\\n        cnt+=1\\n        x=x//2\\n    return cnt\\n\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(map(lambda x: x//2,a))\\n\\nt=f(a[0])\\nfor i in range(n):\\n    if(f(a[i])!=t):\\n        print(0)\\n        return\\n    a[i]=a[i]//(2**t)\\nm=m//(2**t)\\nl=1\\nfor i in range(n):\\n    l=lcm(l,a[i])\\n    if(l>m):\\n        print(0)\\n        return\\nm=m//l\\nprint((m+1)//2)\", \"import math\\n\\nn,m=list(map(int,input().split()))\\na=list(map(int,input().split()))\\n\\nif n==1:\\n  a1=a[0]//2\\n  ans_m=m//a1\\n  if ans_m==0:\\n    print((0))\\n  else:\\n    print(((ans_m-1)//2+1))\\n  \\nelse:\\n  x=a[0]\\n  ch=0\\n  ch1=0\\n  while x%2==0:\\n    x=x//2\\n    ch+=1\\n  dob=2**ch\\n  for i in a:\\n    if i%dob==0 and i%(dob*2)!=0:\\n      ch1+=1\\n  if ch1!=n:\\n    print((0))\\n  else:\\n    ans=a[0]//2\\n    for j in range(1,n):\\n      ans=(ans*(a[j]//2))//math.gcd(ans,a[j]//2)\\n    ans_m=m//ans\\n    if ans_m==0:\\n      print((0))\\n    else:\\n      print(((ans_m-1)//2+1))\\n    \\n      \\n\", \"from math import gcd, ceil\\nN,M = map(int,input().split())\\nA = list(map(int,input().split()))\\nA = [a//2 for a in A]\\nB = 1\\n\\nfor a in A:\\n  B*=a//gcd(B,a)\\n  \\nfor a in A:\\n  if B//a%2==0:\\n    print(0)\\n    return\\n\\nprint(ceil((M//B)/2))\", \"def solve():\\n    import math\\n    N,M = [int(i) for i in input().split()]\\n    A = list(map(int, input().split()))\\n\\n    lcm = A[0]\\n    for i in range(1, N):\\n        lcm = lcm * A[i] // math.gcd(lcm, A[i])\\n    first = lcm // 2\\n\\n    ans_exists = True\\n    for i in range(N):\\n        if first % A[i] == 0:\\n            ans_exists = False\\n\\n    if ans_exists:\\n        ans = int((M-first) // lcm + 1)\\n        print(ans)\\n    else:\\n        print('0')\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# -*- coding: utf-8 -*-\\n\\\"\\\"\\\"\\nCreated on Wed Sep  9 14:33:00 2020\\n\\n@author: liang\\n\\\"\\\"\\\"\\nfrom math import gcd\\n\\nN, M = map(int, input().split())\\nA = [int(i) for i in input().split()]\\n\\nflag = False\\nres = 1\\nfor a in A:\\n    a //= 2\\n    res *= a//gcd(res,a)\\n    if res > M:\\n        flag = True\\n        break\\n    #print(res)\\n\\\"\\\"\\\"\\n\\u5b58\\u5728\\u30c1\\u30a7\\u30c3\\u30af\\n\\uff12\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u500b\\u6570\\u540c\\u3058\\uff1f\\n\\\"\\\"\\\"\\n\\nfor a in A:\\n    if int(res/a) == res/a:\\n        flag = True\\n        \\nif flag:\\n    ans = 0\\n    print(ans)\\nelse:\\n    #ans = (M - res(A)//2)//res + 1\\n    #ans = (M-1)//res//2 + 1\\n    ans= (M//res + 1)//2\\n    print(ans)\", \"import math\\n\\nN, M = map(int,input().split())\\nA = list(map(int,input().split()))\\n\\npow2 = 0\\nwhile A[0] % 2 == 0:\\n    A[0] //= 2\\n    pow2 += 1\\n\\nfor i in range(1,N):\\n    cnt = 0\\n    while A[i] % 2 == 0:\\n        A[i] //= 2\\n        cnt += 1\\n    if cnt != pow2:\\n        print(0)\\n        return\\n\\nLCM = 2**max(0,pow2-1)\\nfor i in range(N):\\n    LCM = LCM * A[i] // math.gcd(LCM,A[i])\\n\\nans = M // LCM\\nprint((ans+1)//2)\", \"from math import gcd\\nfrom functools import reduce\\nimport sys\\ninput = sys.stdin.readline\\n\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a, b)\\n\\n\\ndef count_factor_2(num):\\n    count = 0\\n    while num % 2 == 0:\\n        num //= 2\\n        count += 1\\n    return count\\n\\n\\ndef main():\\n    n, m = list(map(int, input().split()))\\n    A = list([x//2 for x in set(map(int, input().split()))])\\n\\n    check = len(set(map(count_factor_2, A)))\\n    if check != 1:\\n        print((0))\\n        return\\n\\n    lcm_a = reduce(lcm, A)\\n    step = lcm_a * 2\\n    ans = (m + lcm_a) // step\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nA = list(map(lambda x: int(x)//2, input().split()))\\n\\nimport math\\n\\ndef lcm(x, y):\\n  return (x // math.gcd(x, y)) * y\\n\\ndef pow2(x):\\n  ret = 0\\n  while x%2 == 0:\\n    ret += 1\\n    x //= 2\\n  return ret\\n\\nP = []\\nfor a in A:\\n  P.append(pow2(a))\\n\\nif len(set(P)) != 1:\\n  print(0)\\nelse:\\n  m = 1\\n  for a in A:\\n    m = lcm(m, a)\\n  print(-(-(M//m)//2))\", \"def GCM(x, y):\\n  if x%y==0:\\n    return y\\n  else:\\n    return GCM(y, x%y)\\n\\nN, M = map(int, input().split())\\n\\nA = list(map(int, input().split()))\\n\\ncount2 = [0 for i in range(N)]\\nfor i in range(N):\\n  a = A[i]\\n  while a%2==0:\\n    count2[i] += 1\\n    a = a//2\\n  A[i] = a\\nif sum(count2) == count2[0]*N:\\n  count2 = count2[0]\\n  buf = 1\\n  for i in range(N):\\n    buf = A[i]*buf//GCM(buf, A[i])\\n  buf *= 2**(count2-1)\\n  #print(buf)\\n  n = M//buf\\n  print((n+1)//2)\\n  \\nelse:\\n  print(0)\", \"import fractions\\nimport math\\nfrom functools import reduce\\n\\ndef lcm_base(x, y):\\n    return (x * y) // fractions.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\nb=lcm_list(map(lambda x: x//2, a))\\nswt=0\\n\\nfor i in range(n):\\n  if 0==(b//(a[i]//2))%2:\\n    swt=1\\n    break\\n\\nif 0==swt:\\n  print(math.ceil((m//b)/2))\\nelse:\\n  print(0)\", \"import math\\nimport numpy as np\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nc=1\\ntest=A[0]\\nl=0\\n\\nwhile test%2 == 0:\\n  test=test//2\\n  c*=2\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n  \\nfor i in np.arange(N-1):\\n  if A[i+1]%c!=0:\\n    print(0)\\n    l=1\\n    break\\n  elif A[i+1]%(c*2)==0:\\n    print(0)\\n    l=1\\n    break\\n  else:\\n    k=A[i+1]//c\\n    test=lcm_base(test, k)\\nif l==0:\\n  k=test*c//2\\n  print(M//k//2 + M//k%2)\", \"from math import gcd\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nmemo = {}\\n\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\n\\nb = 1\\n\\nfor a in A:\\n    b = lcm(a//2, b)\\n    if b > M:\\n        break\\n\\nif any([2 * b // a % 2 == 0 for a in A]):\\n    print(0)\\nelse:\\n    ans = M // b\\n    print(ans - ans // 2)\", \"import copy\\n# from math import gcd\\n\\n\\ndef gcd(a, b):\\n    if b == 0:\\n        return a\\n    else:\\n        return gcd(b, a%b)\\n\\ndef lcm(a, b):\\n    return (a // gcd(a, b)) * b\\ndef main():\\n    n, m = map(int, input().split())\\n    A = set([int(x) for x in input().split()])\\n    a_lcm = 1\\n    for a in A:\\n        a_lcm = lcm(a_lcm, a)\\n        # m\\u304clcm\\u306e\\u534a\\u5206\\u3088\\u308a\\u3082\\u5c0f\\u3055\\u304b\\u3063\\u305f\\u30890\\n        if (a_lcm / 2) > m:\\n            print(0)\\n            return\\n    for a in A:\\n        if (a_lcm / 2) % a == 0:\\n            print(0)\\n            return\\n    # # \\u3042\\u3068\\u306f\\u5b9a\\u6570\\u500d\\u306e\\u6570\\u8abf\\u3079\\u3066\\u7d42\\u308f\\u308a\\n    ans = int((m - (a_lcm / 2)) // a_lcm) + 1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"from math import gcd\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\ndef lcm(ab):\\n    l=len(ab)\\n    ret=ab[0]\\n    for i in range(1,l):\\n        ret=ret//gcd(ab[i],ret)*ab[i]\\n    return ret\\ndef count2(a):\\n    ret=0\\n    while a%2==0:\\n        a//=2\\n        ret+=1\\n    return 2**ret\\nn,m=map(int,input().split())\\nA=list(map(int,input().split()))\\n#\\u3053\\u308c\\u306f\\u3044\\u3089\\u306a\\u3044\\u3067\\u3059\\nif any(i%2 for i in A):\\n    print(0);return\\nA=[i//2 for i in A]\\n#\\u5168\\u4f53\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\np=lcm(A)\\nc=count2(p)\\n#2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3082\\u306e\\u304c\\u3042\\u308b\\u5834\\u5408\\nif any(i%c for i in A):\\n    print(0);return\\nx=m//p\\n#print(p//c)\\nprint(-(-x//2))\", \"from math import gcd\\n\\nn, m = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = [a//2 for a in  A]\\nlcm = 1\\n\\nfor i in range(n):\\n    lcm = lcm * A[i] // gcd(lcm, A[i])\\n    if lcm > m:\\n        print((0))\\n        return\\n        \\nfor a in A:\\n    if lcm // a % 2 == 0:\\n        print((0))\\n        return\\n\\nprint(((m//lcm + 1) // 2))\\n\", \"from fractions import gcd\\n\\ndef lcm_base(x, y):\\n    return (x * y) // gcd(x, y)\\ndef lcm(numbers):\\n    x = numbers[0]\\n    for y in numbers:\\n        x = lcm_base(x, y)\\n    return x\\n\\nN, M = list(map(int, input().split()))\\naaa = list(map(int, input().split()))\\na = aaa[0]\\ncnt = 0\\nwhile a % 2 == 0:\\n    cnt += 1\\n    a //= 2\\nfor a in aaa:\\n    if a % 2 ** cnt != 0 or a % 2 ** (cnt + 1) == 0:\\n        print((0))\\n        return        \\nbbb = [a // 2 for a in aaa]\\nlc = lcm(bbb)\\nq, r = divmod(M // lc , 2)\\nprint((q + r))\\n\", \"N, M = map(int, input().split())\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print(0)\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7, 11]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print(0)\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\", \"import math\\nfrom functools import reduce\\nn, m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\na0 = A[0]\\ncnt = 0\\nwhile a0%2 == 0:\\n    a0 //= 2\\n    cnt += 1\\n\\na = []\\nfor aa in A:\\n    if cnt == 1:\\n        if aa%4 == 0:\\n            print(0)\\n            return\\n    else:\\n        if aa%(2**(cnt-1)) != 0 or aa%(2**cnt) != 0 or aa%(2**(cnt+1)) == 0:\\n            print(0)\\n            return\\n    a.append(aa//2)\\n\\n\\ndef lcm_base(p, q):\\n    return (p * q) // math.gcd(p, q)\\n\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\nlcm = lcm_list(a)\\nprint(m//lcm - m//(lcm*2))\", \"def main():\\n    import math\\n    n,m = list(map(int,input().split()))\\n    a = sorted(list(map(int,input().split())))\\n    for i in range(n):\\n        a[i] //= 2\\n    g=1\\n    for i in range(n):\\n        g = a[i] * g // math.gcd(g,a[i])\\n    for i in range(n):\\n        if g//a[i] % 2 == 0:\\n            print((0))\\n            return\\n    if g>m:\\n        print((0))\\n        return\\n    print((1 + (m-g)//(2*g)))\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nfrom functools import reduce\\nn, m = input().split()\\na = list(map(int, input().split()))\\nb =[0]*int(n)\\nfor i in range(len(a)):\\n  b[i] = a[i]//2\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\nc = 0\\n\\nx = lcm_list(b)\\nfor i in range(int(n)):\\n  if (x // b[i]) % 2 == 0:\\n    c = -1\\n    break\\n  else:\\n    continue\\n    \\nif c == -1:\\n  print((0))\\nelse:\\n  print((math.floor(((int(m)/x)+1)/2)))\\n\\n\", \"N, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\n\\nfrom fractions import gcd\\ndef two(n):\\n    ans = 0\\n    while n%2==0:\\n        n //= 2\\n        ans += 1\\n    return ans\\n\\ndef multi_lcm(A):\\n    ans = A[0]\\n    for a in A:\\n        ans *= a//gcd(ans,a)\\n    return ans\\n\\ndef solve(N,M,A):\\n    ans = 0\\n    num_two = len(set(map(two,A)))\\n    if num_two != 1:\\n        return 0\\n    l = multi_lcm(A)\\n    ans = (M+l//2)//l\\n    return ans\\nprint((solve(N,M,A)))\\n\", \"from math import gcd\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nf = lambda n: 0 if n%2 else f(n>>1)+1\\nx = f(A[0])\\n\\nif sum(x!=f(a) for a in A):\\n    print(0)\\n    return\\n\\nA = [a>>x for a in A]\\n\\ny = 1\\nfor a in A:\\n    y = y*a//gcd(y, a)\\n    if y<<(x-1) > M:\\n        print(0)\\n        return\\n\\nprint((M//(y<<(x-1))+1)//2)\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = [i // 2 for i in A]\\nlcd = 1\\nfor a in A:\\n    lcd *= a // gcd(lcd, a)\\nfor a in A:\\n    if lcd // a % 2 == 0:\\n        print((0))\\n        return\\nprint(((M//lcd+1)//2))\\n\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7, 11]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\ndef euclid(a, b):\\n  while b:\\n    a, b = b, a%b\\n  return a\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // euclid(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"N, M = map(int, input().split())\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print(0)\\n    return\\nans = 0\\n\\nimport math\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print(0)\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\", \"from math import gcd\\ndef readinput():\\n    n,m=list(map(int,input().split()))\\n    a=list(map(int,input().split()))\\n    return n,m,a\\n\\ndef lcm(a,b):\\n    return a*b//gcd(a,b)\\n\\ndef main(n,m,a):\\n    #s=set(a)\\n    #print(s)\\n    x=a[0]//2\\n    for i in range(1,n):\\n        x=lcm(x,a[i]//2)\\n    #print(x)\\n    gusubai=False\\n    kisubai=False\\n    for i in range(n):\\n        if x%a[i]!=0:\\n            gusubai=True\\n        else:\\n            kisubai=True\\n    \\n    y=m//x\\n    #print(y,x,m)\\n    if gusubai and not kisubai:\\n        ans=y//2+y%2\\n    elif gusubai and kisubai:\\n        ans=0\\n    else:\\n        ans=y\\n    return ans\\n\\ndef __starting_point():\\n    n,m,a=readinput()\\n    ans=main(n,m,a)\\n    print(ans)\\n\\n__starting_point()\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    N, M = MI()\\n    L = LI()\\n    L = [i//2 for i in L]\\n    \\n    past = L[0]\\n\\n    for i in L:\\n        past = (past // math.gcd(i, past)) * i\\n        if past > M or (past // i) % 2 == 0:\\n            print(0)\\n            return\\n    \\n    temp = M // past\\n    ans = (temp+1)//2\\n    print(ans)        \\n    \\n\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"from fractions import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(lambda x: int(x),input().split()))\\n\\ncnt = [0 for _ in range(N)]\\nfor i in range(N):\\n  a = A[i]\\n  while a%2 == 0:\\n    a = a // 2\\n    cnt[i] += 1\\n\\nif max(cnt) > min(cnt):\\n  print(0)\\n  return\\nC = max(cnt)\\n\\nA = list(map(lambda x: x // pow(2,C), A))\\ndef gcd(a,b):\\n  if a<b:\\n    a,b = b,a\\n  while a%b > 0:\\n    a,b = b,a%b\\n  return b\\n\\ndef lcm(a,b):\\n  return a*b//gcd(a,b)\\n\\nx = A[0]\\nfor a in A[1:]:\\n  x = lcm(x,a)\\nx = x * pow(2,C-1)\\n\\nprint((M // x + 1) // 2)\", \"from math import gcd\\nfrom functools import reduce\\n\\nn,m=map(int,input().split())\\nlst=list(map(lambda x : int(x)//2,input().split()))\\ndivi=0\\nx=lst[0]\\nwhile x%2==0:\\n    x//=2\\n    divi+=1\\n\\nfor i in range(1,n):\\n    divi2=0\\n    x=lst[i]\\n    while x%2==0:\\n        x//=2\\n        divi2+=1\\n    if divi!=divi2 :\\n        print(0)\\n        return\\n\\nwork=reduce(lambda x,y: x*y//gcd(x,y),lst)\\nprint((m//work+1)//2)\", \"n, m = map(int, input().split())\\naas = set(list(map(int, input().split())))\\na = [i//2 for i in aas]\\nimport math\\nN = len(a)\\ndef n_of_twos(x):\\n    res = 0\\n    while x%(2**(res+1))==0:\\n        res += 1\\n    return res\\nif N>=2:\\n    n_of_twos_0 = n_of_twos(a[0])\\n    for i in range(1,N):\\n        if n_of_twos(a[i]) != n_of_twos_0:\\n            print(0)\\n            return\\nans = a[0]\\nfor i in range(1, N):\\n    ans = ans * a[i] // math.gcd(ans, a[i])\\nif ans > m:\\n    print(0)\\n    return\\nprint(1 + (m//ans-1)//2)\", \"from math import gcd, ceil\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print(0)\\n        return\\nprint(ceil((m // l) / 2))\", \"import queue\\nimport numpy as np\\nimport math\\n\\nN, M = map(int, input().split())\\na2 = list(map(int, input().split()))\\na = []\\nfor i in a2:\\n    a.append(i//2)\\n\\nlcm = a[0]\\n\\nfor i in a:\\n    lcm *= i // math.gcd(lcm, i)\\n\\nhasAns = True\\nfor i in a:\\n    if (lcm // i) % 2 == 0:\\n        hasAns = False\\n        break\\n\\nans = 0\\n\\nif hasAns:\\n    ans = ((M // lcm) + 1 )// 2\\n\\nprint(ans)\", \"from math import gcd\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(set(a))\\na=list(map(lambda x: x//2, a))\\n\\ndef lcm(q):\\n  x = q[0]\\n  for i in range(1, len(q)):\\n    x = (x * q[i]) // gcd(x, q[i])\\n  return x\\n\\nlcma=lcm(a)\\nfor i in range(len(a)):\\n  if (lcma//a[i])%2==0:\\n    print(0)\\n    return\\ntemp=m//lcma\\nprint(-(-temp//2))\", \"import sys\\nimport math\\n# import bisect\\n# import numpy as np\\n# from decimal import Decimal\\n# from numba import njit, i8, u1, b1 #JIT compiler\\n# from itertools import combinations, product\\n# from collections import Counter, deque, defaultdict\\n\\n# sys.setrecursionlimit(10 ** 6)\\nMOD = 10 ** 9 + 7\\nINF = 10 ** 9\\nPI = 3.14159265358979323846\\n\\ndef read_str():      return sys.stdin.readline().strip()\\ndef read_int():      return int(sys.stdin.readline().strip())\\ndef read_ints():     return map(int, sys.stdin.readline().strip().split())\\ndef read_ints2(x):   return map(lambda num: int(num) - x, sys.stdin.readline().strip().split())\\ndef read_str_list(): return list(sys.stdin.readline().strip().split())\\ndef read_int_list(): return list(map(int, sys.stdin.readline().strip().split()))\\ndef GCD(a: int, b: int) -> int: return b if a%b==0 else GCD(b, a%b)\\ndef LCM(a: int, b: int) -> int: return (a * b) // GCD(a, b)\\n\\ndef Main():\\n    n, m = read_ints()\\n    a = read_int_list()\\n    a = [x // 2 for x in a]\\n    lcm = 1\\n    for x in a:\\n        lcm *= x // math.gcd(lcm, x)\\n    for x in a:\\n        if lcm // x % 2 == 0:\\n            print(0)\\n            return\\n    print(math.ceil((m // lcm) / 2))\\n\\ndef __starting_point():\\n    Main()\\n__starting_point()\", \"import sys\\ninput=sys.stdin.readline\\nimport math\\n\\nN,M=(int(x) for x in input().rstrip('\\\\n').split())\\nAs=[int(x) for x in input().rstrip('\\\\n').split()]\\nn = 1\\nuse2 = 0\\ncheck = 0\\nfor i in range(N):\\n  x = As[i]\\n  if i==0:\\n    while x % 2==0:\\n      use2+=1 \\n      x = x//2\\n    lcm=x\\n  else:\\n    use=0\\n    while x%2==0:\\n      x = x//2\\n      use += 1\\n    if use2 != use:\\n      check += 1\\n      break\\n    lcm=lcm*x//(math.gcd(lcm,x))\\nif check > 0:\\n  print(0)\\nelse:\\n  LCM=2**(use2-1)\\n  LCM=LCM*lcm\\n  print(((M//LCM)+1)//2)\", \"def lcm(a, b):\\n  return a // gcd(a, b) * b\\n\\ndef gcd(a, b):\\n  if(b == 0): return a\\n  else: return gcd(b, a % b)\\n\\ndef cnt(a):\\n  res = 0\\n  while(a and a % 2 == 0):\\n    a //= 2\\n    res += 1\\n  return res\\n\\nn, m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nl = 1\\nc = cnt(A[0])\\nfor a in A:\\n  if cnt(a) != c or c == 0:\\n    print(0)\\n    return\\n  else:\\n    l = lcm(l, a // 2)\\nd = m // l\\nprint((d + 1) // 2)\", \"from math import gcd\\nfrom functools import reduce\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a,b)\\n\\na = [i//2 for i in a]\\n\\nl = reduce(lcm, a)\\n\\nif any((l//i) % 2 == 0 for i in a):\\n    print(0)\\n    return\\n\\nprint(-(-(m//l)//2))\", \"import math\\nn,m= list(map(int,input().split()))\\nal= list(map(int,input().split()))\\ntwos = set()\\nfor c in al:\\n    temp,tempc=0,c\\n    while tempc%2==0:\\n        tempc//=2\\n        temp+=1\\n    twos.add(temp)\\nif len(twos)>1:print((0))\\nelse:\\n    lcmv=al[0]\\n    for i in range(1,n):lcmv = lcmv*al[i] // math.gcd(lcmv,al[i])\\n    print((max(0,1 + (m-lcmv//2)//lcmv)))\\n\", \"from functools import reduce\\n\\ndef main():\\n  N,M=map(int,input().split())\\n  *A,=map(int,input().split())\\n\\n  A = list(set(A))\\n  N = len(A)\\n\\n  B = [A[i]//2 for i in range(N)]\\n\\n  def factorize(n):\\n      out=[]\\n      i = 2\\n      while i==2:\\n          if n%i==0:\\n              out.append(i)\\n              n //= i\\n          else:\\n              i += 1\\n          if n == 1:break\\n          if i > int(n**.5+3):\\n              out.append(n)\\n              break\\n      return out\\n\\n  ord_list=[len(factorize(B[i])) for i in range(N)]\\n\\n  if len(set(ord_list)) != 1:\\n    print(0)\\n    return\\n\\n  def gcd(a,b):\\n    if b == 0: return a\\n    return gcd(b,a%b)\\n\\n  def lcm(a,b):\\n    return a*b//gcd(a,b)\\n\\n  LCM = reduce(lcm,B)\\n  print((M//LCM+1)//2)\\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"from math import gcd\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\ndef lcm_g(A):\\n    ret = 1\\n    for a in A:\\n        ret = lcm(ret, a)\\n    return ret\\n\\ndef is_hcm(x, A):\\n    for i in range(N):\\n        if x % A[i] != A[i] // 2:\\n            return False\\n    return True\\n\\nN, M = [int(x) for x in input().split()]\\nA = [int(x) for x in input().split()]\\n\\nl = lcm_g(A)\\nif is_hcm(l // 2, A):\\n    ans = (2 * M + l) // (2 * l)\\nelse:\\n    ans = 0\\n\\nprint(ans)\", \"import math\\nimport fractions\\nfrom functools import reduce\\n \\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na=[t//2 for t in a] # \\u30ea\\u30b9\\u30c8\\u306e\\u8981\\u7d20\\u3092\\u5168\\u30662\\u3067\\u5272\\u308b\\n \\ndef lcm_base(x, y):\\n    return (x * y) // fractions.gcd(x, y)\\n \\ndef lcm_list(numbers): # \\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3092\\u6c42\\u3081\\u308b\\n    return reduce(lcm_base, numbers, 1)\\n \\ndef num_dev2(x): # 2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n    return format(x, 'b')[::-1].find('1')\\n \\nlcm = lcm_list(a)\\nq = m // lcm # m\\u306f\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3067\\u4f55\\u56de\\u5272\\u308c\\u308b\\u304b\\n \\ncount = 0\\ndev2 = num_dev2(a[0])\\nfor i in range(1, n):\\n    if dev2 != num_dev2(a[i]): # \\u30ea\\u30b9\\u30c8\\u306e\\u5168\\u3066\\u306e\\u8981\\u7d20\\u306e\\u30012\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u306f\\u7b49\\u3057\\u3044\\u304b\\uff1f\\n        count += 1\\n        break\\nif count != 0:\\n    print(0)\\nelse:\\n    print(math.ceil(q/2))\", \"import sys, re\\nfrom collections import deque, defaultdict, Counter\\nfrom math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd\\nfrom itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby\\nfrom operator import itemgetter, mul\\nfrom copy import deepcopy\\nfrom string import ascii_lowercase, ascii_uppercase, digits\\nfrom bisect import bisect, bisect_left, insort, insort_left\\nfrom heapq import heappush, heappop\\nfrom functools import reduce, lru_cache\\ndef input(): return sys.stdin.readline().strip()\\ndef INT(): return int(input())\\ndef MAP(): return map(int, input().split())\\ndef LIST(): return list(map(int, input().split()))\\ndef TUPLE(): return tuple(map(int, input().split()))\\ndef ZIP(n): return zip(*(MAP() for _ in range(n)))\\nsys.setrecursionlimit(10 ** 9)\\nINF = 10**6#float('inf')\\n#mod = 10 ** 9 + 7 \\nmod = 998244353\\n#from decimal import *\\n#import numpy as np\\n#decimal.getcontext().prec = 10\\n\\nN, M = MAP()\\na = LIST()\\n\\nA = sorted([x//2 for x in a], reverse=True)\\n\\nb = A[0]\\ncnt = 0\\nwhile b%2 == 0:\\n\\tb //= 2\\n\\tcnt += 1\\n\\nfor x in A:\\n\\tif x%pow(2, cnt) or (x//pow(2, cnt))%2 == 0:\\n\\t\\tprint(0)\\n\\t\\treturn\\n\\nlcm = A[-1]\\nfor x in A:\\n\\tlcm = lcm*x//gcd(lcm, x)\\n\\nr = lcm//A[0]\\nn = M//A[0]\\n\\n#2p+1\\u304c1<=2p+1<=n \\u306e\\u7bc4\\u56f2\\u3067 r\\u306e\\u500d\\u6570\\u3068\\u306a\\u308bp\\u306e\\u500b\\u6570\\nif r%2 == 0:\\n\\tprint(0)\\nelse:\\n\\tprint(n//r - n//(2*r))\", \"from math import gcd, ceil\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print((0))\\n        return\\nprint((ceil((m // l) / 2)))\\n\", \"from functools import reduce\\nimport math\\ndef lcm_base(x, y):\\n  return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n  return reduce(lcm_base, numbers, 1)\\n\\ndef lcm_list(numbers):\\n  return reduce(lcm_base, numbers, 1)\\n\\nn,m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i//2 for i in list(set(a))]\\nnothing = False\\ncnt_common = -1\\nfor i in a:\\n  cnt = 0\\n  while i % 2 == 0:\\n    i = i//2\\n    cnt += 1\\n  if cnt_common == -1:\\n    cnt_common = cnt\\n    continue\\n  if cnt_common != cnt:\\n    nothing = True\\n    break\\n\\nb=lcm_list(a)\\nif nothing:\\n  print(0)\\nelse:\\n  ans = (m-b)//(2*b) + 1\\n  print(max(ans,0))\", \"from fractions import gcd\\ndef lcm(a,b):\\n    return (a*b)//gcd(a,b)\\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\nans = 1\\nfor i in a:\\n    ans = lcm(ans,i)\\nfor i in a:\\n    if (ans//i) % 2 == 0:\\n        print(0)\\n        return\\nprint(((m//(ans//2))+1)//2)\", \"import math\\nN, M = map(int, input().split())\\nB = tuple(int(a) // 2 for a in input().split())\\n\\nx = B[0]\\nfor i in range(1, N):\\n    x = (x * B[i]) // math.gcd(x, B[i])\\n\\nfor b in B:\\n    if (x // b) % 2 == 0:\\n        print(0)\\n        break\\nelse:\\n    ans = (M // x) - (M // (2 * x))\\n    print(ans)\", \"import math\\nfrom functools import reduce\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef div2_n(x):\\n    n = 0\\n    while x % 2 == 0:\\n      if x % 2 == 0:\\n          n += 1\\n          x >>= 1\\n    return n\\n  \\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\n\\na2 = [i//2 for i in a]\\nn0 = div2_n(a2[0])\\nfor i in range(1,n):\\n    if div2_n(a2[i]) != n0:\\n        print((0))\\n        return\\n\\na2_l = lcm(*a2)\\nprint((m//a2_l - m//(a2_l*2)))\\n\", \"N, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\ndef gcd(a,b):\\n    while b > 0:\\n        a, b = b, a % b\\n    return a\\n\\n\\nG = A[0]/2\\nfor a in A[1:]:\\n    G *= (a/2)/gcd(G,a//2)\\nfor a in A:\\n    if G % a == 0:\\n        print(0)\\n        return\\nprint(int(M//G - M//G//2))\", \"n , m = list(map(int, input().split()))\\na = list(map(int,input().split()))\\n\\ndef gcd(num1,num2):\\n    r=1\\n    while r>0:\\n        r=num1%num2\\n        num1=num2\\n        num2=r\\n    return num1\\n\\ndef lcm(num1,num2):\\n    gcd1=gcd(num1,num2)\\n    return num1*num2//gcd1\\n\\nlcm1=a[0]//2\\nlcm2=a[0]\\n\\nfor i in range(1,n):\\n    t=a[i]\\n    lcm1=lcm(lcm1,t//2)\\n    lcm2=lcm(lcm2,t)\\n    ta=max(t//2,lcm1)\\n    tb=min(t//2,lcm1)\\n    if ta!=tb and ta//tb%2==0:\\n        lcm1=0\\n        lcm2=0\\n        break\\n\\nif lcm1!=0:\\n    ans1=m//lcm1\\n    ans2=m//lcm2\\n    ans=ans1-ans2\\nelse:\\n    ans=0\\n\\nprint(ans)\\n\", \"import sys, re\\nfrom collections import deque, defaultdict, Counter\\nfrom math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd\\nfrom itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby\\nfrom operator import itemgetter, mul\\nfrom copy import deepcopy\\nfrom string import ascii_lowercase, ascii_uppercase, digits\\nfrom bisect import bisect, bisect_left, insort, insort_left\\nfrom heapq import heappush, heappop\\nfrom functools import reduce, lru_cache\\ndef input(): return sys.stdin.readline().strip()\\ndef INT(): return int(input())\\ndef MAP(): return map(int, input().split())\\ndef LIST(): return list(map(int, input().split()))\\ndef TUPLE(): return tuple(map(int, input().split()))\\ndef ZIP(n): return zip(*(MAP() for _ in range(n)))\\nsys.setrecursionlimit(10 ** 9)\\nINF = 10**6#float('inf')\\n#mod = 10 ** 9 + 7 \\nmod = 998244353\\n#from decimal import *\\n#import numpy as np\\n#decimal.getcontext().prec = 10\\n\\nN, M = MAP()\\na = LIST()\\n\\nA = sorted([x//2 for x in a], reverse=True)\\n\\nlcm = A[-1]\\nfor x in A:\\n\\tlcm = lcm*x//gcd(lcm, x)\\n\\nr = lcm//A[0]\\nn = M//A[0]\\n\\n\\nfor x in A:\\n\\tif lcm//x%2 == 0:\\n\\t\\tprint(0)\\n\\t\\treturn\\n#2p+1\\u304c1<=2p+1<=n \\u306e\\u7bc4\\u56f2\\u3067 r\\u306e\\u500d\\u6570\\u3068\\u306a\\u308bp\\u306e\\u500b\\u6570\\nif r%2 == 0:\\n\\tprint(0)\\nelse:\\n\\tprint(n//r - n//(2*r))\", \"import math\\nfrom functools import reduce\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nN,M = map(int,input().split())\\na = list(map(lambda a: int(a)//2, input().split()))\\ng = lcm(*a)\\nif any([g // item % 2 == 0 for item in a]):\\n    print(0)\\nelse:\\n    ans = M//g\\n    ans = max(math.ceil(ans/2),0)   \\n    print(ans)\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = [a//2 for a in map(int, input().split())]\\n\\nlcm = 1\\nfor a in A:\\n    lcm = lcm*a//gcd(lcm, a)\\n    if lcm > M:\\n        print((0))\\n        return\\n\\nfor a in A:\\n    div = lcm//a\\n    if div % 2 == 0:\\n        print((0))\\n        return\\n\\nans = (M//lcm+1)//2\\nprint(ans)\\n\", \"import math\\ndef LCM(a, b):\\n    g = math.gcd(a, b)\\n    return a * b // g\\n\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = list(set(A))\\nN = len(A)\\na0 = A[0]\\ndiv = 1\\nwhile a0 % 2 == 0:\\n    div *= 2\\n    a0 //= 2\\n\\nfor i in range(1, N):\\n    a = A[i] % div\\n    b = A[i] // div\\n    if (b % 2 == 0) or (a != 0):\\n        print((0))\\n        return\\n\\nfor i in range(N):\\n    A[i] //= 2\\n\\nif N > 1:\\n    lcm = LCM(A[0], A[1])\\n    for i in range(2, N):\\n        lcm = LCM(lcm, A[i])\\n\\nif N == 1:\\n    lcm = A[0]\\n\\nans = M // lcm\\nif ans % 2 == 1:\\n    print((ans // 2 + 1))\\nelse:\\n    print((ans // 2))\\n\", \"import math\\ndef lcm(x,y):\\n    return(x*y)//math.gcd(x,y)\\nn,m=map(int,input().split())\\nl=list(map(int,input().split()))\\na=l[0]//2\\nfor i in range(n-1):\\n    a=lcm(a,l[i+1]//2)\\n \\nok = True\\nfor i in range(n):\\n  if (a//(l[i]//2))%2!=1:\\n    ok=False\\n    break\\nans = 0\\nif ok:\\n    ans = ((m//a)+1)//2\\nprint(ans)\", \"import sys\\nN,M = list(map(int,input().split()))\\nA = list(map(int,input().split()))\\na = []\\nfor i in A:\\n  i = i//2\\n  a.append(i)\\ndef gcd(p,q):\\n  p,q = max(p,q),min(p,q)\\n  while q!=0:\\n    p,q = q,p%q\\n  return p\\ndef lcm(p,q):\\n  return(p*q//gcd(p,q))\\ndef aaa(i):\\n  count = 0\\n  while i%2==0:\\n    i = i//2\\n    count+=1\\n  return count\\nmax_num = a[0]\\naa = aaa(a[0])\\nfor i in a:\\n  max_num = lcm(i,max_num)\\n  if aa != aaa(i):\\n    print((0))\\n    return\\nprint((((M//max_num)+1)//2))\\n\", \"import math\\ndef lcm(a,b):\\n  return (a*b)//math.gcd(a,b)\\ndef co(num):\\n  return format(num, 'b')[::-1].find('1')\\nN,M=map(int,input().split())\\nL=list(map(int,input().split()))\\nL2=[co(i) for i in L]\\nif len(set(L2))!=1:\\n  print(0)\\n  return\\nL=[i//2 for i in L]\\ns=L[0]\\nfor i in range(N):\\n  s=lcm(s,L[i])\\nc=M//s\\nprint((c+1)//2)\", \"import math\\nfrom functools import reduce\\n\\nN,M=list(map(int,input().split()))\\nA=[int(x)//2 for x in input().split()]\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nLCM=lcm(*A)\\nfor a in A:\\n  if LCM//a%2==0:\\n    print((0))\\n    break\\nelse:\\n  print(((M//LCM+1)//2))\\n\", \"import numpy as np\\nfrom math import ceil\\n\\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\na = [x//2 for x in a]\\nlcm = np.lcm.reduce(a)\\nans = 0\\n\\nfor i in a:\\n    if lcm // i % 2 == 0:\\n        break\\nelse:\\n    ans = ceil((m//lcm)/2)\\n\\nprint(ans)\", \"import math\\n\\ndef n_2(n):\\n  c=0\\n  while n%2==0:\\n    c+=1\\n    n>>=1\\n  return (n,c)\\n\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nA[0],a=n_2(A[0])\\np=False\\nfor i in range(1,N):\\n  A[i],b=n_2(A[i])\\n  if a!=b:\\n    p=True\\n    break\\nif p:\\n  print(0)\\n  return\\nn=1\\nfor _ in range(a-1):\\n  n*=2\\nl=n\\nfor a in A:\\n  l=l*a//math.gcd(l,a)\\nans=M//l-M//(2*l)\\nprint(ans)\", \"def abc150_d():\\n    n, m = (int(x) for x in input().split())\\n    A = [int(x) // 2 for x in input().split()]\\n\\n    from math import gcd\\n    def lcm(a, b):\\n        return a * b // gcd(a, b)\\n\\n    x = 1\\n    for a in A:\\n        x = lcm(x, a)\\n\\n    valid = True\\n    for a in A:\\n        if (x // a) % 2 == 0:\\n            valid = False\\n            break\\n\\n    if valid: ans = (m // x + 1) // 2\\n    else: ans = 0\\n    print(ans)\\n\\ndef __starting_point():\\n    abc150_d()\\n__starting_point()\", \"from math import gcd\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(set(a))\\na=list(map(lambda x: x//2, a))\\n\\ndef lcm(q):\\n  x = q[0]\\n  for i in range(1, len(q)):\\n    x = (x * q[i]) // gcd(x, q[i])\\n  return x\\n\\nlcma=lcm(a)\\nfor i in range(len(a)):\\n  if (lcma//a[i])%2==0:\\n    print(0)\\n    return\\ntemp=m//lcma\\nprint(temp//2 if temp%2==0 else temp//2+1)\", \"from math import gcd, ceil\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print(0)\\n        return\\nprint(ceil((m // l) / 2))\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ndef lcm(a, b):\\n    \\\"\\\"\\\"\\u6700\\u5c0f\\u516c\\u500d\\u6570\\\"\\\"\\\"\\n    from math import gcd\\n    return (a * b) // gcd(a, b)\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, M, As):\\n    if sum([a % 2 for a in As]) > 0:\\n        print((0))\\n        return\\n\\n    As = [a // 2 for a in As]\\n    all_lcm = 1\\n    for a in As:\\n        all_lcm = lcm(all_lcm, a)\\n        if all_lcm > M:\\n            print((0))\\n            return\\n\\n    for a in As:\\n        if (all_lcm // a) % 2 == 0:\\n            print((0))\\n            return\\n    from math import ceil\\n    print((ceil(M // all_lcm / 2)))\\n\\n\\ndef __starting_point():\\n    N, M = list(map(int, input().split()))\\n    As = [int(i) for i in input().split()]\\n\\n    # import random\\n    # N, M = 10 ** 5, 10 ** 9\\n    # As = [random.randint(5, 5) * 2 for _ in range(N)]\\n    solve(N, M, As)\\n\\n__starting_point()\", \"import sys,math\\nr=sys.stdin.readline\\ndef gcd(a,b):\\n    a,b=max(a,b),min(a,b)\\n    while b>0:\\n        a,b=b,a%b\\n    return a\\ndef lcm(arr):\\n    while len(arr)!=1:\\n        a=arr.pop()\\n        b=arr.pop()\\n        c=gcd(a,b)\\n        arr.insert(0,int(a*b/c))\\n    return arr[0]\\ndef cnt2(num):\\n    cnt=0\\n    while num%2==0:\\n        num/=2\\n        cnt+=1\\n    return cnt\\nN,M=list(map(int,r().split()))\\nseq=list(map(int,r().split()))\\nseq=list(set(seq))\\ntmp=cnt2(seq[0])\\nfor num in seq:\\n    if tmp!=cnt2(num):\\n        print((0))\\n        return\\nT=lcm(list([x//2 for x in seq]))\\nif T>M:\\n    print((0))\\n    return\\nprint((math.floor(M//T/2+0.5)))\\n\\n\\n\\n\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"from math import gcd\\n\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nl = [0] * n\\nfor i in range(n):\\n    tmp = a[i]\\n    while tmp % 2 == 0:\\n        tmp //= 2\\n        l[i] += 1\\n    if i > 0 and l[i] != l[i - 1]:\\n        print((0))\\n        return\\nres = 1\\nfor i in range(n):\\n    res = lcm(res, a[i] // 2)\\nprint((m // res - m // (res * 2)))\\n\", \"def main():\\n    N, M = map(int, input().split())\\n    A = tuple(map(int,input().split()))\\n    ans = count(A, N, M)\\n    print(ans)\\ndef count(A, N, M):\\n    t = hMt(A[0])\\n    B = [A[0]//(2**t)]\\n    for val in A[1:]:\\n        if hMt(val) != t:\\n            ans = 0\\n            return ans\\n        B.append(val//(2**t))\\n    T = nlcm(B)\\n    MdivT = (M//(2**(t-1)))//T\\n    ans = countodd(MdivT)\\n    return ans\\ndef countodd(num):\\n    if num%2 == 0:\\n        ans = num//2\\n    else:\\n        ans = num//2 + num%2\\n    return ans\\ndef nlcm(A):\\n    LCM = A[0]\\n    for val in A[1:]:\\n        #print(\\\"%d %d gcm:%d LCM:%d\\\"%(LCM,val,gcm(LCM,val),lcm(LCM,val)))\\n        LCM = lcm(LCM,val)\\n    return LCM\\n    \\ndef gcm(a, b):\\n    abtuple = (a,b)\\n    abmin = min([0,1], key=lambda x:abtuple[x])\\n    remainder = abtuple[1-abmin]%abtuple[abmin]\\n    if remainder == 0:\\n        return abtuple[abmin]\\n    return gcm(abtuple[abmin], remainder)\\ndef lcm(a,b):\\n    prod = a*b\\n    ans = prod//gcm(a,b)\\n    return ans\\ndef hMt(num):\\n    ans = 0\\n    tmp = num\\n    while tmp%2 == 0:\\n        tmp = tmp//2\\n        ans += 1\\n    return ans\\nmain()\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"from math import gcd\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\ndef lcm(ab):\\n    l=len(ab)\\n    ret=ab[0]\\n    for i in range(1,l):\\n        ret=ret//gcd(ab[i],ret)*ab[i]\\n    return ret\\ndef count2(a):\\n    ret=0\\n    while a%2==0:\\n        a//=2\\n        ret+=1\\n    return 2**ret\\nn,m=map(int,input().split())\\nA=list(map(int,input().split()))\\nif any(i%2 for i in A):\\n    print(0);return\\nA=[i//2 for i in A]\\n#\\u5168\\u4f53\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\np=lcm(A)\\nc=count2(p)\\n#2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3082\\u306e\\u304c\\u3042\\u308b\\u5834\\u5408\\n#\\u9055\\u3046\\u3058\\u3083\\u3093\\nif any(i%c for i in A):\\n    print(0);return\\nx=m//p\\n#print(p//c)\\nif x%2==0:\\n    print(x//2)\\nelse:\\n    print(x//2+1)\", \"def gcd(a, b):\\n    if b == 0:\\n        return a\\n    r = a % b   \\n    return gcd(b, r)\\n\\ndef lcm(a, b):\\n    x = gcd(a, b)\\n    return a * b // x\\n\\ndef gcdN(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = gcd(x, a[i])\\n    return x\\n\\ndef lcmN(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = lcm(x, a[i])\\n    return x\\n\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))  #;print(a)\\n\\ng = gcdN(a)\\nfor i in a:\\n    if (i//g) % 2 == 0:\\n        print((0))\\n        break\\nelse:\\n    l = lcmN(a) \\n    k = 2*m // l\\n    print(((k+1)//2))\\n\", \"from math import gcd, ceil\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print((0))\\n        return\\n#print(ceil((m // l) / 2))\\nprint(((m//l+1)//2))\\n\", \"n,m=list(map(int,input().split()))\\na=list(map(int,input().split()))\\n\\nfor i in range(n):\\n  a[i]=a[i]//2\\n  \\ndef gcd(a,b):\\n  if b==0:\\n    return a\\n  else:\\n    return gcd(b,a%b)\\n  \\ndef lcm(a,b):\\n  return a*b//gcd(a,b)\\n\\ndef check(x):\\n  cnt=0\\n  while(1):\\n    if x%2==0:\\n      x=x//2\\n      cnt+=1\\n    else:\\n      break\\n  return cnt\\n\\ncnt=a[0]\\nfor i in range(n):\\n  cnt=lcm(cnt,a[i])\\n\\n\\nl=check(a[0])\\nfor i in range(1,n):\\n  x=check(a[i])\\n  if x!=l:\\n    print((0))\\n    return\\n\\n\\ns=m//cnt\\nif s%2==0:\\n  print((s//2))\\nelse:\\n  print((s//2+1))\\n\\n  \\n\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nlcm = 1\\nfor a in A:\\n    lcm = lcm * a // gcd(lcm, a)\\n    if lcm > M*2:\\n        print((0))\\n        return\\nfor a in A:\\n    if lcm // a % 2 == 0:\\n        print((0))\\n        return\\nans = M // (lcm//2) - M // lcm\\nprint(ans)\\n\", \"from math import gcd\\ndef lcm(x,y):\\n    return x*y//gcd(x,y)\\ndef cnt(x):\\n    i = 0\\n    while x%2 == 0:\\n        x = x//2\\n        i += 1\\n    return i \\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\nmemo = cnt(a[0])\\nfor i in range(n):\\n    if cnt(a[i]) != memo:\\n        print(0)\\n        return\\n    a[i] = a[i]//2\\n\\nt = 1\\nfor i in range(n):\\n    t = lcm(t,a[i])\\nprint(m//t-m//(2*t))\", \"import math\\nimport numpy as np\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nc=1\\ntest=A[0]\\nl=0\\n\\nwhile test%2 == 0:\\n  test=test//2\\n  c*=2\\n  \\nfor i in np.arange(N-1):\\n  if A[i+1]%c!=0:\\n    print(0)\\n    l=1\\n    break\\n  elif A[i+1]%(c*2)==0:\\n    print(0)\\n    l=1\\n    break\\n  else:\\n    k=A[i+1]//c\\n    test=test*k//math.gcd(test,k)\\nif l==0:\\n  k=test*c//2\\n  print(M//k//2+M//k%2)\", \"# \\u53c2\\u8003 : https://at274.hatenablog.com/entry/2020/01/15/060000\\nfrom functools import reduce\\nimport math\\n\\n\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\ndef lcm_list(numbers):  # \\u30ea\\u30b9\\u30c8\\u3092\\u6295\\u3052\\u308b\\u3068\\u5168\\u8981\\u7d20\\u306elcm\\u304c\\u8fd4\\u3063\\u3066\\u304f\\u308b\\n    return reduce(lcm, numbers, 1)\\n\\n\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\n\\n# \\u6700\\u521d\\u3001A\\u306e\\u8981\\u7d20\\u306f\\u5168\\u3066\\u5076\\u6570\\u30022\\u3067\\u5272\\u3063\\u305f\\u3082\\u306e\\u306b\\u7f6e\\u304d\\u63db\\u3048\\nA = [a // 2 for a in A]\\n\\n# \\u5168\\u3066\\u306e\\u8981\\u7d20\\u306b\\u3064\\u3044\\u3066\\u3001\\uff12\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3068\\u984c\\u610f\\u306f\\u6e80\\u305f\\u305b\\u306a\\u3044\\ncount_div_2 = None\\nfor a in A:\\n    cnt = 0\\n    while a % 2 == 0:\\n        a //= 2\\n        cnt += 1\\n    # 1\\u500b\\u76ee\\u306f\\u7121\\u6761\\u4ef6\\u3067\\u4fdd\\u5b58\\n    if count_div_2 is None:\\n        count_div_2 = cnt\\n    # 2\\u500b\\u76ee\\u304b\\u3089\\u30c1\\u30a7\\u30c3\\u30af\\n    elif cnt != count_div_2:\\n        print((0))\\n        return\\n\\n# my_lcm = A\\u306e\\u5168\\u8981\\u7d20\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3002\\u3000\\u3053\\u306e\\u5947\\u6570\\u500d\\u304c\\u984c\\u610f\\u3092\\u6e80\\u305f\\u3059\\u3002\\n# my_lcm\\u304cM\\u3092\\u8d85\\u3048\\u3066\\u3044\\u305f\\u30891\\u3064\\u3082\\u4f5c\\u308c\\u306a\\u3044\\nmy_lcm = lcm_list(A)\\nif my_lcm > M:\\n    print((0))\\n    return\\n\\ntmp = M // my_lcm\\n# my_lcm\\u306e1,2,...M\\u500d\\u307e\\u3067\\u4f7f\\u3048\\u308b\\u304c\\u3001\\u5076\\u6570\\u306f\\u4f7f\\u3048\\u306a\\u3044\\n# tmp=1or2\\u306a\\u30891\\u500b, 3or4\\u306a\\u30892\\u500b, 5or6\\u306a\\u30893\\u500b,...\\nans = (tmp + 1) // 2\\nprint(ans)\\n\", \"import math\\nimport collections\\nimport sys\\n\\ninput = sys.stdin.readline\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\n\\nn,m=MI()\\nA=LI()\\ndef num2(x):\\n    ans=0\\n    while x%2==0:\\n        x=x//2\\n        ans+=1\\n    return ans\\nmod=2**(num2(A[0]))\\nfor i in range(1,n):\\n    if A[i]%mod!=0:\\n        print((0))\\n        return\\n    if A[i]%mod==0 and (A[i]//mod)%2==0:\\n        print((0))\\n        return\\n#print(A)\\nfor i in range(n):\\n    A[i]//=2\\n#print(A)\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b\\n\\nL=A[0]   \\nfor i in range(1,n):\\n    L=lcm(L,A[i])\\n#print(L)\\nif L>m:\\n    an=0\\nelse:\\n    an=int(((m/L)-1)/2)+1\\nprint(an)\\n\", \"import math\\n\\ndef lcm(a, b):\\n  return a*b//math.gcd(a, b)\\n\\ndef f(num):\\n  cnt = 0\\n  while num % 2 == 0:\\n    num = num // 2\\n    cnt += 1\\n  return cnt\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\n\\nfor i in range(n):\\n  a[i] = a[i] // 2\\n\\nt = f(a[0])\\nfor i in range(n):\\n  if f(a[i]) != t:\\n    print(0)\\n    return\\n  a[i] = a[i] >> t\\nm = m >> t\\nl = 1\\nfor i in range(n):\\n  l = lcm(l, a[i])\\n  if l > m:\\n    print(0)\\n    return\\n\\nm = m // l\\nprint((m+1)//2)\", \"import math\\nfrom functools import reduce\\n\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\ndef my_round(val, digit=0):\\n    p = 10 ** digit\\n    return (val * p * 2 + 1) // 2 / p\\n\\n\\nn, m = list(map(int, input().split()))\\na_pr = [i // 2 for i in list(map(int, input().split()))]\\nlcm_ = lcm_list(a_pr)\\nres, div2 = 0, None\\nfor ai in a_pr:\\n    cnt = 0\\n    while ai % 2 == 0:\\n        ai //= 2\\n        cnt += 1\\n    if div2 is None:\\n        div2 = cnt\\n    elif cnt != div2:\\n        print((0))\\n        return\\n\\nprint((int(my_round(m // lcm_ / 2))))\\n\", \"from math import gcd, ceil\\nfrom functools import reduce\\nimport sys\\n\\ndef lcm_base(x, y):\\n    return (x * y) // gcd(x, y)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nN, M = map(int, input().split())\\na = [int(i)//2 for i in input().split()]\\n\\ns = set()\\nfor x in a:\\n    cur = 0\\n    y = x\\n    while y%2 == 0:\\n        cur += 1\\n        y //= 2\\n    s.add(cur)\\n    if len(s) >= 2:\\n        print(0)\\n        return\\nlcm = lcm_list(a)\\nprint((M//lcm+1)//2)\", \"from math import gcd, ceil\\n\\n\\ndef lcm(a, b):\\n    return (a*b)//gcd(a, b)\\n\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    a[i] = a[i]//2\\n\\nlcm_v = a[0]\\nfor i in range(1, n):\\n    lcm_v = lcm(lcm_v, a[i])\\n\\nok = True\\nfor aa in a:\\n    if (lcm_v//aa) % 2 != 1:\\n        ok = False\\n        break\\nans = 0\\nif ok:\\n    ans = ((m//lcm_v)+1)//2\\nprint(ans)\\n\", \"from collections import deque,defaultdict\\ndef gcd(a,b):\\n    return b if not a%b else gcd(b,a%b)\\ndef lcm(a,b):\\n    return (a*b)//gcd(a,b)\\nn,m=list(map(int, input().split()))\\nA=[int(i) for i in input().split()]\\ntmp = A[0]\\nfor i in range(1,n):\\n    tmp = lcm(tmp,A[i])\\nans = m//tmp\\nlis = set()\\nfor i in A:\\n    r = i\\n    k=0\\n    while(r%2==0):\\n        k+=1\\n        r//=2\\n    lis.add(k)\\nif(m//(tmp)*tmp+tmp//2<=m):\\n    ans += 1\\nif(len(lis)!=1):\\n    ans=0\\n\\nprint(ans)\\n\\n\", \"import math\\nfrom decimal import Decimal, ROUND_HALF_UP\\ndef lcm(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = (x * a[i]) // math.gcd(x, a[i])\\n    return x\\ndef gcd(a):\\n  temp = math.gcd(a[0], a[1])\\n  for i in a:\\n    temp = math.gcd(temp,  i)\\n  return temp\\nn,m = map(int, input().split(\\\" \\\"))\\na = list(map(int, input().split(\\\" \\\")))\\nzero = False\\ncount = 0\\n#a = list(map(lambda x: x // 2, na))\\nmini = lcm(a)\\nif len(a) != 1:\\n  maxi = gcd(a)\\nelse:\\n  maxi = a[0]\\nmaxi2 = maxi\\nnibai = 1\\nwhile(True):\\n  if maxi2 % 2 == 0:\\n    nibai *= 2\\n    maxi2 //= 2\\n  else:\\n    break\\nfor i in a:\\n  if i % (2 * nibai) == 0:\\n    zero = True\\n    break\\n#print(nibai, maxi, mini)\\nif not zero:\\n  t = Decimal(str((m * 2 // mini) / 2))\\n  #print(t)\\n  print(t.quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nelse:\\n  print(0)\", \"from math import gcd\\nimport sys\\n\\ndef lcm(x,y):\\n    return x*y//gcd(x,y)\\n\\ndef count(x):\\n    res=0\\n    while True:\\n        if x%2==0:\\n            res+=1\\n            x//=2\\n        else:\\n            break\\n    return res\\n\\nn,m=list(map(int,input().split()))\\nA=list(map(int,input().split()))\\nA=list(set(A))\\nn=len(A)\\n\\nA.sort(reverse=True)\\n\\ntemp=A[0]\\nfor i in range(1,n):\\n    if count(A[i])!=count(temp):\\n        print((0))\\n        return\\n    else:\\n        temp=lcm(temp,A[i])\\n\\nans=m//(temp//2)-m//temp\\nprint(ans)\\n\", \"import math\\nimport fractions\\nfrom functools import reduce\\n\\nn, m = map(int,input().split())\\na = list(map(int,input().split()))\\na = [t // 2 for t in a]#\\u30ea\\u30b9\\u30c8\\u306e\\u8981\\u7d20\\u3059\\u3079\\u3066\\u30922\\u3067\\u5272\\u308b\\n\\ndef lcm_base(x, y):\\n    return (x * y)//fractions.gcd(x,y)\\n\\ndef lcm_list(numbers): #\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3092\\u6c42\\u3081\\u308b\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef num_dev2(x):\\n    return bin(x)[::-1].find(\\\"1\\\") #\\uff12\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u3092\\u78ba\\u8a8d\\n\\nlcm = lcm_list(a)\\nq = m//lcm #m\\u306f\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3067\\u4f55\\u56de\\u5272\\u308c\\u308b\\u304b\\n\\ncount = 0\\ndev2 = num_dev2(a[0])\\nfor i in range(1,n):\\n    if dev2 != num_dev2(a[i]):#\\u30ea\\u30b9\\u30c8\\u306e\\u3059\\u3079\\u3066\\u306e\\u8981\\u7d20\\u306e\\uff12\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u306f\\u7b49\\u3057\\u3044\\u304b\\n        count += 1\\n        break\\nif count != 0:\\n    print(0)\\nelse:\\n    print(math.ceil(q/2))\", \"from math import gcd\\n\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b \\n\\nN, M = map(int, input().split())\\nAs = list(map(int, input().split()))\\n\\nrightmostbit = As[0] & -As[0]\\nfor A in As[1:]:\\n    if rightmostbit != A & -A:\\n        print(0)\\n        return \\n\\n\\nlcm_of_half_As = 1\\nfor A in As:\\n    lcm_of_half_As = lcm(lcm_of_half_As, A //  2)\\n    if lcm_of_half_As > M:\\n        break\\n\\nprint((M // lcm_of_half_As + 1) // 2)\", \"import sys\\nimport numpy as np\\ndef input(): return sys.stdin.readline().rstrip()\\n\\ndef kosuu(x):\\n    re = [0,0]\\n    while x % 2 == 0:\\n        x = x//2\\n        re[1]+=1\\n    re[0]=x\\n    return re\\n\\n        \\n \\ndef main():\\n    n,m=map(int, input().split())\\n    a=list(map(int, input().split()))\\n    li = [kosuu(a[0])[0]]\\n    hantei = kosuu(a[0])[1]\\n    for i in a[1:]:\\n        hantei2 = kosuu(i)\\n        if hantei2[1] != hantei:\\n            print(0)\\n            break\\n        else:\\n            li.append(hantei2[0])\\n    else:\\n        lc = np.lcm.reduce(li)\\n        print(((m//(lc*2**(hantei-1)))+1)//2)\\n            \\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nimport sys\\nfrom functools import reduce\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nfor i in range(N):\\n  A[i] = A[i] // 2\\n  \\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n  \\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nC = lcm_list(A)\\nB = [0 for _ in range(N)]\\n\\nfor i in range(N):\\n  B[i] = C // A[i]\\n  if B[i] % 2 == 0:\\n    print(0)\\n    return\\n\\nprint( (M // C + 1) // 2)\", \"import math\\nfrom functools import reduce\\n\\nn,m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\ndef lcm_base(x,y):\\n  return x*y//math.gcd(x,y)\\n\\ndef lcm(target_list):\\n  return reduce(lcm_base, target_list)\\n\\nA_gcd = reduce(math.gcd, A)\\nflg = True\\n\\nfor a in A:\\n  if a//A_gcd%2==0:\\n    flg = False\\n    break\\n    \\nif flg:\\n  min_x = int(lcm(A))//2\\n  ans = m//min_x - m//(2*min_x)\\n  print(ans)\\nelse:\\n  print(0)\", \"from math import gcd\\nfrom functools import reduce\\nimport sys\\ninput = sys.stdin.readline\\n\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a, b)\\n\\n\\ndef count_factor_2(num):\\n    count = 0\\n    while num % 2 == 0:\\n        num //= 2\\n        count += 1\\n    return count\\n\\n\\ndef main():\\n    n, m = list(map(int, input().split()))\\n    A = list([int(x)//2 for x in input().split()])\\n\\n    check = len(set(map(count_factor_2, A)))\\n    if check != 1:\\n        print((0))\\n        return\\n\\n    lcm_a = reduce(lcm, A)\\n    step = lcm_a * 2\\n    ans = (m + lcm_a) // step\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\"]",
        "difficulty": "interview",
        "input": "3 100\n14 22 40\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc150/tasks/abc150_d"
    },
    {
        "id": 254,
        "task_id": 2498,
        "test_case_id": 3,
        "question": "Given are a sequence A= {a_1,a_2,......a_N} of N positive even numbers, and an integer M.\nLet a semi-common multiple of A be a positive integer X that satisfies the following condition for every k (1 \\leq k \\leq N):\n - There exists a non-negative integer p such that X= a_k \\times (p+0.5).\nFind the number of semi-common multiples of A among the integers between 1 and M (inclusive).\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^5\n - 1 \\leq M \\leq 10^9\n - 2 \\leq a_i \\leq 10^9\n - a_i is an even number.\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN M\na_1 a_2 ... a_N\n\n-----Output-----\nPrint the number of semi-common multiples of A among the integers between 1 and M (inclusive).\n\n-----Sample Input-----\n2 50\n6 10\n\n-----Sample Output-----\n2\n\n - 15 = 6  \\times 2.5 \n - 15 = 10 \\times 1.5 \n - 45 = 6  \\times 7.5 \n - 45 = 10 \\times 4.5 \nThus, 15 and 45 are semi-common multiples of A. There are no other semi-common multiples of A between 1 and 50, so the answer is 2.",
        "solutions": "[\"n, m = map( int, input().split() )\\na = list( map( int, input().split() ) )\\n\\ndef f( a_k ): # 2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\n    count = 0\\n    while a_k % 2 == 0:\\n        count += 1\\n        a_k = a_k // 2\\n    return count\\n\\nb = []\\nf_0 = f( a[ 0 ] )\\nfor a_k in a:\\n    f_k = f( a_k )\\n    if f_k != f_0:\\n        print( 0 )\\n        return\\n    b.append( a_k // pow( 2, f_k ) )\\n\\nimport math\\ndef lcm( x, y ):\\n    return x * y // math.gcd( x, y )\\n\\nb_lcm = 1\\nfor b_k in b:\\n    b_lcm = lcm( b_lcm, b_k )\\n\\na_lcm = b_lcm * pow( 2, f_0 )\\n# print( b_lcm, f_0, b )\\nprint( ( m + a_lcm // 2 ) // a_lcm )\", \"from functools import reduce\\n\\nN, M = list(map(int, input().split()))\\nAs = list(map(int, input().split()))\\n\\nBs = [A//2 for A in As]\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a%b\\n    return a\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b\\n\\nnums = []\\nfor B in Bs:\\n    num = 0\\n    while B%2 == 0:\\n        B //= 2\\n        num += 1\\n    nums.append(num)\\n\\nif len(set(nums)) != 1:\\n    ans = 0\\nelse:\\n    L = reduce(lcm, Bs)\\n    ans = M//L - M//(2*L)\\n\\nprint(ans)\\n\", \"import math\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\nb = {}\\nfor i in range(n):\\n    count = 0\\n    temp = a[i]\\n    while temp % 2 == 0:\\n        count += 1\\n        temp //= 2\\n    b.setdefault(count, 0)\\n    b[count] += 1\\nif len(b.keys()) >= 2:\\n    ans = 0\\nelse:\\n    temp = 1\\n    for i in range(n):\\n        temp = temp * a[i] // math.gcd(temp, a[i])\\n    temp2 = temp // 2\\n    ans = m // temp2 - m // temp\\nprint(ans)\", \"import numpy as np\\nimport sys\\n\\ndef main():\\n    N,M=list(map(int,input().split()))\\n    A=list(map(int,input().split()))\\n    A_double=list([x//2 for x in A])\\n\\n    mini_multi=int(np.lcm.reduce(A_double))\\n\\n    res=M//mini_multi\\n    \\n    for i in A_double:\\n        if (mini_multi//i)%2==0:\\n            print((0))\\n            return\\n\\n    if res%2!=0:\\n        res+=1\\n\\n\\n    print((res//2))\\n\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# ABC150D\\n\\nimport sys\\ninput=sys.stdin.readline\\nfrom math import gcd,ceil\\n\\ndef main():\\n    N,M=list(map(int,input().split()))\\n    A=list([int(x)//2 for x in input().split()])\\n    lcm=A[0]\\n    for i in range(1,N):\\n        lcm=lcm*A[i]//gcd(lcm,A[i])\\n    allo=1\\n    for i in range(N):\\n        allo&=(lcm//A[i])%2\\n    if allo:\\n        print((ceil(int(M//lcm)/2)))\\n    else:\\n        print((0))\\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import sys\\nfrom math import gcd\\nfrom copy import deepcopy\\n\\nsys.setrecursionlimit(10 ** 7)\\ninput = sys.stdin.readline\\nf_inf = float('inf')\\nmod = 10 ** 9 + 7\\n\\n\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\n\\ndef resolve():\\n    n, m = list(map(int, input().split()))\\n    A = list(map(int, input().split()))\\n\\n    A_ = deepcopy(A)\\n    cnt = [0] * n\\n    for i in range(n):\\n        while A_[i] % 2 == 0:\\n            A_[i] //= 2\\n            cnt[i] += 1\\n        if i != 0 and cnt[i] != cnt[i - 1]:\\n            print((0))\\n            return\\n\\n    L = 1\\n    for a in A:\\n        L = lcm(L, a // 2)\\n\\n    res = m // L - (m // (L * 2))\\n    print(res)\\n\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"from math import gcd\\ndef lcm(a,b):return (a*b)//(gcd(a,b))\\n\\ndef f(x):\\n    cnt=0\\n    while(x%2==0):\\n        cnt+=1\\n        x=x//2\\n    return cnt\\n\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(map(lambda x: x//2,a))\\n\\nt=f(a[0])\\nfor i in range(n):\\n    if(f(a[i])!=t):\\n        print(0)\\n        return\\n    a[i]=a[i]//(2**t)\\nm=m//(2**t)\\nl=1\\nfor i in range(n):\\n    l=lcm(l,a[i])\\n    if(l>m):\\n        print(0)\\n        return\\nm=m//l\\nprint((m+1)//2)\", \"import math\\n\\nn,m=list(map(int,input().split()))\\na=list(map(int,input().split()))\\n\\nif n==1:\\n  a1=a[0]//2\\n  ans_m=m//a1\\n  if ans_m==0:\\n    print((0))\\n  else:\\n    print(((ans_m-1)//2+1))\\n  \\nelse:\\n  x=a[0]\\n  ch=0\\n  ch1=0\\n  while x%2==0:\\n    x=x//2\\n    ch+=1\\n  dob=2**ch\\n  for i in a:\\n    if i%dob==0 and i%(dob*2)!=0:\\n      ch1+=1\\n  if ch1!=n:\\n    print((0))\\n  else:\\n    ans=a[0]//2\\n    for j in range(1,n):\\n      ans=(ans*(a[j]//2))//math.gcd(ans,a[j]//2)\\n    ans_m=m//ans\\n    if ans_m==0:\\n      print((0))\\n    else:\\n      print(((ans_m-1)//2+1))\\n    \\n      \\n\", \"from math import gcd, ceil\\nN,M = map(int,input().split())\\nA = list(map(int,input().split()))\\nA = [a//2 for a in A]\\nB = 1\\n\\nfor a in A:\\n  B*=a//gcd(B,a)\\n  \\nfor a in A:\\n  if B//a%2==0:\\n    print(0)\\n    return\\n\\nprint(ceil((M//B)/2))\", \"def solve():\\n    import math\\n    N,M = [int(i) for i in input().split()]\\n    A = list(map(int, input().split()))\\n\\n    lcm = A[0]\\n    for i in range(1, N):\\n        lcm = lcm * A[i] // math.gcd(lcm, A[i])\\n    first = lcm // 2\\n\\n    ans_exists = True\\n    for i in range(N):\\n        if first % A[i] == 0:\\n            ans_exists = False\\n\\n    if ans_exists:\\n        ans = int((M-first) // lcm + 1)\\n        print(ans)\\n    else:\\n        print('0')\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"# -*- coding: utf-8 -*-\\n\\\"\\\"\\\"\\nCreated on Wed Sep  9 14:33:00 2020\\n\\n@author: liang\\n\\\"\\\"\\\"\\nfrom math import gcd\\n\\nN, M = map(int, input().split())\\nA = [int(i) for i in input().split()]\\n\\nflag = False\\nres = 1\\nfor a in A:\\n    a //= 2\\n    res *= a//gcd(res,a)\\n    if res > M:\\n        flag = True\\n        break\\n    #print(res)\\n\\\"\\\"\\\"\\n\\u5b58\\u5728\\u30c1\\u30a7\\u30c3\\u30af\\n\\uff12\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u500b\\u6570\\u540c\\u3058\\uff1f\\n\\\"\\\"\\\"\\n\\nfor a in A:\\n    if int(res/a) == res/a:\\n        flag = True\\n        \\nif flag:\\n    ans = 0\\n    print(ans)\\nelse:\\n    #ans = (M - res(A)//2)//res + 1\\n    #ans = (M-1)//res//2 + 1\\n    ans= (M//res + 1)//2\\n    print(ans)\", \"import math\\n\\nN, M = map(int,input().split())\\nA = list(map(int,input().split()))\\n\\npow2 = 0\\nwhile A[0] % 2 == 0:\\n    A[0] //= 2\\n    pow2 += 1\\n\\nfor i in range(1,N):\\n    cnt = 0\\n    while A[i] % 2 == 0:\\n        A[i] //= 2\\n        cnt += 1\\n    if cnt != pow2:\\n        print(0)\\n        return\\n\\nLCM = 2**max(0,pow2-1)\\nfor i in range(N):\\n    LCM = LCM * A[i] // math.gcd(LCM,A[i])\\n\\nans = M // LCM\\nprint((ans+1)//2)\", \"from math import gcd\\nfrom functools import reduce\\nimport sys\\ninput = sys.stdin.readline\\n\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a, b)\\n\\n\\ndef count_factor_2(num):\\n    count = 0\\n    while num % 2 == 0:\\n        num //= 2\\n        count += 1\\n    return count\\n\\n\\ndef main():\\n    n, m = list(map(int, input().split()))\\n    A = list([x//2 for x in set(map(int, input().split()))])\\n\\n    check = len(set(map(count_factor_2, A)))\\n    if check != 1:\\n        print((0))\\n        return\\n\\n    lcm_a = reduce(lcm, A)\\n    step = lcm_a * 2\\n    ans = (m + lcm_a) // step\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N, M = map(int, input().split())\\nA = list(map(lambda x: int(x)//2, input().split()))\\n\\nimport math\\n\\ndef lcm(x, y):\\n  return (x // math.gcd(x, y)) * y\\n\\ndef pow2(x):\\n  ret = 0\\n  while x%2 == 0:\\n    ret += 1\\n    x //= 2\\n  return ret\\n\\nP = []\\nfor a in A:\\n  P.append(pow2(a))\\n\\nif len(set(P)) != 1:\\n  print(0)\\nelse:\\n  m = 1\\n  for a in A:\\n    m = lcm(m, a)\\n  print(-(-(M//m)//2))\", \"def GCM(x, y):\\n  if x%y==0:\\n    return y\\n  else:\\n    return GCM(y, x%y)\\n\\nN, M = map(int, input().split())\\n\\nA = list(map(int, input().split()))\\n\\ncount2 = [0 for i in range(N)]\\nfor i in range(N):\\n  a = A[i]\\n  while a%2==0:\\n    count2[i] += 1\\n    a = a//2\\n  A[i] = a\\nif sum(count2) == count2[0]*N:\\n  count2 = count2[0]\\n  buf = 1\\n  for i in range(N):\\n    buf = A[i]*buf//GCM(buf, A[i])\\n  buf *= 2**(count2-1)\\n  #print(buf)\\n  n = M//buf\\n  print((n+1)//2)\\n  \\nelse:\\n  print(0)\", \"import fractions\\nimport math\\nfrom functools import reduce\\n\\ndef lcm_base(x, y):\\n    return (x * y) // fractions.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\nb=lcm_list(map(lambda x: x//2, a))\\nswt=0\\n\\nfor i in range(n):\\n  if 0==(b//(a[i]//2))%2:\\n    swt=1\\n    break\\n\\nif 0==swt:\\n  print(math.ceil((m//b)/2))\\nelse:\\n  print(0)\", \"import math\\nimport numpy as np\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nc=1\\ntest=A[0]\\nl=0\\n\\nwhile test%2 == 0:\\n  test=test//2\\n  c*=2\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n  \\nfor i in np.arange(N-1):\\n  if A[i+1]%c!=0:\\n    print(0)\\n    l=1\\n    break\\n  elif A[i+1]%(c*2)==0:\\n    print(0)\\n    l=1\\n    break\\n  else:\\n    k=A[i+1]//c\\n    test=lcm_base(test, k)\\nif l==0:\\n  k=test*c//2\\n  print(M//k//2 + M//k%2)\", \"from math import gcd\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nmemo = {}\\n\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\n\\nb = 1\\n\\nfor a in A:\\n    b = lcm(a//2, b)\\n    if b > M:\\n        break\\n\\nif any([2 * b // a % 2 == 0 for a in A]):\\n    print(0)\\nelse:\\n    ans = M // b\\n    print(ans - ans // 2)\", \"import copy\\n# from math import gcd\\n\\n\\ndef gcd(a, b):\\n    if b == 0:\\n        return a\\n    else:\\n        return gcd(b, a%b)\\n\\ndef lcm(a, b):\\n    return (a // gcd(a, b)) * b\\ndef main():\\n    n, m = map(int, input().split())\\n    A = set([int(x) for x in input().split()])\\n    a_lcm = 1\\n    for a in A:\\n        a_lcm = lcm(a_lcm, a)\\n        # m\\u304clcm\\u306e\\u534a\\u5206\\u3088\\u308a\\u3082\\u5c0f\\u3055\\u304b\\u3063\\u305f\\u30890\\n        if (a_lcm / 2) > m:\\n            print(0)\\n            return\\n    for a in A:\\n        if (a_lcm / 2) % a == 0:\\n            print(0)\\n            return\\n    # # \\u3042\\u3068\\u306f\\u5b9a\\u6570\\u500d\\u306e\\u6570\\u8abf\\u3079\\u3066\\u7d42\\u308f\\u308a\\n    ans = int((m - (a_lcm / 2)) // a_lcm) + 1\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"from math import gcd\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\ndef lcm(ab):\\n    l=len(ab)\\n    ret=ab[0]\\n    for i in range(1,l):\\n        ret=ret//gcd(ab[i],ret)*ab[i]\\n    return ret\\ndef count2(a):\\n    ret=0\\n    while a%2==0:\\n        a//=2\\n        ret+=1\\n    return 2**ret\\nn,m=map(int,input().split())\\nA=list(map(int,input().split()))\\n#\\u3053\\u308c\\u306f\\u3044\\u3089\\u306a\\u3044\\u3067\\u3059\\nif any(i%2 for i in A):\\n    print(0);return\\nA=[i//2 for i in A]\\n#\\u5168\\u4f53\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\np=lcm(A)\\nc=count2(p)\\n#2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3082\\u306e\\u304c\\u3042\\u308b\\u5834\\u5408\\nif any(i%c for i in A):\\n    print(0);return\\nx=m//p\\n#print(p//c)\\nprint(-(-x//2))\", \"from math import gcd\\n\\nn, m = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = [a//2 for a in  A]\\nlcm = 1\\n\\nfor i in range(n):\\n    lcm = lcm * A[i] // gcd(lcm, A[i])\\n    if lcm > m:\\n        print((0))\\n        return\\n        \\nfor a in A:\\n    if lcm // a % 2 == 0:\\n        print((0))\\n        return\\n\\nprint(((m//lcm + 1) // 2))\\n\", \"from fractions import gcd\\n\\ndef lcm_base(x, y):\\n    return (x * y) // gcd(x, y)\\ndef lcm(numbers):\\n    x = numbers[0]\\n    for y in numbers:\\n        x = lcm_base(x, y)\\n    return x\\n\\nN, M = list(map(int, input().split()))\\naaa = list(map(int, input().split()))\\na = aaa[0]\\ncnt = 0\\nwhile a % 2 == 0:\\n    cnt += 1\\n    a //= 2\\nfor a in aaa:\\n    if a % 2 ** cnt != 0 or a % 2 ** (cnt + 1) == 0:\\n        print((0))\\n        return        \\nbbb = [a // 2 for a in aaa]\\nlc = lcm(bbb)\\nq, r = divmod(M // lc , 2)\\nprint((q + r))\\n\", \"N, M = map(int, input().split())\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print(0)\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7, 11]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print(0)\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\", \"import math\\nfrom functools import reduce\\nn, m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\na0 = A[0]\\ncnt = 0\\nwhile a0%2 == 0:\\n    a0 //= 2\\n    cnt += 1\\n\\na = []\\nfor aa in A:\\n    if cnt == 1:\\n        if aa%4 == 0:\\n            print(0)\\n            return\\n    else:\\n        if aa%(2**(cnt-1)) != 0 or aa%(2**cnt) != 0 or aa%(2**(cnt+1)) == 0:\\n            print(0)\\n            return\\n    a.append(aa//2)\\n\\n\\ndef lcm_base(p, q):\\n    return (p * q) // math.gcd(p, q)\\n\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\nlcm = lcm_list(a)\\nprint(m//lcm - m//(lcm*2))\", \"def main():\\n    import math\\n    n,m = list(map(int,input().split()))\\n    a = sorted(list(map(int,input().split())))\\n    for i in range(n):\\n        a[i] //= 2\\n    g=1\\n    for i in range(n):\\n        g = a[i] * g // math.gcd(g,a[i])\\n    for i in range(n):\\n        if g//a[i] % 2 == 0:\\n            print((0))\\n            return\\n    if g>m:\\n        print((0))\\n        return\\n    print((1 + (m-g)//(2*g)))\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nfrom functools import reduce\\nn, m = input().split()\\na = list(map(int, input().split()))\\nb =[0]*int(n)\\nfor i in range(len(a)):\\n  b[i] = a[i]//2\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\nc = 0\\n\\nx = lcm_list(b)\\nfor i in range(int(n)):\\n  if (x // b[i]) % 2 == 0:\\n    c = -1\\n    break\\n  else:\\n    continue\\n    \\nif c == -1:\\n  print((0))\\nelse:\\n  print((math.floor(((int(m)/x)+1)/2)))\\n\\n\", \"N, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\n\\nfrom fractions import gcd\\ndef two(n):\\n    ans = 0\\n    while n%2==0:\\n        n //= 2\\n        ans += 1\\n    return ans\\n\\ndef multi_lcm(A):\\n    ans = A[0]\\n    for a in A:\\n        ans *= a//gcd(ans,a)\\n    return ans\\n\\ndef solve(N,M,A):\\n    ans = 0\\n    num_two = len(set(map(two,A)))\\n    if num_two != 1:\\n        return 0\\n    l = multi_lcm(A)\\n    ans = (M+l//2)//l\\n    return ans\\nprint((solve(N,M,A)))\\n\", \"from math import gcd\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nf = lambda n: 0 if n%2 else f(n>>1)+1\\nx = f(A[0])\\n\\nif sum(x!=f(a) for a in A):\\n    print(0)\\n    return\\n\\nA = [a>>x for a in A]\\n\\ny = 1\\nfor a in A:\\n    y = y*a//gcd(y, a)\\n    if y<<(x-1) > M:\\n        print(0)\\n        return\\n\\nprint((M//(y<<(x-1))+1)//2)\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = [i // 2 for i in A]\\nlcd = 1\\nfor a in A:\\n    lcd *= a // gcd(lcd, a)\\nfor a in A:\\n    if lcd // a % 2 == 0:\\n        print((0))\\n        return\\nprint(((M//lcd+1)//2))\\n\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7, 11]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\ndef euclid(a, b):\\n  while b:\\n    a, b = b, a%b\\n  return a\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // euclid(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"N, M = map(int, input().split())\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print(0)\\n    return\\nans = 0\\n\\nimport math\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print(0)\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\", \"from math import gcd\\ndef readinput():\\n    n,m=list(map(int,input().split()))\\n    a=list(map(int,input().split()))\\n    return n,m,a\\n\\ndef lcm(a,b):\\n    return a*b//gcd(a,b)\\n\\ndef main(n,m,a):\\n    #s=set(a)\\n    #print(s)\\n    x=a[0]//2\\n    for i in range(1,n):\\n        x=lcm(x,a[i]//2)\\n    #print(x)\\n    gusubai=False\\n    kisubai=False\\n    for i in range(n):\\n        if x%a[i]!=0:\\n            gusubai=True\\n        else:\\n            kisubai=True\\n    \\n    y=m//x\\n    #print(y,x,m)\\n    if gusubai and not kisubai:\\n        ans=y//2+y%2\\n    elif gusubai and kisubai:\\n        ans=0\\n    else:\\n        ans=y\\n    return ans\\n\\ndef __starting_point():\\n    n,m,a=readinput()\\n    ans=main(n,m,a)\\n    print(ans)\\n\\n__starting_point()\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    N, M = MI()\\n    L = LI()\\n    L = [i//2 for i in L]\\n    \\n    past = L[0]\\n\\n    for i in L:\\n        past = (past // math.gcd(i, past)) * i\\n        if past > M or (past // i) % 2 == 0:\\n            print(0)\\n            return\\n    \\n    temp = M // past\\n    ans = (temp+1)//2\\n    print(ans)        \\n    \\n\\n    \\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"from fractions import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(lambda x: int(x),input().split()))\\n\\ncnt = [0 for _ in range(N)]\\nfor i in range(N):\\n  a = A[i]\\n  while a%2 == 0:\\n    a = a // 2\\n    cnt[i] += 1\\n\\nif max(cnt) > min(cnt):\\n  print(0)\\n  return\\nC = max(cnt)\\n\\nA = list(map(lambda x: x // pow(2,C), A))\\ndef gcd(a,b):\\n  if a<b:\\n    a,b = b,a\\n  while a%b > 0:\\n    a,b = b,a%b\\n  return b\\n\\ndef lcm(a,b):\\n  return a*b//gcd(a,b)\\n\\nx = A[0]\\nfor a in A[1:]:\\n  x = lcm(x,a)\\nx = x * pow(2,C-1)\\n\\nprint((M // x + 1) // 2)\", \"from math import gcd\\nfrom functools import reduce\\n\\nn,m=map(int,input().split())\\nlst=list(map(lambda x : int(x)//2,input().split()))\\ndivi=0\\nx=lst[0]\\nwhile x%2==0:\\n    x//=2\\n    divi+=1\\n\\nfor i in range(1,n):\\n    divi2=0\\n    x=lst[i]\\n    while x%2==0:\\n        x//=2\\n        divi2+=1\\n    if divi!=divi2 :\\n        print(0)\\n        return\\n\\nwork=reduce(lambda x,y: x*y//gcd(x,y),lst)\\nprint((m//work+1)//2)\", \"n, m = map(int, input().split())\\naas = set(list(map(int, input().split())))\\na = [i//2 for i in aas]\\nimport math\\nN = len(a)\\ndef n_of_twos(x):\\n    res = 0\\n    while x%(2**(res+1))==0:\\n        res += 1\\n    return res\\nif N>=2:\\n    n_of_twos_0 = n_of_twos(a[0])\\n    for i in range(1,N):\\n        if n_of_twos(a[i]) != n_of_twos_0:\\n            print(0)\\n            return\\nans = a[0]\\nfor i in range(1, N):\\n    ans = ans * a[i] // math.gcd(ans, a[i])\\nif ans > m:\\n    print(0)\\n    return\\nprint(1 + (m//ans-1)//2)\", \"from math import gcd, ceil\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print(0)\\n        return\\nprint(ceil((m // l) / 2))\", \"import queue\\nimport numpy as np\\nimport math\\n\\nN, M = map(int, input().split())\\na2 = list(map(int, input().split()))\\na = []\\nfor i in a2:\\n    a.append(i//2)\\n\\nlcm = a[0]\\n\\nfor i in a:\\n    lcm *= i // math.gcd(lcm, i)\\n\\nhasAns = True\\nfor i in a:\\n    if (lcm // i) % 2 == 0:\\n        hasAns = False\\n        break\\n\\nans = 0\\n\\nif hasAns:\\n    ans = ((M // lcm) + 1 )// 2\\n\\nprint(ans)\", \"from math import gcd\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(set(a))\\na=list(map(lambda x: x//2, a))\\n\\ndef lcm(q):\\n  x = q[0]\\n  for i in range(1, len(q)):\\n    x = (x * q[i]) // gcd(x, q[i])\\n  return x\\n\\nlcma=lcm(a)\\nfor i in range(len(a)):\\n  if (lcma//a[i])%2==0:\\n    print(0)\\n    return\\ntemp=m//lcma\\nprint(-(-temp//2))\", \"import sys\\nimport math\\n# import bisect\\n# import numpy as np\\n# from decimal import Decimal\\n# from numba import njit, i8, u1, b1 #JIT compiler\\n# from itertools import combinations, product\\n# from collections import Counter, deque, defaultdict\\n\\n# sys.setrecursionlimit(10 ** 6)\\nMOD = 10 ** 9 + 7\\nINF = 10 ** 9\\nPI = 3.14159265358979323846\\n\\ndef read_str():      return sys.stdin.readline().strip()\\ndef read_int():      return int(sys.stdin.readline().strip())\\ndef read_ints():     return map(int, sys.stdin.readline().strip().split())\\ndef read_ints2(x):   return map(lambda num: int(num) - x, sys.stdin.readline().strip().split())\\ndef read_str_list(): return list(sys.stdin.readline().strip().split())\\ndef read_int_list(): return list(map(int, sys.stdin.readline().strip().split()))\\ndef GCD(a: int, b: int) -> int: return b if a%b==0 else GCD(b, a%b)\\ndef LCM(a: int, b: int) -> int: return (a * b) // GCD(a, b)\\n\\ndef Main():\\n    n, m = read_ints()\\n    a = read_int_list()\\n    a = [x // 2 for x in a]\\n    lcm = 1\\n    for x in a:\\n        lcm *= x // math.gcd(lcm, x)\\n    for x in a:\\n        if lcm // x % 2 == 0:\\n            print(0)\\n            return\\n    print(math.ceil((m // lcm) / 2))\\n\\ndef __starting_point():\\n    Main()\\n__starting_point()\", \"import sys\\ninput=sys.stdin.readline\\nimport math\\n\\nN,M=(int(x) for x in input().rstrip('\\\\n').split())\\nAs=[int(x) for x in input().rstrip('\\\\n').split()]\\nn = 1\\nuse2 = 0\\ncheck = 0\\nfor i in range(N):\\n  x = As[i]\\n  if i==0:\\n    while x % 2==0:\\n      use2+=1 \\n      x = x//2\\n    lcm=x\\n  else:\\n    use=0\\n    while x%2==0:\\n      x = x//2\\n      use += 1\\n    if use2 != use:\\n      check += 1\\n      break\\n    lcm=lcm*x//(math.gcd(lcm,x))\\nif check > 0:\\n  print(0)\\nelse:\\n  LCM=2**(use2-1)\\n  LCM=LCM*lcm\\n  print(((M//LCM)+1)//2)\", \"def lcm(a, b):\\n  return a // gcd(a, b) * b\\n\\ndef gcd(a, b):\\n  if(b == 0): return a\\n  else: return gcd(b, a % b)\\n\\ndef cnt(a):\\n  res = 0\\n  while(a and a % 2 == 0):\\n    a //= 2\\n    res += 1\\n  return res\\n\\nn, m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nl = 1\\nc = cnt(A[0])\\nfor a in A:\\n  if cnt(a) != c or c == 0:\\n    print(0)\\n    return\\n  else:\\n    l = lcm(l, a // 2)\\nd = m // l\\nprint((d + 1) // 2)\", \"from math import gcd\\nfrom functools import reduce\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a,b)\\n\\na = [i//2 for i in a]\\n\\nl = reduce(lcm, a)\\n\\nif any((l//i) % 2 == 0 for i in a):\\n    print(0)\\n    return\\n\\nprint(-(-(m//l)//2))\", \"import math\\nn,m= list(map(int,input().split()))\\nal= list(map(int,input().split()))\\ntwos = set()\\nfor c in al:\\n    temp,tempc=0,c\\n    while tempc%2==0:\\n        tempc//=2\\n        temp+=1\\n    twos.add(temp)\\nif len(twos)>1:print((0))\\nelse:\\n    lcmv=al[0]\\n    for i in range(1,n):lcmv = lcmv*al[i] // math.gcd(lcmv,al[i])\\n    print((max(0,1 + (m-lcmv//2)//lcmv)))\\n\", \"from functools import reduce\\n\\ndef main():\\n  N,M=map(int,input().split())\\n  *A,=map(int,input().split())\\n\\n  A = list(set(A))\\n  N = len(A)\\n\\n  B = [A[i]//2 for i in range(N)]\\n\\n  def factorize(n):\\n      out=[]\\n      i = 2\\n      while i==2:\\n          if n%i==0:\\n              out.append(i)\\n              n //= i\\n          else:\\n              i += 1\\n          if n == 1:break\\n          if i > int(n**.5+3):\\n              out.append(n)\\n              break\\n      return out\\n\\n  ord_list=[len(factorize(B[i])) for i in range(N)]\\n\\n  if len(set(ord_list)) != 1:\\n    print(0)\\n    return\\n\\n  def gcd(a,b):\\n    if b == 0: return a\\n    return gcd(b,a%b)\\n\\n  def lcm(a,b):\\n    return a*b//gcd(a,b)\\n\\n  LCM = reduce(lcm,B)\\n  print((M//LCM+1)//2)\\n  \\ndef __starting_point():\\n  main()\\n__starting_point()\", \"from math import gcd\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\ndef lcm_g(A):\\n    ret = 1\\n    for a in A:\\n        ret = lcm(ret, a)\\n    return ret\\n\\ndef is_hcm(x, A):\\n    for i in range(N):\\n        if x % A[i] != A[i] // 2:\\n            return False\\n    return True\\n\\nN, M = [int(x) for x in input().split()]\\nA = [int(x) for x in input().split()]\\n\\nl = lcm_g(A)\\nif is_hcm(l // 2, A):\\n    ans = (2 * M + l) // (2 * l)\\nelse:\\n    ans = 0\\n\\nprint(ans)\", \"import math\\nimport fractions\\nfrom functools import reduce\\n \\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na=[t//2 for t in a] # \\u30ea\\u30b9\\u30c8\\u306e\\u8981\\u7d20\\u3092\\u5168\\u30662\\u3067\\u5272\\u308b\\n \\ndef lcm_base(x, y):\\n    return (x * y) // fractions.gcd(x, y)\\n \\ndef lcm_list(numbers): # \\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3092\\u6c42\\u3081\\u308b\\n    return reduce(lcm_base, numbers, 1)\\n \\ndef num_dev2(x): # 2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u3092\\u30ab\\u30a6\\u30f3\\u30c8\\n    return format(x, 'b')[::-1].find('1')\\n \\nlcm = lcm_list(a)\\nq = m // lcm # m\\u306f\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3067\\u4f55\\u56de\\u5272\\u308c\\u308b\\u304b\\n \\ncount = 0\\ndev2 = num_dev2(a[0])\\nfor i in range(1, n):\\n    if dev2 != num_dev2(a[i]): # \\u30ea\\u30b9\\u30c8\\u306e\\u5168\\u3066\\u306e\\u8981\\u7d20\\u306e\\u30012\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u306f\\u7b49\\u3057\\u3044\\u304b\\uff1f\\n        count += 1\\n        break\\nif count != 0:\\n    print(0)\\nelse:\\n    print(math.ceil(q/2))\", \"import sys, re\\nfrom collections import deque, defaultdict, Counter\\nfrom math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd\\nfrom itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby\\nfrom operator import itemgetter, mul\\nfrom copy import deepcopy\\nfrom string import ascii_lowercase, ascii_uppercase, digits\\nfrom bisect import bisect, bisect_left, insort, insort_left\\nfrom heapq import heappush, heappop\\nfrom functools import reduce, lru_cache\\ndef input(): return sys.stdin.readline().strip()\\ndef INT(): return int(input())\\ndef MAP(): return map(int, input().split())\\ndef LIST(): return list(map(int, input().split()))\\ndef TUPLE(): return tuple(map(int, input().split()))\\ndef ZIP(n): return zip(*(MAP() for _ in range(n)))\\nsys.setrecursionlimit(10 ** 9)\\nINF = 10**6#float('inf')\\n#mod = 10 ** 9 + 7 \\nmod = 998244353\\n#from decimal import *\\n#import numpy as np\\n#decimal.getcontext().prec = 10\\n\\nN, M = MAP()\\na = LIST()\\n\\nA = sorted([x//2 for x in a], reverse=True)\\n\\nb = A[0]\\ncnt = 0\\nwhile b%2 == 0:\\n\\tb //= 2\\n\\tcnt += 1\\n\\nfor x in A:\\n\\tif x%pow(2, cnt) or (x//pow(2, cnt))%2 == 0:\\n\\t\\tprint(0)\\n\\t\\treturn\\n\\nlcm = A[-1]\\nfor x in A:\\n\\tlcm = lcm*x//gcd(lcm, x)\\n\\nr = lcm//A[0]\\nn = M//A[0]\\n\\n#2p+1\\u304c1<=2p+1<=n \\u306e\\u7bc4\\u56f2\\u3067 r\\u306e\\u500d\\u6570\\u3068\\u306a\\u308bp\\u306e\\u500b\\u6570\\nif r%2 == 0:\\n\\tprint(0)\\nelse:\\n\\tprint(n//r - n//(2*r))\", \"from math import gcd, ceil\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print((0))\\n        return\\nprint((ceil((m // l) / 2)))\\n\", \"from functools import reduce\\nimport math\\ndef lcm_base(x, y):\\n  return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n  return reduce(lcm_base, numbers, 1)\\n\\ndef lcm_list(numbers):\\n  return reduce(lcm_base, numbers, 1)\\n\\nn,m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i//2 for i in list(set(a))]\\nnothing = False\\ncnt_common = -1\\nfor i in a:\\n  cnt = 0\\n  while i % 2 == 0:\\n    i = i//2\\n    cnt += 1\\n  if cnt_common == -1:\\n    cnt_common = cnt\\n    continue\\n  if cnt_common != cnt:\\n    nothing = True\\n    break\\n\\nb=lcm_list(a)\\nif nothing:\\n  print(0)\\nelse:\\n  ans = (m-b)//(2*b) + 1\\n  print(max(ans,0))\", \"from fractions import gcd\\ndef lcm(a,b):\\n    return (a*b)//gcd(a,b)\\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\nans = 1\\nfor i in a:\\n    ans = lcm(ans,i)\\nfor i in a:\\n    if (ans//i) % 2 == 0:\\n        print(0)\\n        return\\nprint(((m//(ans//2))+1)//2)\", \"import math\\nN, M = map(int, input().split())\\nB = tuple(int(a) // 2 for a in input().split())\\n\\nx = B[0]\\nfor i in range(1, N):\\n    x = (x * B[i]) // math.gcd(x, B[i])\\n\\nfor b in B:\\n    if (x // b) % 2 == 0:\\n        print(0)\\n        break\\nelse:\\n    ans = (M // x) - (M // (2 * x))\\n    print(ans)\", \"import math\\nfrom functools import reduce\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef div2_n(x):\\n    n = 0\\n    while x % 2 == 0:\\n      if x % 2 == 0:\\n          n += 1\\n          x >>= 1\\n    return n\\n  \\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\n\\na2 = [i//2 for i in a]\\nn0 = div2_n(a2[0])\\nfor i in range(1,n):\\n    if div2_n(a2[i]) != n0:\\n        print((0))\\n        return\\n\\na2_l = lcm(*a2)\\nprint((m//a2_l - m//(a2_l*2)))\\n\", \"N, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\ndef gcd(a,b):\\n    while b > 0:\\n        a, b = b, a % b\\n    return a\\n\\n\\nG = A[0]/2\\nfor a in A[1:]:\\n    G *= (a/2)/gcd(G,a//2)\\nfor a in A:\\n    if G % a == 0:\\n        print(0)\\n        return\\nprint(int(M//G - M//G//2))\", \"n , m = list(map(int, input().split()))\\na = list(map(int,input().split()))\\n\\ndef gcd(num1,num2):\\n    r=1\\n    while r>0:\\n        r=num1%num2\\n        num1=num2\\n        num2=r\\n    return num1\\n\\ndef lcm(num1,num2):\\n    gcd1=gcd(num1,num2)\\n    return num1*num2//gcd1\\n\\nlcm1=a[0]//2\\nlcm2=a[0]\\n\\nfor i in range(1,n):\\n    t=a[i]\\n    lcm1=lcm(lcm1,t//2)\\n    lcm2=lcm(lcm2,t)\\n    ta=max(t//2,lcm1)\\n    tb=min(t//2,lcm1)\\n    if ta!=tb and ta//tb%2==0:\\n        lcm1=0\\n        lcm2=0\\n        break\\n\\nif lcm1!=0:\\n    ans1=m//lcm1\\n    ans2=m//lcm2\\n    ans=ans1-ans2\\nelse:\\n    ans=0\\n\\nprint(ans)\\n\", \"import sys, re\\nfrom collections import deque, defaultdict, Counter\\nfrom math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd\\nfrom itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby\\nfrom operator import itemgetter, mul\\nfrom copy import deepcopy\\nfrom string import ascii_lowercase, ascii_uppercase, digits\\nfrom bisect import bisect, bisect_left, insort, insort_left\\nfrom heapq import heappush, heappop\\nfrom functools import reduce, lru_cache\\ndef input(): return sys.stdin.readline().strip()\\ndef INT(): return int(input())\\ndef MAP(): return map(int, input().split())\\ndef LIST(): return list(map(int, input().split()))\\ndef TUPLE(): return tuple(map(int, input().split()))\\ndef ZIP(n): return zip(*(MAP() for _ in range(n)))\\nsys.setrecursionlimit(10 ** 9)\\nINF = 10**6#float('inf')\\n#mod = 10 ** 9 + 7 \\nmod = 998244353\\n#from decimal import *\\n#import numpy as np\\n#decimal.getcontext().prec = 10\\n\\nN, M = MAP()\\na = LIST()\\n\\nA = sorted([x//2 for x in a], reverse=True)\\n\\nlcm = A[-1]\\nfor x in A:\\n\\tlcm = lcm*x//gcd(lcm, x)\\n\\nr = lcm//A[0]\\nn = M//A[0]\\n\\n\\nfor x in A:\\n\\tif lcm//x%2 == 0:\\n\\t\\tprint(0)\\n\\t\\treturn\\n#2p+1\\u304c1<=2p+1<=n \\u306e\\u7bc4\\u56f2\\u3067 r\\u306e\\u500d\\u6570\\u3068\\u306a\\u308bp\\u306e\\u500b\\u6570\\nif r%2 == 0:\\n\\tprint(0)\\nelse:\\n\\tprint(n//r - n//(2*r))\", \"import math\\nfrom functools import reduce\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nN,M = map(int,input().split())\\na = list(map(lambda a: int(a)//2, input().split()))\\ng = lcm(*a)\\nif any([g // item % 2 == 0 for item in a]):\\n    print(0)\\nelse:\\n    ans = M//g\\n    ans = max(math.ceil(ans/2),0)   \\n    print(ans)\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = [a//2 for a in map(int, input().split())]\\n\\nlcm = 1\\nfor a in A:\\n    lcm = lcm*a//gcd(lcm, a)\\n    if lcm > M:\\n        print((0))\\n        return\\n\\nfor a in A:\\n    div = lcm//a\\n    if div % 2 == 0:\\n        print((0))\\n        return\\n\\nans = (M//lcm+1)//2\\nprint(ans)\\n\", \"import math\\ndef LCM(a, b):\\n    g = math.gcd(a, b)\\n    return a * b // g\\n\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nA = list(set(A))\\nN = len(A)\\na0 = A[0]\\ndiv = 1\\nwhile a0 % 2 == 0:\\n    div *= 2\\n    a0 //= 2\\n\\nfor i in range(1, N):\\n    a = A[i] % div\\n    b = A[i] // div\\n    if (b % 2 == 0) or (a != 0):\\n        print((0))\\n        return\\n\\nfor i in range(N):\\n    A[i] //= 2\\n\\nif N > 1:\\n    lcm = LCM(A[0], A[1])\\n    for i in range(2, N):\\n        lcm = LCM(lcm, A[i])\\n\\nif N == 1:\\n    lcm = A[0]\\n\\nans = M // lcm\\nif ans % 2 == 1:\\n    print((ans // 2 + 1))\\nelse:\\n    print((ans // 2))\\n\", \"import math\\ndef lcm(x,y):\\n    return(x*y)//math.gcd(x,y)\\nn,m=map(int,input().split())\\nl=list(map(int,input().split()))\\na=l[0]//2\\nfor i in range(n-1):\\n    a=lcm(a,l[i+1]//2)\\n \\nok = True\\nfor i in range(n):\\n  if (a//(l[i]//2))%2!=1:\\n    ok=False\\n    break\\nans = 0\\nif ok:\\n    ans = ((m//a)+1)//2\\nprint(ans)\", \"import sys\\nN,M = list(map(int,input().split()))\\nA = list(map(int,input().split()))\\na = []\\nfor i in A:\\n  i = i//2\\n  a.append(i)\\ndef gcd(p,q):\\n  p,q = max(p,q),min(p,q)\\n  while q!=0:\\n    p,q = q,p%q\\n  return p\\ndef lcm(p,q):\\n  return(p*q//gcd(p,q))\\ndef aaa(i):\\n  count = 0\\n  while i%2==0:\\n    i = i//2\\n    count+=1\\n  return count\\nmax_num = a[0]\\naa = aaa(a[0])\\nfor i in a:\\n  max_num = lcm(i,max_num)\\n  if aa != aaa(i):\\n    print((0))\\n    return\\nprint((((M//max_num)+1)//2))\\n\", \"import math\\ndef lcm(a,b):\\n  return (a*b)//math.gcd(a,b)\\ndef co(num):\\n  return format(num, 'b')[::-1].find('1')\\nN,M=map(int,input().split())\\nL=list(map(int,input().split()))\\nL2=[co(i) for i in L]\\nif len(set(L2))!=1:\\n  print(0)\\n  return\\nL=[i//2 for i in L]\\ns=L[0]\\nfor i in range(N):\\n  s=lcm(s,L[i])\\nc=M//s\\nprint((c+1)//2)\", \"import math\\nfrom functools import reduce\\n\\nN,M=list(map(int,input().split()))\\nA=[int(x)//2 for x in input().split()]\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nLCM=lcm(*A)\\nfor a in A:\\n  if LCM//a%2==0:\\n    print((0))\\n    break\\nelse:\\n  print(((M//LCM+1)//2))\\n\", \"import numpy as np\\nfrom math import ceil\\n\\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\na = [x//2 for x in a]\\nlcm = np.lcm.reduce(a)\\nans = 0\\n\\nfor i in a:\\n    if lcm // i % 2 == 0:\\n        break\\nelse:\\n    ans = ceil((m//lcm)/2)\\n\\nprint(ans)\", \"import math\\n\\ndef n_2(n):\\n  c=0\\n  while n%2==0:\\n    c+=1\\n    n>>=1\\n  return (n,c)\\n\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nA[0],a=n_2(A[0])\\np=False\\nfor i in range(1,N):\\n  A[i],b=n_2(A[i])\\n  if a!=b:\\n    p=True\\n    break\\nif p:\\n  print(0)\\n  return\\nn=1\\nfor _ in range(a-1):\\n  n*=2\\nl=n\\nfor a in A:\\n  l=l*a//math.gcd(l,a)\\nans=M//l-M//(2*l)\\nprint(ans)\", \"def abc150_d():\\n    n, m = (int(x) for x in input().split())\\n    A = [int(x) // 2 for x in input().split()]\\n\\n    from math import gcd\\n    def lcm(a, b):\\n        return a * b // gcd(a, b)\\n\\n    x = 1\\n    for a in A:\\n        x = lcm(x, a)\\n\\n    valid = True\\n    for a in A:\\n        if (x // a) % 2 == 0:\\n            valid = False\\n            break\\n\\n    if valid: ans = (m // x + 1) // 2\\n    else: ans = 0\\n    print(ans)\\n\\ndef __starting_point():\\n    abc150_d()\\n__starting_point()\", \"from math import gcd\\nn,m=map(int,input().split())\\na=list(map(int,input().split()))\\na=list(set(a))\\na=list(map(lambda x: x//2, a))\\n\\ndef lcm(q):\\n  x = q[0]\\n  for i in range(1, len(q)):\\n    x = (x * q[i]) // gcd(x, q[i])\\n  return x\\n\\nlcma=lcm(a)\\nfor i in range(len(a)):\\n  if (lcma//a[i])%2==0:\\n    print(0)\\n    return\\ntemp=m//lcma\\nprint(temp//2 if temp%2==0 else temp//2+1)\", \"from math import gcd, ceil\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print(0)\\n        return\\nprint(ceil((m // l) / 2))\", \"# import sys\\n# sys.setrecursionlimit(10 ** 6)\\n# import bisect\\n# from collections import deque\\ndef lcm(a, b):\\n    \\\"\\\"\\\"\\u6700\\u5c0f\\u516c\\u500d\\u6570\\\"\\\"\\\"\\n    from math import gcd\\n    return (a * b) // gcd(a, b)\\n\\n\\n# from decorator import stop_watch\\n#\\n#\\n# @stop_watch\\ndef solve(N, M, As):\\n    if sum([a % 2 for a in As]) > 0:\\n        print((0))\\n        return\\n\\n    As = [a // 2 for a in As]\\n    all_lcm = 1\\n    for a in As:\\n        all_lcm = lcm(all_lcm, a)\\n        if all_lcm > M:\\n            print((0))\\n            return\\n\\n    for a in As:\\n        if (all_lcm // a) % 2 == 0:\\n            print((0))\\n            return\\n    from math import ceil\\n    print((ceil(M // all_lcm / 2)))\\n\\n\\ndef __starting_point():\\n    N, M = list(map(int, input().split()))\\n    As = [int(i) for i in input().split()]\\n\\n    # import random\\n    # N, M = 10 ** 5, 10 ** 9\\n    # As = [random.randint(5, 5) * 2 for _ in range(N)]\\n    solve(N, M, As)\\n\\n__starting_point()\", \"import sys,math\\nr=sys.stdin.readline\\ndef gcd(a,b):\\n    a,b=max(a,b),min(a,b)\\n    while b>0:\\n        a,b=b,a%b\\n    return a\\ndef lcm(arr):\\n    while len(arr)!=1:\\n        a=arr.pop()\\n        b=arr.pop()\\n        c=gcd(a,b)\\n        arr.insert(0,int(a*b/c))\\n    return arr[0]\\ndef cnt2(num):\\n    cnt=0\\n    while num%2==0:\\n        num/=2\\n        cnt+=1\\n    return cnt\\nN,M=list(map(int,r().split()))\\nseq=list(map(int,r().split()))\\nseq=list(set(seq))\\ntmp=cnt2(seq[0])\\nfor num in seq:\\n    if tmp!=cnt2(num):\\n        print((0))\\n        return\\nT=lcm(list([x//2 for x in seq]))\\nif T>M:\\n    print((0))\\n    return\\nprint((math.floor(M//T/2+0.5)))\\n\\n\\n\\n\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"from math import gcd\\n\\ndef lcm(a, b):\\n    return a * b // gcd(a, b)\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nl = [0] * n\\nfor i in range(n):\\n    tmp = a[i]\\n    while tmp % 2 == 0:\\n        tmp //= 2\\n        l[i] += 1\\n    if i > 0 and l[i] != l[i - 1]:\\n        print((0))\\n        return\\nres = 1\\nfor i in range(n):\\n    res = lcm(res, a[i] // 2)\\nprint((m // res - m // (res * 2)))\\n\", \"def main():\\n    N, M = map(int, input().split())\\n    A = tuple(map(int,input().split()))\\n    ans = count(A, N, M)\\n    print(ans)\\ndef count(A, N, M):\\n    t = hMt(A[0])\\n    B = [A[0]//(2**t)]\\n    for val in A[1:]:\\n        if hMt(val) != t:\\n            ans = 0\\n            return ans\\n        B.append(val//(2**t))\\n    T = nlcm(B)\\n    MdivT = (M//(2**(t-1)))//T\\n    ans = countodd(MdivT)\\n    return ans\\ndef countodd(num):\\n    if num%2 == 0:\\n        ans = num//2\\n    else:\\n        ans = num//2 + num%2\\n    return ans\\ndef nlcm(A):\\n    LCM = A[0]\\n    for val in A[1:]:\\n        #print(\\\"%d %d gcm:%d LCM:%d\\\"%(LCM,val,gcm(LCM,val),lcm(LCM,val)))\\n        LCM = lcm(LCM,val)\\n    return LCM\\n    \\ndef gcm(a, b):\\n    abtuple = (a,b)\\n    abmin = min([0,1], key=lambda x:abtuple[x])\\n    remainder = abtuple[1-abmin]%abtuple[abmin]\\n    if remainder == 0:\\n        return abtuple[abmin]\\n    return gcm(abtuple[abmin], remainder)\\ndef lcm(a,b):\\n    prod = a*b\\n    ans = prod//gcm(a,b)\\n    return ans\\ndef hMt(num):\\n    ans = 0\\n    tmp = num\\n    while tmp%2 == 0:\\n        tmp = tmp//2\\n        ans += 1\\n    return ans\\nmain()\", \"N, M = list(map(int, input().split()))\\na = list(map(int, input().split()))\\nfor k in range(N):\\n  a[k] //= 2\\n\\nfoo = 1\\nwhile a[0]%2 == 0:\\n  foo *= 2\\n  a[0] //= 2\\nfor k in range(1, N):\\n  if a[k] % foo == 0 and a[k]%(2*foo) !=0:\\n    a[k] //= foo\\n    continue\\n  else:\\n    print((0))\\n    return\\nans = 0\\n\\nfor odd in [3, 5, 7]:\\n  flag = False\\n  for k in range(N):\\n    if a[k]%odd == 0:\\n      a[k] //= odd\\n      flag = True\\n  if flag:\\n    foo *= odd\\n \\n \\nimport math\\n\\nlcm = a.pop()\\nfor k in range(1, N):\\n  b = a.pop()\\n  lcm = lcm * b // math.gcd(lcm, b)\\n  if lcm* foo > M:\\n    print((0))\\n    return\\nlcm *= foo\\nans = int((M / lcm -1)//2 + 1)\\nprint(ans)\\n\\n\", \"from math import gcd\\ndef lcm(a,b):\\n    return a//gcd(a,b)*b\\ndef lcm(ab):\\n    l=len(ab)\\n    ret=ab[0]\\n    for i in range(1,l):\\n        ret=ret//gcd(ab[i],ret)*ab[i]\\n    return ret\\ndef count2(a):\\n    ret=0\\n    while a%2==0:\\n        a//=2\\n        ret+=1\\n    return 2**ret\\nn,m=map(int,input().split())\\nA=list(map(int,input().split()))\\nif any(i%2 for i in A):\\n    print(0);return\\nA=[i//2 for i in A]\\n#\\u5168\\u4f53\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\np=lcm(A)\\nc=count2(p)\\n#2\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3082\\u306e\\u304c\\u3042\\u308b\\u5834\\u5408\\n#\\u9055\\u3046\\u3058\\u3083\\u3093\\nif any(i%c for i in A):\\n    print(0);return\\nx=m//p\\n#print(p//c)\\nif x%2==0:\\n    print(x//2)\\nelse:\\n    print(x//2+1)\", \"def gcd(a, b):\\n    if b == 0:\\n        return a\\n    r = a % b   \\n    return gcd(b, r)\\n\\ndef lcm(a, b):\\n    x = gcd(a, b)\\n    return a * b // x\\n\\ndef gcdN(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = gcd(x, a[i])\\n    return x\\n\\ndef lcmN(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = lcm(x, a[i])\\n    return x\\n\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))  #;print(a)\\n\\ng = gcdN(a)\\nfor i in a:\\n    if (i//g) % 2 == 0:\\n        print((0))\\n        break\\nelse:\\n    l = lcmN(a) \\n    k = 2*m // l\\n    print(((k+1)//2))\\n\", \"from math import gcd, ceil\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\na = [i // 2 for i in a]\\nl = 1\\nfor i in a:\\n    l *= i // gcd(l, i)\\nfor i in a:\\n    if l // i % 2 == 0:\\n        print((0))\\n        return\\n#print(ceil((m // l) / 2))\\nprint(((m//l+1)//2))\\n\", \"n,m=list(map(int,input().split()))\\na=list(map(int,input().split()))\\n\\nfor i in range(n):\\n  a[i]=a[i]//2\\n  \\ndef gcd(a,b):\\n  if b==0:\\n    return a\\n  else:\\n    return gcd(b,a%b)\\n  \\ndef lcm(a,b):\\n  return a*b//gcd(a,b)\\n\\ndef check(x):\\n  cnt=0\\n  while(1):\\n    if x%2==0:\\n      x=x//2\\n      cnt+=1\\n    else:\\n      break\\n  return cnt\\n\\ncnt=a[0]\\nfor i in range(n):\\n  cnt=lcm(cnt,a[i])\\n\\n\\nl=check(a[0])\\nfor i in range(1,n):\\n  x=check(a[i])\\n  if x!=l:\\n    print((0))\\n    return\\n\\n\\ns=m//cnt\\nif s%2==0:\\n  print((s//2))\\nelse:\\n  print((s//2+1))\\n\\n  \\n\", \"from math import gcd\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\nlcm = 1\\nfor a in A:\\n    lcm = lcm * a // gcd(lcm, a)\\n    if lcm > M*2:\\n        print((0))\\n        return\\nfor a in A:\\n    if lcm // a % 2 == 0:\\n        print((0))\\n        return\\nans = M // (lcm//2) - M // lcm\\nprint(ans)\\n\", \"from math import gcd\\ndef lcm(x,y):\\n    return x*y//gcd(x,y)\\ndef cnt(x):\\n    i = 0\\n    while x%2 == 0:\\n        x = x//2\\n        i += 1\\n    return i \\nn,m = map(int,input().split())\\na = list(map(int,input().split()))\\nmemo = cnt(a[0])\\nfor i in range(n):\\n    if cnt(a[i]) != memo:\\n        print(0)\\n        return\\n    a[i] = a[i]//2\\n\\nt = 1\\nfor i in range(n):\\n    t = lcm(t,a[i])\\nprint(m//t-m//(2*t))\", \"import math\\nimport numpy as np\\nN,M=map(int,input().split())\\nA=list(map(int,input().split()))\\nc=1\\ntest=A[0]\\nl=0\\n\\nwhile test%2 == 0:\\n  test=test//2\\n  c*=2\\n  \\nfor i in np.arange(N-1):\\n  if A[i+1]%c!=0:\\n    print(0)\\n    l=1\\n    break\\n  elif A[i+1]%(c*2)==0:\\n    print(0)\\n    l=1\\n    break\\n  else:\\n    k=A[i+1]//c\\n    test=test*k//math.gcd(test,k)\\nif l==0:\\n  k=test*c//2\\n  print(M//k//2+M//k%2)\", \"# \\u53c2\\u8003 : https://at274.hatenablog.com/entry/2020/01/15/060000\\nfrom functools import reduce\\nimport math\\n\\n\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\ndef lcm_list(numbers):  # \\u30ea\\u30b9\\u30c8\\u3092\\u6295\\u3052\\u308b\\u3068\\u5168\\u8981\\u7d20\\u306elcm\\u304c\\u8fd4\\u3063\\u3066\\u304f\\u308b\\n    return reduce(lcm, numbers, 1)\\n\\n\\nN, M = list(map(int, input().split()))\\nA = list(map(int, input().split()))\\n\\n# \\u6700\\u521d\\u3001A\\u306e\\u8981\\u7d20\\u306f\\u5168\\u3066\\u5076\\u6570\\u30022\\u3067\\u5272\\u3063\\u305f\\u3082\\u306e\\u306b\\u7f6e\\u304d\\u63db\\u3048\\nA = [a // 2 for a in A]\\n\\n# \\u5168\\u3066\\u306e\\u8981\\u7d20\\u306b\\u3064\\u3044\\u3066\\u3001\\uff12\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u304c\\u540c\\u3058\\u3067\\u306a\\u3044\\u3068\\u984c\\u610f\\u306f\\u6e80\\u305f\\u305b\\u306a\\u3044\\ncount_div_2 = None\\nfor a in A:\\n    cnt = 0\\n    while a % 2 == 0:\\n        a //= 2\\n        cnt += 1\\n    # 1\\u500b\\u76ee\\u306f\\u7121\\u6761\\u4ef6\\u3067\\u4fdd\\u5b58\\n    if count_div_2 is None:\\n        count_div_2 = cnt\\n    # 2\\u500b\\u76ee\\u304b\\u3089\\u30c1\\u30a7\\u30c3\\u30af\\n    elif cnt != count_div_2:\\n        print((0))\\n        return\\n\\n# my_lcm = A\\u306e\\u5168\\u8981\\u7d20\\u306e\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3002\\u3000\\u3053\\u306e\\u5947\\u6570\\u500d\\u304c\\u984c\\u610f\\u3092\\u6e80\\u305f\\u3059\\u3002\\n# my_lcm\\u304cM\\u3092\\u8d85\\u3048\\u3066\\u3044\\u305f\\u30891\\u3064\\u3082\\u4f5c\\u308c\\u306a\\u3044\\nmy_lcm = lcm_list(A)\\nif my_lcm > M:\\n    print((0))\\n    return\\n\\ntmp = M // my_lcm\\n# my_lcm\\u306e1,2,...M\\u500d\\u307e\\u3067\\u4f7f\\u3048\\u308b\\u304c\\u3001\\u5076\\u6570\\u306f\\u4f7f\\u3048\\u306a\\u3044\\n# tmp=1or2\\u306a\\u30891\\u500b, 3or4\\u306a\\u30892\\u500b, 5or6\\u306a\\u30893\\u500b,...\\nans = (tmp + 1) // 2\\nprint(ans)\\n\", \"import math\\nimport collections\\nimport sys\\n\\ninput = sys.stdin.readline\\ndef I(): return int(input())\\ndef MI(): return list(map(int, input().split()))\\ndef LI(): return list(map(int, input().split()))\\ndef LI2(): return [int(input()) for i in range(n)]\\ndef MXI(): return [[LI()]for i in range(n)]\\n\\nn,m=MI()\\nA=LI()\\ndef num2(x):\\n    ans=0\\n    while x%2==0:\\n        x=x//2\\n        ans+=1\\n    return ans\\nmod=2**(num2(A[0]))\\nfor i in range(1,n):\\n    if A[i]%mod!=0:\\n        print((0))\\n        return\\n    if A[i]%mod==0 and (A[i]//mod)%2==0:\\n        print((0))\\n        return\\n#print(A)\\nfor i in range(n):\\n    A[i]//=2\\n#print(A)\\n\\ndef gcd(a, b):\\n    while b:\\n        a, b = b, a % b\\n    return a\\n\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b\\n\\nL=A[0]   \\nfor i in range(1,n):\\n    L=lcm(L,A[i])\\n#print(L)\\nif L>m:\\n    an=0\\nelse:\\n    an=int(((m/L)-1)/2)+1\\nprint(an)\\n\", \"import math\\n\\ndef lcm(a, b):\\n  return a*b//math.gcd(a, b)\\n\\ndef f(num):\\n  cnt = 0\\n  while num % 2 == 0:\\n    num = num // 2\\n    cnt += 1\\n  return cnt\\n\\nn, m = map(int, input().split())\\na = list(map(int, input().split()))\\n\\nfor i in range(n):\\n  a[i] = a[i] // 2\\n\\nt = f(a[0])\\nfor i in range(n):\\n  if f(a[i]) != t:\\n    print(0)\\n    return\\n  a[i] = a[i] >> t\\nm = m >> t\\nl = 1\\nfor i in range(n):\\n  l = lcm(l, a[i])\\n  if l > m:\\n    print(0)\\n    return\\n\\nm = m // l\\nprint((m+1)//2)\", \"import math\\nfrom functools import reduce\\n\\n\\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\ndef lcm(*numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\n\\ndef my_round(val, digit=0):\\n    p = 10 ** digit\\n    return (val * p * 2 + 1) // 2 / p\\n\\n\\nn, m = list(map(int, input().split()))\\na_pr = [i // 2 for i in list(map(int, input().split()))]\\nlcm_ = lcm_list(a_pr)\\nres, div2 = 0, None\\nfor ai in a_pr:\\n    cnt = 0\\n    while ai % 2 == 0:\\n        ai //= 2\\n        cnt += 1\\n    if div2 is None:\\n        div2 = cnt\\n    elif cnt != div2:\\n        print((0))\\n        return\\n\\nprint((int(my_round(m // lcm_ / 2))))\\n\", \"from math import gcd, ceil\\nfrom functools import reduce\\nimport sys\\n\\ndef lcm_base(x, y):\\n    return (x * y) // gcd(x, y)\\n\\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nN, M = map(int, input().split())\\na = [int(i)//2 for i in input().split()]\\n\\ns = set()\\nfor x in a:\\n    cur = 0\\n    y = x\\n    while y%2 == 0:\\n        cur += 1\\n        y //= 2\\n    s.add(cur)\\n    if len(s) >= 2:\\n        print(0)\\n        return\\nlcm = lcm_list(a)\\nprint((M//lcm+1)//2)\", \"from math import gcd, ceil\\n\\n\\ndef lcm(a, b):\\n    return (a*b)//gcd(a, b)\\n\\n\\nn, m = list(map(int, input().split()))\\na = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    a[i] = a[i]//2\\n\\nlcm_v = a[0]\\nfor i in range(1, n):\\n    lcm_v = lcm(lcm_v, a[i])\\n\\nok = True\\nfor aa in a:\\n    if (lcm_v//aa) % 2 != 1:\\n        ok = False\\n        break\\nans = 0\\nif ok:\\n    ans = ((m//lcm_v)+1)//2\\nprint(ans)\\n\", \"from collections import deque,defaultdict\\ndef gcd(a,b):\\n    return b if not a%b else gcd(b,a%b)\\ndef lcm(a,b):\\n    return (a*b)//gcd(a,b)\\nn,m=list(map(int, input().split()))\\nA=[int(i) for i in input().split()]\\ntmp = A[0]\\nfor i in range(1,n):\\n    tmp = lcm(tmp,A[i])\\nans = m//tmp\\nlis = set()\\nfor i in A:\\n    r = i\\n    k=0\\n    while(r%2==0):\\n        k+=1\\n        r//=2\\n    lis.add(k)\\nif(m//(tmp)*tmp+tmp//2<=m):\\n    ans += 1\\nif(len(lis)!=1):\\n    ans=0\\n\\nprint(ans)\\n\\n\", \"import math\\nfrom decimal import Decimal, ROUND_HALF_UP\\ndef lcm(a):\\n    x = a[0]\\n    for i in range(1, len(a)):\\n        x = (x * a[i]) // math.gcd(x, a[i])\\n    return x\\ndef gcd(a):\\n  temp = math.gcd(a[0], a[1])\\n  for i in a:\\n    temp = math.gcd(temp,  i)\\n  return temp\\nn,m = map(int, input().split(\\\" \\\"))\\na = list(map(int, input().split(\\\" \\\")))\\nzero = False\\ncount = 0\\n#a = list(map(lambda x: x // 2, na))\\nmini = lcm(a)\\nif len(a) != 1:\\n  maxi = gcd(a)\\nelse:\\n  maxi = a[0]\\nmaxi2 = maxi\\nnibai = 1\\nwhile(True):\\n  if maxi2 % 2 == 0:\\n    nibai *= 2\\n    maxi2 //= 2\\n  else:\\n    break\\nfor i in a:\\n  if i % (2 * nibai) == 0:\\n    zero = True\\n    break\\n#print(nibai, maxi, mini)\\nif not zero:\\n  t = Decimal(str((m * 2 // mini) / 2))\\n  #print(t)\\n  print(t.quantize(Decimal('0'), rounding=ROUND_HALF_UP))\\nelse:\\n  print(0)\", \"from math import gcd\\nimport sys\\n\\ndef lcm(x,y):\\n    return x*y//gcd(x,y)\\n\\ndef count(x):\\n    res=0\\n    while True:\\n        if x%2==0:\\n            res+=1\\n            x//=2\\n        else:\\n            break\\n    return res\\n\\nn,m=list(map(int,input().split()))\\nA=list(map(int,input().split()))\\nA=list(set(A))\\nn=len(A)\\n\\nA.sort(reverse=True)\\n\\ntemp=A[0]\\nfor i in range(1,n):\\n    if count(A[i])!=count(temp):\\n        print((0))\\n        return\\n    else:\\n        temp=lcm(temp,A[i])\\n\\nans=m//(temp//2)-m//temp\\nprint(ans)\\n\", \"import math\\nimport fractions\\nfrom functools import reduce\\n\\nn, m = map(int,input().split())\\na = list(map(int,input().split()))\\na = [t // 2 for t in a]#\\u30ea\\u30b9\\u30c8\\u306e\\u8981\\u7d20\\u3059\\u3079\\u3066\\u30922\\u3067\\u5272\\u308b\\n\\ndef lcm_base(x, y):\\n    return (x * y)//fractions.gcd(x,y)\\n\\ndef lcm_list(numbers): #\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3092\\u6c42\\u3081\\u308b\\n    return reduce(lcm_base, numbers, 1)\\n\\ndef num_dev2(x):\\n    return bin(x)[::-1].find(\\\"1\\\") #\\uff12\\u3067\\u5272\\u308a\\u5207\\u308c\\u308b\\u56de\\u6570\\u3092\\u78ba\\u8a8d\\n\\nlcm = lcm_list(a)\\nq = m//lcm #m\\u306f\\u6700\\u5c0f\\u516c\\u500d\\u6570\\u3067\\u4f55\\u56de\\u5272\\u308c\\u308b\\u304b\\n\\ncount = 0\\ndev2 = num_dev2(a[0])\\nfor i in range(1,n):\\n    if dev2 != num_dev2(a[i]):#\\u30ea\\u30b9\\u30c8\\u306e\\u3059\\u3079\\u3066\\u306e\\u8981\\u7d20\\u306e\\uff12\\u3067\\u5272\\u308c\\u308b\\u56de\\u6570\\u306f\\u7b49\\u3057\\u3044\\u304b\\n        count += 1\\n        break\\nif count != 0:\\n    print(0)\\nelse:\\n    print(math.ceil(q/2))\", \"from math import gcd\\n\\ndef lcm(a, b):\\n    return a // gcd(a, b) * b \\n\\nN, M = map(int, input().split())\\nAs = list(map(int, input().split()))\\n\\nrightmostbit = As[0] & -As[0]\\nfor A in As[1:]:\\n    if rightmostbit != A & -A:\\n        print(0)\\n        return \\n\\n\\nlcm_of_half_As = 1\\nfor A in As:\\n    lcm_of_half_As = lcm(lcm_of_half_As, A //  2)\\n    if lcm_of_half_As > M:\\n        break\\n\\nprint((M // lcm_of_half_As + 1) // 2)\", \"import sys\\nimport numpy as np\\ndef input(): return sys.stdin.readline().rstrip()\\n\\ndef kosuu(x):\\n    re = [0,0]\\n    while x % 2 == 0:\\n        x = x//2\\n        re[1]+=1\\n    re[0]=x\\n    return re\\n\\n        \\n \\ndef main():\\n    n,m=map(int, input().split())\\n    a=list(map(int, input().split()))\\n    li = [kosuu(a[0])[0]]\\n    hantei = kosuu(a[0])[1]\\n    for i in a[1:]:\\n        hantei2 = kosuu(i)\\n        if hantei2[1] != hantei:\\n            print(0)\\n            break\\n        else:\\n            li.append(hantei2[0])\\n    else:\\n        lc = np.lcm.reduce(li)\\n        print(((m//(lc*2**(hantei-1)))+1)//2)\\n            \\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nimport sys\\nfrom functools import reduce\\n\\nN, M = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\nfor i in range(N):\\n  A[i] = A[i] // 2\\n  \\ndef lcm_base(x, y):\\n    return (x * y) // math.gcd(x, y)\\n  \\ndef lcm_list(numbers):\\n    return reduce(lcm_base, numbers, 1)\\n\\nC = lcm_list(A)\\nB = [0 for _ in range(N)]\\n\\nfor i in range(N):\\n  B[i] = C // A[i]\\n  if B[i] % 2 == 0:\\n    print(0)\\n    return\\n\\nprint( (M // C + 1) // 2)\", \"import math\\nfrom functools import reduce\\n\\nn,m = map(int, input().split())\\nA = list(map(int, input().split()))\\n\\ndef lcm_base(x,y):\\n  return x*y//math.gcd(x,y)\\n\\ndef lcm(target_list):\\n  return reduce(lcm_base, target_list)\\n\\nA_gcd = reduce(math.gcd, A)\\nflg = True\\n\\nfor a in A:\\n  if a//A_gcd%2==0:\\n    flg = False\\n    break\\n    \\nif flg:\\n  min_x = int(lcm(A))//2\\n  ans = m//min_x - m//(2*min_x)\\n  print(ans)\\nelse:\\n  print(0)\", \"from math import gcd\\nfrom functools import reduce\\nimport sys\\ninput = sys.stdin.readline\\n\\n\\ndef lcm(a, b):\\n    return a*b // gcd(a, b)\\n\\n\\ndef count_factor_2(num):\\n    count = 0\\n    while num % 2 == 0:\\n        num //= 2\\n        count += 1\\n    return count\\n\\n\\ndef main():\\n    n, m = list(map(int, input().split()))\\n    A = list([int(x)//2 for x in input().split()])\\n\\n    check = len(set(map(count_factor_2, A)))\\n    if check != 1:\\n        print((0))\\n        return\\n\\n    lcm_a = reduce(lcm, A)\\n    step = lcm_a * 2\\n    ans = (m + lcm_a) // step\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\"]",
        "difficulty": "interview",
        "input": "5 1000000000\n6 6 2 6 2\n",
        "output": "166666667\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc150/tasks/abc150_d"
    },
    {
        "id": 255,
        "task_id": 2649,
        "test_case_id": 1,
        "question": "There are N points on the 2D plane, i-th of which is located on (x_i, y_i).\nThere can be multiple points that share the same coordinate.\nWhat is the maximum possible Manhattan distance between two distinct points?\nHere, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.\n\n-----Constraints-----\n - 2 \\leq N \\leq 2 \\times 10^5\n - 1 \\leq x_i,y_i \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\n-----Output-----\nPrint the answer.\n\n-----Sample Input-----\n3\n1 1\n2 4\n3 2\n\n-----Sample Output-----\n4\n\nThe Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.",
        "solutions": "[\"n = int(input())\\na = []\\nb = []\\nfor i in range(n):\\n  x,y = list(map(int, input().split()))\\n  a.append(x+y)\\n  b.append(x-y)\\na.sort()\\nb.sort()\\n\\nans = a[-1]-a[0]\\nc = b[-1]-b[0]\\nprint((max(ans,c)))\\n\", \"\\n\\ndef main():\\n    n = int(input())\\n    z = [[], []]\\n    for i in range(n):\\n        x, y = list(map(int, input().split()))\\n        z[0].append(x + y)\\n        z[1].append(x - y)\\n    z[0] = sorted(z[0])\\n    z[1] = sorted(z[1])\\n    print((max(z[0][-1] - z[0][0], z[1][-1] - z[1][0])))\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def mdmax(x):\\n    a = []\\n    b = []\\n    for i in range(len(x)):\\n        a.append(x[i][0] - x[i][1])\\n        b.append(x[i][0] + x[i][1])\\n    return max(max(a) - min(a), max(b) - min(b))\\n\\nn = int(input())\\ndata = []\\nfor i in range(n):\\n    ininput_data = input()\\n    input_data = list(map(int, ininput_data.split()))\\n    data.append(input_data)\\nprint(mdmax(data))\", \"N = int(input())\\na,b = [], []\\nfor i in range(N):\\n  x,y = map(int, input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"n = int(input())\\n\\nx, y = [], []\\nfor i in range(n):\\n    xi, yi = map(int, input().split())\\n    x.append(xi+yi)\\n    y.append(xi-yi)\\n\\nx.sort()\\ny.sort()\\n\\nans = max((x[-1]-x[0]), (y[-1]-y[0]))\\nprint(ans)\", \"n = int(input())\\nxy = [list(map(int, input().split())) for i in range(n)]\\nans = []\\nl = [xy[i][0]+xy[i][1] for i in range(n)]\\nans.append(max(l)-min(l))\\nl = [xy[i][0]-xy[i][1] for i in range(n)]\\nans.append(max(l)-min(l))\\nl = [-xy[i][0]+xy[i][1] for i in range(n)]\\nans.append(max(l)-min(l))\\nl = [-xy[i][0]-xy[i][1] for i in range(n)]\\nans.append(max(l)-min(l))\\nprint(max(ans))\", \"n=int(input())\\nzp=[]\\nzl=[]\\nfor i in range(n):\\n    a,b=map(int,input().split())\\n    zp.append(a+b)\\n    zl.append(a-b)\\nans=max((max(zp)-min(zp)),(max(zl)-min(zl)))\\nprint(ans)\", \"def solve(n, x, y):\\n    z = [u + v for u, v in zip(x, y)]\\n    w = [u - v for u, v in zip(x, y)]\\n    return max([max(z) - min(z), max(w) - min(w)])\\n\\nn = int(input())\\nx, y = zip(*[map(int, input().split()) for i in range(n)])\\nprint(solve(n, x, y))\", \"N=int(input())\\nA=[]\\nB=[]\\nfor _ in range(N):\\n    x,y=map(int, input().split())\\n    A.append(x+y)\\n    B.append(x-y)\\n\\nA=sorted(A)\\nB=sorted(B)\\n\\nprint(max(A[-1]-A[0],B[-1]-A[0],A[-1]-A[0],B[-1]-B[0]))\", \"n = int(input())\\nu = []\\nv = []\\nfor i in range(n):\\n    x, y = map(int, input().split())\\n    u.append(x + y)\\n    v.append(x - y)\\n    \\nu.sort()\\nv.sort()\\nprint(max(u[-1] - u[0], v[-1] - v[0]))\", \"import sys\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    N = int(input())\\n    dx = []\\n    dy = []\\n    for _ in range(N):\\n        x, y = map(int, input().split())\\n        dx.append(x + y)\\n        dy.append(x - y)\\n    dx.sort()\\n    dy.sort()\\n    print(max(dx[N-1] - dx[0], dy[N-1] - dy[0]))\\n\\n    return\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"n=int(input())\\na,b,c,d=-10**9,10**9,-10**9,10**9\\nfor _ in range(n):\\n\\tx,y=map(int,input().split())\\n\\ta=max(a,x+y)\\n\\tb=min(b,x+y)\\n\\tc=max(c,x-y)\\n\\td=min(d,x-y)\\nprint(max(a-b,c-d))\", \"n=int(input())\\nxy=[list(map(int, input().split())) for i in range(n)]\\nz=list(map(lambda x: x[0]+x[1], xy))\\nw=list(map(lambda x: x[0]-x[1], xy))\\nprint(max(max(z)-min(z), max(w)-min(w)))\", \"N = int(input())\\nx, y = map(int, input().split())\\nd = [x - y, x - y, x + y, x + y]\\nfor i in range(1,N):\\n  x, y = map(int, input().split())\\n  d[0] = max(d[0], x-y)\\n  d[1] = min(d[1], x-y)\\n  d[2] = max(d[2], x+y)\\n  d[3] = min(d[3], x+y)\\nprint(max(d[0]-d[1], d[2]-d[3]))\", \"# coding: utf-8\\n# Your code here!\\nN=int(input())\\n\\nZ=[]\\nW=[]\\n\\nfor _ in range(N):\\n    x,y=map(int,input().split())\\n    Z.append(x+y)\\n    W.append(x-y)\\n    \\nprint(max(max(Z)-min(Z),max(W)-min(W)))\", \"n = int(input())\\nxy_array = [list(map(int, input().split())) for _ in range(n)]\\n\\nth = pow(10, 9)\\nright_up_max = -th\\nleft_down_min = th\\nleft_up_max = -th\\nright_down_min = th\\n\\nfor x, y in xy_array:\\n    right_up_max = max(x + y, right_up_max)\\n    left_down_min = min(x + y, left_down_min)\\n    left_up_max = max(x - y, left_up_max)\\n    right_down_min = min(x - y, right_down_min)\\n\\nans = max(right_up_max - left_down_min, left_up_max - right_down_min)\\nprint(ans)\", \"# import itertools\\n# import math\\n# from functools import reduce\\n# import sys\\n# sys.setrecursionlimit(500*500)\\n# import numpy as np\\n# from collections import deque\\n# import heapq\\n\\n# \\u5165\\u529b\\nN = int(input())\\n# S = input()\\n# n, *a = map(int, open(0))\\n# H, N = map(int, input().split())\\n# A = list(map(int, input().split()))\\n# A = list(map(lambda x: int(x)*(-1), input().split()))\\n# B = list(map(int, input().split()))\\nx_y = [list(map(int,input().split())) for _ in range(N)]\\n# S = input()\\n\\n# B_C = sorted(B_C, reverse=True, key=lambda x:x[1])\\n# all_cases = list(itertools.permutations(P))\\n# a = list(itertools.combinations_with_replacement(range(1, M + 1), N))\\n# itertools.product((0,1), repeat=n)\\n\\n# A = np.array(A)\\n# cum_A = np.cumsum(A)\\n# cum_A = np.insert(cum_A, 0, 0)\\n\\n# edges = [list(map(int,input().split())) for _ in range(N - 1)]\\n# tree = [[] for _ in range(N + 1)]\\n\\n# for edge in edges:\\n#     tree[edge[0]].append(edge[1])\\n#     tree[edge[1]].append(edge[0])\\n\\n# depth = [-1] * (N + 1)\\n# depth[1] = 0\\n# count = [0] * (N + 1)\\n\\n# for i in range(Q):\\n#     p, x = map(int, input().split())\\n#     count[p] += x\\n\\n# def dfs(tree, s):\\n#     for l in tree[s]:\\n#         if depth[l[0]] == -1:\\n#             depth[l[0]] = depth[s] + 1\\n#             dfs(tree, l[0])\\n# dfs(tree, 1)\\n\\n# \\u7d20\\u56e0\\u6570\\u5206\\u89e3\\n# def factorization(n):\\n#     arr = []\\n#     temp = n\\n#     for i in range(2, int(-(-n**0.5//1))+1):\\n#         if temp%i==0:\\n#             cnt=0\\n#             while temp%i==0:\\n#                 cnt+=1\\n#                 temp //= i\\n#             arr.append([i, cnt])\\n#     if temp!=1:\\n#         arr.append([temp, 1])\\n#     if arr==[]:\\n#         arr.append([n, 1])\\n#     return arr\\n\\n# \\u7d04\\u6570\\u5217\\u6319\\n# def make_divisors(n):\\n#     lower_divisors , upper_divisors = [], []\\n#     i = 1\\n#     while i*i <= n:\\n#         if n % i == 0:\\n#             lower_divisors.append(i)\\n#             if i != n // i:\\n#                 upper_divisors.append(n//i)\\n#         i += 1\\n#     return lower_divisors + upper_divisors[::-1]\\n\\n# bfs\\n# tree = [[] for _ in range(N + 1)]\\n# edges = [list(map(int,input().split())) for _ in range(M)]\\n\\n# for edge in edges:\\n#     tree[edge[0]].append(edge[1])\\n#     tree[edge[1]].append(edge[0])\\n\\n# depth = [-1] * (N + 1)\\n# depth[1] = 0\\n\\n# d = deque()\\n# d.append(1)\\n\\n# ans = [0] * (N + 1)\\n# while d:\\n#  v = d.popleft()\\n#  for i in tree[v]:\\n#    if depth[i] != -1:\\n#      continue\\n#    depth[i] = depth[v] + 1\\n#    ans[i] = v\\n#    d.append(i)\\n\\n# # ans = depth[2:]\\n# print('Yes')\\n# print(*ans[2:], sep=\\\"\\\\n\\\")\\n\\n# def gcd_list(numbers):\\n#     return reduce(math.gcd, numbers)\\n\\n# # \\u9ad8\\u901f\\u7d20\\u56e0\\u6570\\u5206\\u89e3\\u6e96\\u5099\\n# MAXN = 10**6+10\\n# sieve = [i for i in range(MAXN+1)]\\n# p = 2\\n# while p*p <= MAXN:\\n#     if sieve[p] == p:\\n#         for q in range(2*p, MAXN+1, p):\\n#             if sieve[q] == q:\\n#                 sieve[q] = p\\n#     p += 1\\n\\n\\n# 45\\u5ea6\\u56de\\u8ee2\\nZ = []\\nW = []\\nfor l in x_y:\\n    Z.append(l[0] + l[1])\\n    W.append(l[0] - l[1])\\n\\nprint(max((max(Z) - min(Z)), (max(W) - min(W))))\", \"a,b=[],[]\\nn=int(input())\\nfor _ in range(n):\\n  x,y=map(int,input().split())\\n  a+=[x-y]\\n  b+=[x+y]\\nprint(max(max(a)-min(a),max(b)-min(b)))\", \"n=int(input())\\na,b=[],[]\\nfor i in range(n):\\n  x,y=list(map(int,input().split()))\\n  a.append(x+y)\\n  b.append(x-y)\\nprint((max(max(a)-min(a),max(b)-min(b))))\\n\", \"N = int(input())\\na = []\\nb = []\\nfor i in range(N):\\n  x,y = map(int, input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\n\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"n = int(input())\\na = [0] * n\\nb = [0] * n\\nfor i in range(n):\\n    x, y = list(map(int, input().split()))\\n    a[i] = x + y\\n    b[i] = x - y\\nprint((max(max(a) - min(a), max(b) - min(b))))\\n\", \"N=int(input())\\n\\na,b=[],[]\\n\\nfor i in range(N):\\n  x,y=map(int,input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\na.sort()\\nb.sort()\\n\\nans=max(a[-1]-a[0],b[-1]-b[0])\\nprint(ans)\", \"n=int(input())\\na=[]\\nj=k=0\\ndef s(a):\\n    return a[0]+a[1]\\ndef ss(a):\\n    return a[0]-a[1]\\nfor i in range(n):\\n    f=list(map(int,input().split()))\\n    a.append(f)\\naa=min(map(s,a))\\nb=max(map(s,a))\\nc=min(map(ss,a))\\nd=max(map(ss,a))\\nprint(max(abs(d-c),abs(b-aa)))\", \"n = int(input())\\na, b = [], []\\nfor _ in range(n):\\n    x, y = map(int, input().split())\\n    a.append(x+y)\\n    b.append(x-y)\\n \\na.sort()\\nb.sort()\\n \\nans = max(a[-1]-a[0], b[-1]-b[0])\\nprint(ans)\", \"n=int(input())\\nl=[]\\nar=[]\\nbr=[]\\nfor i in range(n):\\n  l.append(list(map(int,input().split())))\\n  ar.append(l[-1][0]+l[-1][1])\\n  br.append(l[-1][0]-l[-1][1])\\nar.sort()\\nbr.sort()\\nan=max(abs(ar[-1]-ar[0]),abs(br[-1]-br[0]))\\nprint(an)\", \"N = int(input())\\nXY = [list(map(int, input().split())) for _ in range(N)]\\n\\nz = []\\nw = []\\nfor x, y in XY:\\n    z.append(x + y)\\n    w.append(x - y)\\n\\nprint(max(max(z) - min(z), max(w) - min(w)))\", \"n=int(input())\\nmaxa=maxb=-2e9\\nmina=minb=2e9\\nfor i in range(n):\\n  x,y=list(map(int,input().split()))\\n  maxa=max(maxa,x+y)\\n  mina=min(mina,x+y)\\n  maxb=max(maxb,x-y)\\n  minb=min(minb,x-y)\\nprint((max(maxa-mina,maxb-minb)))\\n\", \"N = int(input())\\nL = [[int(l) for l in input().split()] for _ in range(N)]\\n\\nL1 = [0]*N\\nL2 = [0]*N\\nfor i in range(N):\\n    L1[i] = L[i][0]+L[i][1]\\n    L2[i] = L[i][0]-L[i][1]\\n\\nL1.sort()\\nL2.sort()\\nprint(max(L1[-1]-L1[0], L2[-1]-L2[0]))\", \"N = int(input())\\nxy = [list(map(int, input().split())) for _ in range(N)]\\n\\nadd = sorted([x+y for x, y in xy])\\nsub = sorted([x-y for x, y in xy])\\n\\nprint(max(add[-1]-add[0], sub[-1]-sub[0]))\", \"n=int(input())\\nlx=[]\\nly=[]\\nfor i in range(n):\\n  x,y=map(int,input().split())\\n  lx.append(x+y)\\n  ly.append(x-y)\\nprint(max(max(lx)-min(lx),max(ly)-min(ly)))\", \"N = int(input())\\nl0 = [[int(i) for i in input().split()] for _ in range(N)]\\nl1 = [0] * N\\nl2 = [0] * N\\nfor cnt, val in enumerate(l0):\\n    l1[cnt] = val[0] + val[1]\\n    l2[cnt] = val[0] - val[1]\\nl1.sort()\\nl2.sort()\\nprint((max(l1[-1] - l1[0], l2[-1] - l2[0])))\\n\", \"def main():\\n    n = int(input())\\n    xym, xyM, x_ym, x_yM = 10**9, -10**9, 10**9, -10**9\\n    for _ in range(n):\\n        x, y = map(int, input().split())\\n        xy, x_y = x+y, x-y\\n        xym, xyM, x_ym, x_yM = min(xym, xy), max(xyM, xy), min(x_ym, x_y), max(x_yM, x_y)\\n    print(max(xyM-xym, x_yM-x_ym))\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N=int(input())\\nA=[0]*(N)\\nB=[0]*(N)\\nfor i in range(N):\\n    x,y=map(int, input().split())\\n    A[i]=x+y\\n    B[i]=x-y\\n\\nA=sorted(A)\\nB=sorted(B)\\n\\nprint(max(A[-1]-A[0],B[-1]-A[0],A[-1]-A[0],B[-1]-B[0]))\", \"n = int(input())\\nu = []\\nv = []\\nfor i in range(n):\\n    x, y = map(int, input().split())\\n    u.append(x + y)\\n    v.append(x - y)\\n    \\nu.sort()\\nv.sort()\\nprint(max(u[-1] - u[0], v[-1] - v[0]))\", \"N = int(input())\\nA = []; B = []\\nfor i in range(N):\\n  x,y = map(int,input().split())\\n  a = x+y; A.append(a)\\n  b = x-y; B.append(b)\\nA.sort();B.sort()\\nMax_A = A[-1] - A[0]\\nMax_B = B[-1] - B[0]\\nans = max(Max_A,Max_B)\\nprint(ans)\", \"import sys\\n\\nleft_right_max = 0\\nleft_right_min = float('inf')\\nright_left_max = float('-inf')\\nright_left_min = float('inf')\\nr3_max = float('-inf')\\nr3_min = float('inf')\\n\\nn = int(sys.stdin.readline().strip())\\n\\nfor idx in range(n):\\n    x, y = sys.stdin.readline().strip().split(' ')\\n    x = int(x)\\n    y = int(y)\\n\\n    left_right_tmp = x + y\\n    if left_right_tmp > left_right_max:\\n        left_right_max = left_right_tmp\\n      \\n    if left_right_tmp < left_right_min:\\n        left_right_min = left_right_tmp\\n        #res_lr[2] = (x, y)\\n\\n    right_left_tmp = x - y\\n    if right_left_tmp > right_left_max:\\n        right_left_max = right_left_tmp\\n        #res_rl[1] = (x, y)\\n    if right_left_tmp < right_left_min:\\n        right_left_min = right_left_tmp\\n        #res_rl[2] = (x, y)\\n        \\n    r3_tmp = y - x\\n    if r3_tmp > r3_max:\\n        r3_max = r3_tmp\\n        #res_3[1] = (x, y)\\n    if r3_tmp < r3_min:\\n        r3_min = r3_tmp\\n        #res_3[2] = (x, y)\\n\\nreslr_dist = left_right_max - left_right_min\\nresrl_dist = right_left_max - right_left_min\\nres3_dist = r3_max - r3_min\\n\\nprint((max(resrl_dist, reslr_dist, res3_dist)))\\n\", \"N = int(input())\\nlst = []\\nfor i in range(N):\\n    lst.append(tuple(map(lambda i: int(i), input().split())))\\nlstP = [xy[0]+xy[1] for xy in lst]\\nlstM = [xy[0]-xy[1] for xy in lst]\\nlstP, lstM\\nz = max(lstP) - min(lstP)\\nw = max(lstM) - min(lstM)\\nprint(max(z,w))\", \"import sys\\nfrom operator import itemgetter\\n\\nN = int(input())\\nV = set()\\nfor s in sys.stdin.readlines():\\n    x, y = list(map(int, s.split()))\\n    V.add((x + y, x - y))\\n\\ny_max = max(V, key=itemgetter(1))[1]\\ny_min = min(V, key=itemgetter(1))[1]\\nx_max = max(V, key=itemgetter(0))[0]\\nx_min = min(V, key=itemgetter(0))[0]\\n\\nprint((max(x_max - x_min, y_max - y_min)))\\n\", \"N = int(input())\\na = list()\\nb = list()\\nfor i in range(N):\\n  x,y = map(int, input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"def get_ints():\\n    return list(map(int,input().split()))\\n\\nn = int(input())\\na, b = [], []\\nfor i in range(n):\\n    x, y = get_ints()\\n    a.append(x-y)\\n    b.append(x+y)\\n\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"\\\"\\\"\\\"AtCoder Beginner Contest 178.\\n\\nE\\n\\\"\\\"\\\"\\n\\nimport sys\\n\\n\\ndef input() -> str:  # noqa: A001\\n    \\\"\\\"\\\"Input.\\\"\\\"\\\"\\n    return sys.stdin.readline()[:-1]\\n\\n\\ndef calc(p1: list, p2: list) -> int:\\n    \\\"\\\"\\\"Calc Manhattan Distance.\\\"\\\"\\\"\\n    return abs(p2[1] - p1[1]) + abs(p2[0] - p1[0])\\n\\n\\ndef main():\\n    \\\"\\\"\\\"Run.\\\"\\\"\\\"\\n    n = int(input())\\n\\n    patterns = {\\n        'lt': (1, 1),\\n        'rt': (-1, 1),\\n        'lb': (-1, -1),\\n        'rb': (1, -1),\\n    }\\n\\n    points: dict = {k: None for k in list(patterns.keys())}\\n\\n    for _ in range(n):\\n        p = list(map(int, input().split(' ')))\\n\\n        for k, (x, y) in list(patterns.items()):\\n            max_p = points[k]\\n\\n            if max_p:\\n                max_p_pos = (max_p[0] * x) + (max_p[1] * y)\\n                p_pos = (p[0] * x) + (p[1] * y)\\n                if max_p_pos < p_pos:\\n                    points[k] = p\\n            else:\\n                points[k] = p\\n\\n    ans = 0\\n    for i, p1 in enumerate(points.values()):\\n        for p2 in list(points.values())[i + 1:]:\\n            ans = max(ans, calc(p1, p2))\\n\\n    print(ans)\\n\\n\\nmain()\\n\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN = int(readline())\\nX,Y = [None] * N, [None] * N\\nfor i in range(N):\\n  x,y = list(map(int,readline().split()))\\n  X[i],Y[i] = x + y,x - y\\n\\nprint((max(abs(max(X) - min(X)),abs(max(Y) - min(Y)))))\\n\", \"n = int(input())\\na, b = [], []\\nfor _ in range(n):\\n    x, y = map(int, input().split())\\n    a.append(x+y)\\n    b.append(x-y)\\n\\na.sort()\\nb.sort()\\n\\nans = max(a[-1]-a[0], b[-1]-b[0])\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\n\\ndef get_points_and_convert(pts):\\n    x, y = pts\\n    return x + y, x - y\\n\\n\\ndef main():\\n    n = int(input())\\n    points = [\\n        get_points_and_convert(list(map(int, input().split())))\\n        for _ in range(n)\\n    ]\\n    plus_coords, minus_coords = list(zip(*points))\\n    plus_dist = max(plus_coords) - min(plus_coords)\\n    minus_dist = max(minus_coords) - min(minus_coords)\\n    print((max(plus_dist, minus_dist)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nXY = [[int(_) for _ in input().split()] for _ in range(N)]\\nans = -1\\nfor dx, dy in ((1, 1), (-1, 1), (-1, -1), (1, -1)):\\n    xy2 = [x * dx + y * dy for x, y in XY]\\n    ans = max(ans, max(xy2) - min(xy2))\\nprint(ans)\\n\", \"N = int(input())\\nA = [0]*N\\nB = [0]*N\\nfor i in range(N):\\n  x,y = map(int,input().split())\\n  A[i] = x+y\\n  B[i] = x-y\\na = max(A)-min(A)\\nb = max(B)-min(B)\\nprint(max(a,b))\", \"n = int(input())\\nl = [[] for i in range(4)]\\nfor i in range(n):\\n    x, y = list(map(int, input().split()))\\n    l[0].append(x+y)\\n    l[1].append(x-y)\\n    l[2].append(-x+y)\\n    l[3].append(-x-y)\\nfor i in range(4):\\n    l[i].sort()\\nans = 0\\nfor i in range(4):\\n    ans = max(ans, l[i][-1] - l[i][0])\\nprint(ans)\\n\", \"N = int(input())\\na = []\\nb = []\\nfor i in range(N):\\n  x,y = map(int,input().split())\\n  a.append(x-y)\\n  b.append(x+y)\\n  \\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"N=int(input())\\nzls=[0 for _ in range(N)]\\nwls=[0 for _ in range(N)]\\nfor i in range(N):\\n  x,y=[int(s) for s in input().split()]\\n  zls[i]=x+y\\n  wls[i]=x-y\\nprint(max([max(zls)-min(zls),max(wls)-min(wls)]))\", \"n=int(input())\\na=[]\\nb=[]\\nfor i in range(n):\\n  x,y=map(int,input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\nprint(max(max(a)-min(a),max(b)-min(b)))\", \"import sys\\nimport re\\nimport queue\\nfrom math import ceil, floor, sqrt, pi, factorial, gcd\\nfrom copy import deepcopy\\nfrom collections import Counter, deque\\nfrom heapq import heapify, heappop, heappush\\nfrom itertools import accumulate, product, combinations, combinations_with_replacement\\nfrom bisect import bisect, bisect_left, bisect_right\\nfrom functools import reduce\\nfrom decimal import Decimal, getcontext\\n# input = sys.stdin.readline\\ndef i_input(): return int(input())\\ndef i_map(): return map(int, input().split())\\ndef i_list(): return list(i_map())\\ndef i_row(N): return [i_input() for _ in range(N)]\\ndef i_row_list(N): return [i_list() for _ in range(N)]\\ndef s_input(): return input()\\ndef s_map(): return input().split()\\ndef s_list(): return list(s_map())\\ndef s_row(N): return [s_input for _ in range(N)]\\ndef s_row_str(N): return [s_list() for _ in range(N)]\\ndef s_row_list(N): return [list(s_input()) for _ in range(N)]\\ndef lcm(a, b): return a * b // gcd(a, b)\\nsys.setrecursionlimit(10 ** 6)\\nINF = float('inf')\\nMOD = 10 ** 9 + 7\\nnum_list = []\\nstr_list = []\\n\\n\\n\\ndef main():\\n\\tN = i_input()\\n\\n\\tx_y_list = []\\n\\n\\tfor i in range(0,N):\\n\\t\\ttmpx,tmpy = i_map()\\n\\t\\tx_y_list.append((tmpx,tmpy))\\n\\n\\tz_list = []\\n\\tw_list = []\\n\\tfor i in range(0,N):\\n\\t\\ttmpz = x_y_list[i][0] + x_y_list[i][1]\\n\\t\\ttmpw = x_y_list[i][0] - x_y_list[i][1]\\n\\t\\tz_list.append(tmpz)\\n\\t\\tw_list.append(tmpw)\\n\\n\\tprint(max(max(map(lambda x : (x),z_list))-min(map(lambda x: (x), z_list)),max(map(lambda x : (x),w_list))-min(map(lambda x: (x),w_list))))\\n\\t\\n\\treturn\\n\\n\\ndef __starting_point():\\n\\tmain()\\n__starting_point()\", \"n=int(input())\\na,b,c,d=2*10**9,0,10**9,-10**9\\n\\nfor i in range(n):\\n  x,y=list(map(int,input().split()))\\n  a=a if a<x+y else x+y\\n  b=b if b>x+y else x+y\\n  c=c if c<y-x else y-x\\n  d=d if d>y-x else y-x\\n\\nprint((b-a if b-a>d-c else d-c))\\n\", \"n=int(input())\\np=[]\\nq=[]\\nfor _ in range(n):\\n  x,y=map(int,input().split())\\n  p.append(x+y)\\n  q.append(x-y)\\nprint(max(max(p)-min(p),max(q)-min(q)))\", \"n=int(input())\\nl=[list(map(int,input().split())) for i in range(n)]\\na=10**9\\nz_max=-1*a\\nz_min=a\\nw_max=-1*a\\nw_min=a\\nfor x,y in l: #\\u70b9\\u306ex\\u5ea7\\u6a19\\u3068y\\u5ea7\\u6a19\\u306e\\u548c\\u306e\\u6700\\u5927\\u5024\\u3068\\u6700\\u5c0f\\u5024\\u306e\\u5dee\\u304b\\u5ea7\\u6a19\\u306e\\u5dee\\u306e\\u6700\\u5927\\u5024\\u3068\\u6700\\u5c0f\\u5024\\u306e\\u5dee\\u304c\\u7b54\\u3048\\n  z_max=max(z_max,x+y)\\n  z_min=min(z_min,x+y)\\n  w_max=max(w_max,x-y)\\n  w_min=min(w_min,x-y)\\nprint(max(z_max-z_min,w_max-w_min))\", \"n = int(input())\\nu = []\\nv = []\\nfor i in range(n):\\n    x, y = map(int, input().split())\\n    u.append(x + y)\\n    v.append(x - y)\\n    \\nu.sort()\\nv.sort()\\nprint(max(u[-1] - u[0], v[-1] - v[0]))\", \"n = int(input())\\nxy_array = [list(map(int, input().split())) for _ in range(n)]\\n\\nth = pow(10, 9)\\nz_max = -th\\nz_min = th\\nw_max = -th\\nw_min = th\\n\\nfor x, y in xy_array:\\n    z_max = max(x + y, z_max)\\n    z_min = min(x + y, z_min)\\n    w_max = max(x - y, w_max)\\n    w_min = min(x - y, w_min)\\n\\nans = max(z_max - z_min, w_max - w_min)\\nprint(ans)\", \"n = int(input())\\n\\nxy = []\\nfor index in range(n):\\n  x, y = map(int, input().split())\\n  xy.append([x, y])\\n\\npos_max = xy[0][0]+xy[0][1]\\npos_min = xy[0][0]+xy[0][1]\\nneg_max = xy[0][0]-xy[0][1]\\nneg_min = xy[0][0]-xy[0][1]\\nfor item in xy:\\n  pos_v = item[0] + item[1]\\n  neg_v = item[0] - item[1]\\n  pos_max = pos_v if pos_v > pos_max else pos_max\\n  pos_min = pos_v if pos_v < pos_min else pos_min\\n  neg_max = neg_v if neg_v > neg_max else neg_max\\n  neg_min = neg_v if neg_v < neg_min else neg_min\\n\\npos_result = pos_max - pos_min\\nneg_result = neg_max - neg_min\\nprint(pos_result if pos_result >= neg_result else neg_result)\", \"n = int(input())\\nu = []\\nv = []\\nfor _ in range(n):\\n    x, y = list(map(int, input().split()))\\n    u.append(x + y)\\n    v.append(x - y)\\n\\nans = max(max(u) - min(u), max(v) - min(v))\\nprint(ans)\\n\", \"import numpy as np\\ndef solve(n, x, y):\\n    x = np.asarray(x)\\n    y = np.asarray(y)\\n    z = x + y\\n    w = x - y\\n    return max(np.max(z) - np.min(z), np.max(w) - np.min(w))\\n\\nn = int(input())\\nx, y = list(zip(*[list(map(int, input().split())) for i in range(n)]))\\nprint((solve(n, x, y)))\\n\", \"import sys\\ndef Ii():return int(sys.stdin.readline())\\ndef Mi():return map(int,sys.stdin.readline().split())\\ndef Li():return list(map(int,sys.stdin.readline().split()))\\n\\nn = Ii()\\nans = 0\\npoints = []\\nxymax = 0\\nxymin = 10**11\\ndxymax = -10**11\\ndxymin = 10**11\\nfor i in range(n):\\n  point = Li()\\n  xy = point[0]+point[1]\\n  if xy > xymax:\\n    xymax = xy\\n  if xy < xymin:\\n    xymin = xy\\n  dxy = point[0]-point[1]\\n  if dxy > dxymax:\\n    dxymax = dxy\\n  if dxy < dxymin:\\n    dxymin = dxy\\nans = max(dxymax-dxymin,xymax-xymin)\\nprint(ans)\", \"n = int(input())\\n# n = 2*10**5\\n\\nmin_u = float('inf')\\nmax_u = -float('inf')\\nmin_v = float('inf')\\nmax_v = -float('inf')\\n\\n\\nfor i in range(n):\\n    x, y = list(map(int, input().split()))\\n    # x, y = (10**9 , 10**9)\\n    u, v = (x+y, x-y)\\n    if u <= min_u:\\n        min_u = u\\n    if u >= max_u:\\n        max_u = u\\n    if v <= min_v:\\n        min_v = v\\n    if v >= max_v:\\n        max_v = v\\n\\nprint((max(max_u - min_u, max_v - min_v)))\\n\", \"import numpy as np\\n\\nN = int(input())\\nxy = [list(map(int, input().split())) for _ in range(N)]\\n\\nxy45 = [[xy[i][0] - xy[i][1], xy[i][0] + xy[i][1]] for i in range(N)]\\nxy45 = np.array(xy45)\\n\\nprint((max(max(xy45[:, 0]) - min(xy45[:, 0]), max(xy45[:, 1]) - min(xy45[:, 1]))))\\n\", \"import sys\\n\\n\\ndef input():\\n    return sys.stdin.readline()[:-1]\\n\\n\\nN = int(input())\\n\\nplus = []\\nminus = []\\nfor _ in range(N):\\n    x, y = list(map(int, input().split()))\\n    plus.append(x+y)\\n    minus.append(x-y)\\n\\nprint((max(max(plus)-min(plus), max(minus)-min(minus))))\\n\", \"n = int(input())\\n\\nplus,minus = [],[]\\nfor i in range(n):\\n    a,b = map(int,input().split())\\n    plus.append(a+b)\\n    minus.append(a-b)\\n\\nplus.sort()\\nminus.sort()\\n\\nprint(max(plus[-1]-plus[0],minus[-1]-minus[0]))\", \"def get_ints():\\n  return list(map(int,input().split()))\\n\\nn = int(input())\\na,b = [],[]\\nfor i in range(n):\\n  x,y = get_ints()\\n  a.append(x+y)\\n  b.append(x-y)\\n\\na.sort()\\nb.sort()\\nans = max(a[-1]-a[0], b[-1]-b[0])\\nprint(ans)\\n\\n\\n\\n\", \"n = int(input())\\npoints = [tuple(map(int, input().split())) for _ in range(n)]\\nplus = [p[0] + p[1] for p in points]\\nminus = [p[0] - p[1] for p in points]\\nprint(max(max(plus) - min(plus), max(minus) - min(minus)))\", \"n = int(input())\\na, b = [], []\\n\\nfor _ in range(n):\\n    x, y = list(map(int, input().split()))\\n    a.append(x - y)\\n    b.append(x + y)\\n\\nans = max(max(a) - min(a), max(b) - min(b))\\nprint(ans)\\n\", \"N = int(input())\\nx = [0 for _ in range(N)]\\ny = [0 for _ in range(N)]\\n\\nfor i in range(N):\\n    x[i], y[i] = map(int,input().split())\\n\\nX = [0 for _ in range(N)]\\nY = [0 for _ in range(N)]\\n\\nfor i in range(N):\\n    X[i], Y[i] = x[i] - y[i], x[i] + y[i]\\n\\nans = 0\\nans = max(max(X)-min(X),max(Y)-min(Y))\\n\\nprint(ans)\", \"def main():\\n    n = int(input())\\n    X, Y = [], []\\n    for _ in range(n):\\n        x, y = list(map(int, input().split()))\\n        X.append(x + y)\\n        Y.append(x - y)\\n    X.sort()\\n    Y.sort()\\n    print((max(X[-1] - X[0], Y[-1] - Y[0])))\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"import numpy as np\\nN = int(input())\\n\\nx = []\\ny = []\\nxy1 = []\\nxy2 = []\\n\\nfor i in range(N):\\n    a, b = (int(t) for t in input().split())\\n    x.append(a)\\n    y.append(b)\\n    xy1.append(a + b)\\n    xy2.append(a - b)\\n\\nmax1 = max(xy1) - min(xy1)\\nmax2 = max(xy2) - min(xy2)\\nprint((max((max1, max2))))\\n\", \"def manhattan(n, x, y):\\n    x2 = [0] * n\\n    y2 = [0] * n\\n    for i in range(n):\\n        x2[i] = x[i] - y[i]\\n        y2[i] = x[i] + y[i]\\n    print((max(max(x2) - min(x2), max(y2) - min(y2))))\\n\\nn = int(input())\\nx = [0] * n\\ny = [0] * n\\nfor i in range(n):\\n    x[i] , y[i] = list(map(int, input().split()))\\nmanhattan(n, x, y)\\n\", \"# -*- coding: utf-8 -*-\\n\\nN = int(input())\\n\\nXY = []\\nfor n in range(N):\\n    (x, y) = (int(i) for i in input().split())\\n    XY.append([x, y])\\n\\nplus = []\\nminus = []\\nfor [x, y] in XY:\\n    plus.append(x + y)\\n    minus.append(x - y)\\n\\nprint((max(max(plus)- min(plus), max(minus) - min(minus))))\\n\", \"_,*Z=open(0);A,B=[],[]\\nfor z in Z:x,y=map(int,z.split());A+=[x+y];B+=[x-y]\\nprint(max(max(A)-min(A),max(B)-min(B)))\", \"N=int(input())\\na = []\\nb = []\\nfor i in range(N):\\n  x,y=map(int,input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\nA = max(a)-min(a)\\nB = max(b)-min(b)\\nprint(max(A,B))\", \"n=int(input())\\nzmi=wmi=int(1e+10)\\nzma=wma=int(-1e+10)\\nfor i in range(n):\\n    xi,yi=list(map(int,input().split()))\\n    zma=max(xi+yi,zma)\\n    wma=max(xi-yi,wma)\\n    zmi=min(xi+yi,zmi)\\n    wmi=min(xi-yi,wmi)\\nprint((max(zma-zmi,wma-wmi)))\\n\", \"n = int(input())\\nk = [0] * n\\nl = [0] * n\\nfor i in range(n):\\n  x, y = [int(i) for i in input().split()]\\n  k[i] = x + y\\n  l[i] = x - y\\nprint(max(max(k)-min(k), max(l)-min(l)))\", \"def main():\\n    N = int(input())\\n    x, y = list(map(int, input().split()))\\n    a1 = x + y\\n    a2 = x + y\\n    b1 = y - x\\n    b2 = y - x\\n    N -= 1\\n    while N != 0:\\n        x, y = list(map(int, input().split()))\\n        a1 = max(a1, x + y)\\n        a2 = min(a2, x + y)\\n        b1 = max(b1, y - x)\\n        b2 = min(b2, y - x)\\n        N = N - 1\\n    print((max(a1 - a2, b1 - b2)))\\n\\nmain()\\n\", \"N =  int(input())\\nA =  [list(map(int, (input().split(' ')))) for i in range(N)]\\n\\nhoge = [sum(a) for a in A]\\nfuga = [a[0] - a[1] for a in A]\\nprint((max(max(hoge) - min(hoge), max(fuga) - min(fuga))))\\n\", \"n = int(input())\\n\\np_one = input()\\np_one_list = p_one.split(' ')\\n\\nzmax = int(p_one_list[0]) + int(p_one_list[1])\\nzmin = int(p_one_list[0]) + int(p_one_list[1])\\nwmax = int(p_one_list[0]) - int(p_one_list[1])\\nwmin = int(p_one_list[0]) - int(p_one_list[1])\\n\\n\\nfor i in range(1, n):\\n    line = input()\\n    tmp = line.split(' ')\\n    z = int(tmp[0]) + int(tmp[1])\\n    w = int(tmp[0]) - int(tmp[1])\\n    zmax = max(zmax, z)\\n    wmax = max(wmax, w)\\n    zmin = min(zmin, z)\\n    wmin = min(wmin, w)\\n\\n\\nz_ans = zmax - zmin\\nw_ans = wmax - wmin\\n\\n\\nprint(f'{max(z_ans, w_ans)}')\\n\", \"N=int(input())\\nL=[list(map(int,input().split())) for i in range(N)]\\nzmax=zmin=L[0][0]+L[0][1]\\nwmax=wmin=L[0][0]-L[0][1]\\nfor a,b in L:\\n    z,w=a+b,a-b\\n    zmax=max(zmax,z)\\n    zmin=min(zmin,z)\\n    wmax=max(wmax,w)\\n    wmin=min(wmin,w)\\nprint(max(zmax-zmin,wmax-wmin))\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nimport heapq#.heapify:Priority Queue\\u306b\\u5909\\u63db \\n#.heappop:\\u6700\\u5c0f\\u5024\\u53d6\\u5f97, .heappush:\\u8981\\u7d20\\u633f\\u5165\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\nimport numpy as np  \\nfrom scipy.spatial.distance import euclidean, cityblock  \\n\\nn = k()\\np = 0\\n\\na = []\\nb = []\\nfor i in range(n):\\n    A,B = I()\\n    a.append(A)\\n    b.append(B)\\n\\nz = []\\nw = []\\n\\nfor i in range(n):\\n    z.append(a[i]+b[i])\\n    w.append(a[i]-b[i])\\n\\nprint((max(max(z)-min(z), max(w)-min(w))))\\n\", \"N = int(input())\\na,b = [], []\\nfor i in range(N):\\n  x,y = map(int, input().split())\\n  a.append(x-y)\\n  b.append(x+y)\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"n=int(input())\\na,b,c,d=2*10**9,0,10**9,-10**9\\n\\nfor i in range(n):\\n  x,y=list(map(int,input().split()))\\n  a=min(a,x+y)\\n  b=max(b,x+y)\\n  c=min(c,y-x)\\n  d=max(d,y-x)\\n\\nprint((max(b-a,d-c)))\\n\", \"n = int(input())\\nz = []\\nw = []\\nfor i in range(n):\\n    x,y = map(int,input().split())\\n    z.append(x+y)\\n    w.append(x-y)\\nzmax = max(z)-min(z)\\nwmax = max(w)-min(w)\\nprint(max(zmax,wmax))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\nn = int(input())\\nA = [[int(i) for i in input().split()]for j in range(n)]    # n\\u306f\\u884c\\u6570\\n\\ntmp = 0\\nres = 0\\n\\nul = INF\\nur = INF\\nbl = INF\\nbr = INF\\nul_index = 0\\nur_index = 0\\nbl_index = 1\\nbr_index = 1\\nfor i in range(n):\\n    x, y = A[i]\\n    if x + 10e9 - y <= ul:\\n        ul = x + 10e9 - y\\n        ul_index = i\\n    if 10e9 - x + 10e9 - y <= ur:\\n        ur = 10e9 - x + 10e9 - y\\n        ur_index = i\\n    if x + y <= bl:\\n        bl = x + y\\n        bl_index = i\\n    if 10e9 - x + y <= br:\\n        br = 10e9 - x + y\\n        br_index = i\\nres = max(abs(A[ul_index][0] - A[br_index][0]) + abs(A[ul_index][1] - A[br_index][1]), abs(A[ur_index][0] - A[bl_index][0]) + abs(A[ur_index][1] - A[bl_index][1]))\\n\\nprint(res)\\n\", \"n= int(input())\\na = [list(map(int, input().split())) for i in range(n)]\\nb = []\\nc = []\\nfor i in range(n):\\n  b.append(a[i][0]+a[i][1])\\n  c.append(a[i][0]-a[i][1])\\nmaxbc=[max(b)-min(b), max(c)-min(c)]\\nprint(max(maxbc))\", \"def main():\\n    n = int(input())\\n    pt = []\\n    for _ in range(n):\\n        x,y = map(int,input().split())\\n        pt.append([x,y])\\n    a,b,c = [],[],[]\\n    for p in pt:\\n        a.append(p[0]+p[1])\\n        b.append(p[0]-p[1])\\n        c.append(p[1]-p[0])\\n    ans = 0\\n    if max(a)-min(a)>ans:\\n        ans = max(a)-min(a)\\n    if max(b)-min(b)>ans:\\n        ans = max(b)-min(b)\\n    if max(c)-min(c)>ans:\\n        ans = max(c)-min(c)\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"#!/usr/bin/env python3\\n\\n\\ndef main():\\n    n = int(input())\\n\\n    ls = []\\n    for i in range(n):\\n        p = list(map(int, input().split()))\\n        np = (p[0] + p[1], p[0] - p[1])\\n        ls.append(np)\\n\\n    minx = float(\\\"inf\\\")\\n    miny = float(\\\"inf\\\")\\n    maxx = -float(\\\"inf\\\")\\n    maxy = -float(\\\"inf\\\")\\n\\n    for i in range(len(ls)):\\n        x, y = ls[i]\\n        minx = min(minx, x)\\n        miny = min(miny, y)\\n        maxx = max(maxx, x)\\n        maxy = max(maxy, y)\\n\\n    print((max(maxx - minx, maxy - miny)))\\n\\n\\nmain()\\n\\n\", \"N=int(input())\\nz=[]\\nw=[]\\nfor _ in range(N):\\n    x,y=map(int,input().split())\\n    z.append(x+y)\\n    w.append(x-y)\\nz.sort()\\nw.sort()\\nans=max(abs(z[-1]-z[0]),abs(w[-1]-w[0]))\\nprint(ans)\", \"N = int(input())\\n\\nxyp = []\\nxym = []\\n\\nfor _ in range(N):\\n    x, y = map(int, input().split())\\n    xyp.append(x+y)\\n    xym.append(x-y)\\n    \\nxyp.sort()\\nxym.sort()\\n\\nprint(max(xyp[-1] - xyp[0], xym[-1] - xym[0]))\", \"n = int(input())\\nz,w = [],[]\\nfor _ in range(n):\\n  x,y = map(int,input().split())\\n  z.append(x+y)\\n  w.append(x-y)\\nprint(max(max(z)-min(z),max(w)-min(w)))\", \"import sys\\ninput=sys.stdin.readline\\n\\nn=int(input())\\na,b,c,d=-10**9,10**9,-10**9,10**9\\nfor _ in range(n):\\n\\tx,y=map(int,input().split())\\n\\ta=max(a,x+y)\\n\\tb=min(b,x+y)\\n\\tc=max(c,x-y)\\n\\td=min(d,x-y)\\nprint(max(a-b,c-d))\", \"def solve():\\n    n = int(input())\\n    z = [0 for _ in range(n)]\\n    w = [0 for _ in range(n)]\\n    for i in range(n):\\n        a, b = list(map(int, input().split()))\\n        z[i] = a+b\\n        w[i] = a-b\\n    print((max(max(z)-min(z), max(w)-min(w))))\\n\\n\\ndef __starting_point():\\n    solve()\\n\\n__starting_point()\", \"N = int(input())\\na, b = [], []\\nfor i in range(N):\\n    x, y = list(map(int, input().split()))\\n    a.append(x - y)\\n    b.append(x + y)\\n\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\n\\nprint(ans)\\n\", \"def ans():\\n    N = int(input())\\n    Z = []  # x + y\\n    W = []  # x - y\\n    for _ in range(N):\\n        x, y = map(int, input().split())\\n        Z.append(x + y)\\n        W.append(x - y)\\n\\n    z_max, z_min = max(Z), min(Z)\\n    w_max, w_min = max(W), min(W)\\n\\n    max_d = max((z_max - z_min, w_max - w_min))\\n    print(max_d)\\n\\n\\ndef __starting_point():\\n    ans()\\n__starting_point()\", \"N = int(input())\\n\\nxpy = []\\nxmy = []\\n\\n\\nfor _ in range(N):\\n    x, y = map(int, input().split())\\n\\n    xpy.append(x + y)\\n    xmy.append(x - y)\\n\\nprint(max(max(xpy) - min(xpy), max(xmy) - min(xmy)))\", \"import sys\\n\\nleft_right_max = 0\\nleft_right_min = float('inf')\\nright_left_max = float('-inf')\\nright_left_min = float('inf')\\nr3_max = float('-inf')\\nr3_min = float('inf')\\n\\nn = int(sys.stdin.readline().strip())\\n\\nfor idx in range(n):\\n    x, y = sys.stdin.readline().strip().split(' ')\\n    x = int(x)\\n    y = int(y)\\n\\n    left_right_tmp = x + y\\n    if left_right_tmp > left_right_max:\\n        left_right_max = left_right_tmp\\n    if left_right_tmp < left_right_min:\\n        left_right_min = left_right_tmp\\n\\n    right_left_tmp = x - y\\n    if right_left_tmp > right_left_max:\\n        right_left_max = right_left_tmp\\n    if right_left_tmp < right_left_min:\\n        right_left_min = right_left_tmp\\n        \\n    r3_tmp = y - x\\n    if r3_tmp > r3_max:\\n        r3_max = r3_tmp\\n    if r3_tmp < r3_min:\\n        r3_min = r3_tmp\\n\\nprint(max(left_right_max - left_right_min, right_left_max - right_left_min, r3_max - r3_min))\"]",
        "difficulty": "interview",
        "input": "3\n1 1\n2 4\n3 2\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc178/tasks/abc178_e"
    },
    {
        "id": 256,
        "task_id": 2649,
        "test_case_id": 2,
        "question": "There are N points on the 2D plane, i-th of which is located on (x_i, y_i).\nThere can be multiple points that share the same coordinate.\nWhat is the maximum possible Manhattan distance between two distinct points?\nHere, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.\n\n-----Constraints-----\n - 2 \\leq N \\leq 2 \\times 10^5\n - 1 \\leq x_i,y_i \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\nx_1 y_1\nx_2 y_2\n:\nx_N y_N\n\n-----Output-----\nPrint the answer.\n\n-----Sample Input-----\n3\n1 1\n2 4\n3 2\n\n-----Sample Output-----\n4\n\nThe Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.",
        "solutions": "[\"n = int(input())\\na = []\\nb = []\\nfor i in range(n):\\n  x,y = list(map(int, input().split()))\\n  a.append(x+y)\\n  b.append(x-y)\\na.sort()\\nb.sort()\\n\\nans = a[-1]-a[0]\\nc = b[-1]-b[0]\\nprint((max(ans,c)))\\n\", \"\\n\\ndef main():\\n    n = int(input())\\n    z = [[], []]\\n    for i in range(n):\\n        x, y = list(map(int, input().split()))\\n        z[0].append(x + y)\\n        z[1].append(x - y)\\n    z[0] = sorted(z[0])\\n    z[1] = sorted(z[1])\\n    print((max(z[0][-1] - z[0][0], z[1][-1] - z[1][0])))\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def mdmax(x):\\n    a = []\\n    b = []\\n    for i in range(len(x)):\\n        a.append(x[i][0] - x[i][1])\\n        b.append(x[i][0] + x[i][1])\\n    return max(max(a) - min(a), max(b) - min(b))\\n\\nn = int(input())\\ndata = []\\nfor i in range(n):\\n    ininput_data = input()\\n    input_data = list(map(int, ininput_data.split()))\\n    data.append(input_data)\\nprint(mdmax(data))\", \"N = int(input())\\na,b = [], []\\nfor i in range(N):\\n  x,y = map(int, input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"n = int(input())\\n\\nx, y = [], []\\nfor i in range(n):\\n    xi, yi = map(int, input().split())\\n    x.append(xi+yi)\\n    y.append(xi-yi)\\n\\nx.sort()\\ny.sort()\\n\\nans = max((x[-1]-x[0]), (y[-1]-y[0]))\\nprint(ans)\", \"n = int(input())\\nxy = [list(map(int, input().split())) for i in range(n)]\\nans = []\\nl = [xy[i][0]+xy[i][1] for i in range(n)]\\nans.append(max(l)-min(l))\\nl = [xy[i][0]-xy[i][1] for i in range(n)]\\nans.append(max(l)-min(l))\\nl = [-xy[i][0]+xy[i][1] for i in range(n)]\\nans.append(max(l)-min(l))\\nl = [-xy[i][0]-xy[i][1] for i in range(n)]\\nans.append(max(l)-min(l))\\nprint(max(ans))\", \"n=int(input())\\nzp=[]\\nzl=[]\\nfor i in range(n):\\n    a,b=map(int,input().split())\\n    zp.append(a+b)\\n    zl.append(a-b)\\nans=max((max(zp)-min(zp)),(max(zl)-min(zl)))\\nprint(ans)\", \"def solve(n, x, y):\\n    z = [u + v for u, v in zip(x, y)]\\n    w = [u - v for u, v in zip(x, y)]\\n    return max([max(z) - min(z), max(w) - min(w)])\\n\\nn = int(input())\\nx, y = zip(*[map(int, input().split()) for i in range(n)])\\nprint(solve(n, x, y))\", \"N=int(input())\\nA=[]\\nB=[]\\nfor _ in range(N):\\n    x,y=map(int, input().split())\\n    A.append(x+y)\\n    B.append(x-y)\\n\\nA=sorted(A)\\nB=sorted(B)\\n\\nprint(max(A[-1]-A[0],B[-1]-A[0],A[-1]-A[0],B[-1]-B[0]))\", \"n = int(input())\\nu = []\\nv = []\\nfor i in range(n):\\n    x, y = map(int, input().split())\\n    u.append(x + y)\\n    v.append(x - y)\\n    \\nu.sort()\\nv.sort()\\nprint(max(u[-1] - u[0], v[-1] - v[0]))\", \"import sys\\n\\ndef solve():\\n    input = sys.stdin.readline\\n    N = int(input())\\n    dx = []\\n    dy = []\\n    for _ in range(N):\\n        x, y = map(int, input().split())\\n        dx.append(x + y)\\n        dy.append(x - y)\\n    dx.sort()\\n    dy.sort()\\n    print(max(dx[N-1] - dx[0], dy[N-1] - dy[0]))\\n\\n    return\\n\\ndef __starting_point():\\n    solve()\\n__starting_point()\", \"n=int(input())\\na,b,c,d=-10**9,10**9,-10**9,10**9\\nfor _ in range(n):\\n\\tx,y=map(int,input().split())\\n\\ta=max(a,x+y)\\n\\tb=min(b,x+y)\\n\\tc=max(c,x-y)\\n\\td=min(d,x-y)\\nprint(max(a-b,c-d))\", \"n=int(input())\\nxy=[list(map(int, input().split())) for i in range(n)]\\nz=list(map(lambda x: x[0]+x[1], xy))\\nw=list(map(lambda x: x[0]-x[1], xy))\\nprint(max(max(z)-min(z), max(w)-min(w)))\", \"N = int(input())\\nx, y = map(int, input().split())\\nd = [x - y, x - y, x + y, x + y]\\nfor i in range(1,N):\\n  x, y = map(int, input().split())\\n  d[0] = max(d[0], x-y)\\n  d[1] = min(d[1], x-y)\\n  d[2] = max(d[2], x+y)\\n  d[3] = min(d[3], x+y)\\nprint(max(d[0]-d[1], d[2]-d[3]))\", \"# coding: utf-8\\n# Your code here!\\nN=int(input())\\n\\nZ=[]\\nW=[]\\n\\nfor _ in range(N):\\n    x,y=map(int,input().split())\\n    Z.append(x+y)\\n    W.append(x-y)\\n    \\nprint(max(max(Z)-min(Z),max(W)-min(W)))\", \"n = int(input())\\nxy_array = [list(map(int, input().split())) for _ in range(n)]\\n\\nth = pow(10, 9)\\nright_up_max = -th\\nleft_down_min = th\\nleft_up_max = -th\\nright_down_min = th\\n\\nfor x, y in xy_array:\\n    right_up_max = max(x + y, right_up_max)\\n    left_down_min = min(x + y, left_down_min)\\n    left_up_max = max(x - y, left_up_max)\\n    right_down_min = min(x - y, right_down_min)\\n\\nans = max(right_up_max - left_down_min, left_up_max - right_down_min)\\nprint(ans)\", \"# import itertools\\n# import math\\n# from functools import reduce\\n# import sys\\n# sys.setrecursionlimit(500*500)\\n# import numpy as np\\n# from collections import deque\\n# import heapq\\n\\n# \\u5165\\u529b\\nN = int(input())\\n# S = input()\\n# n, *a = map(int, open(0))\\n# H, N = map(int, input().split())\\n# A = list(map(int, input().split()))\\n# A = list(map(lambda x: int(x)*(-1), input().split()))\\n# B = list(map(int, input().split()))\\nx_y = [list(map(int,input().split())) for _ in range(N)]\\n# S = input()\\n\\n# B_C = sorted(B_C, reverse=True, key=lambda x:x[1])\\n# all_cases = list(itertools.permutations(P))\\n# a = list(itertools.combinations_with_replacement(range(1, M + 1), N))\\n# itertools.product((0,1), repeat=n)\\n\\n# A = np.array(A)\\n# cum_A = np.cumsum(A)\\n# cum_A = np.insert(cum_A, 0, 0)\\n\\n# edges = [list(map(int,input().split())) for _ in range(N - 1)]\\n# tree = [[] for _ in range(N + 1)]\\n\\n# for edge in edges:\\n#     tree[edge[0]].append(edge[1])\\n#     tree[edge[1]].append(edge[0])\\n\\n# depth = [-1] * (N + 1)\\n# depth[1] = 0\\n# count = [0] * (N + 1)\\n\\n# for i in range(Q):\\n#     p, x = map(int, input().split())\\n#     count[p] += x\\n\\n# def dfs(tree, s):\\n#     for l in tree[s]:\\n#         if depth[l[0]] == -1:\\n#             depth[l[0]] = depth[s] + 1\\n#             dfs(tree, l[0])\\n# dfs(tree, 1)\\n\\n# \\u7d20\\u56e0\\u6570\\u5206\\u89e3\\n# def factorization(n):\\n#     arr = []\\n#     temp = n\\n#     for i in range(2, int(-(-n**0.5//1))+1):\\n#         if temp%i==0:\\n#             cnt=0\\n#             while temp%i==0:\\n#                 cnt+=1\\n#                 temp //= i\\n#             arr.append([i, cnt])\\n#     if temp!=1:\\n#         arr.append([temp, 1])\\n#     if arr==[]:\\n#         arr.append([n, 1])\\n#     return arr\\n\\n# \\u7d04\\u6570\\u5217\\u6319\\n# def make_divisors(n):\\n#     lower_divisors , upper_divisors = [], []\\n#     i = 1\\n#     while i*i <= n:\\n#         if n % i == 0:\\n#             lower_divisors.append(i)\\n#             if i != n // i:\\n#                 upper_divisors.append(n//i)\\n#         i += 1\\n#     return lower_divisors + upper_divisors[::-1]\\n\\n# bfs\\n# tree = [[] for _ in range(N + 1)]\\n# edges = [list(map(int,input().split())) for _ in range(M)]\\n\\n# for edge in edges:\\n#     tree[edge[0]].append(edge[1])\\n#     tree[edge[1]].append(edge[0])\\n\\n# depth = [-1] * (N + 1)\\n# depth[1] = 0\\n\\n# d = deque()\\n# d.append(1)\\n\\n# ans = [0] * (N + 1)\\n# while d:\\n#  v = d.popleft()\\n#  for i in tree[v]:\\n#    if depth[i] != -1:\\n#      continue\\n#    depth[i] = depth[v] + 1\\n#    ans[i] = v\\n#    d.append(i)\\n\\n# # ans = depth[2:]\\n# print('Yes')\\n# print(*ans[2:], sep=\\\"\\\\n\\\")\\n\\n# def gcd_list(numbers):\\n#     return reduce(math.gcd, numbers)\\n\\n# # \\u9ad8\\u901f\\u7d20\\u56e0\\u6570\\u5206\\u89e3\\u6e96\\u5099\\n# MAXN = 10**6+10\\n# sieve = [i for i in range(MAXN+1)]\\n# p = 2\\n# while p*p <= MAXN:\\n#     if sieve[p] == p:\\n#         for q in range(2*p, MAXN+1, p):\\n#             if sieve[q] == q:\\n#                 sieve[q] = p\\n#     p += 1\\n\\n\\n# 45\\u5ea6\\u56de\\u8ee2\\nZ = []\\nW = []\\nfor l in x_y:\\n    Z.append(l[0] + l[1])\\n    W.append(l[0] - l[1])\\n\\nprint(max((max(Z) - min(Z)), (max(W) - min(W))))\", \"a,b=[],[]\\nn=int(input())\\nfor _ in range(n):\\n  x,y=map(int,input().split())\\n  a+=[x-y]\\n  b+=[x+y]\\nprint(max(max(a)-min(a),max(b)-min(b)))\", \"n=int(input())\\na,b=[],[]\\nfor i in range(n):\\n  x,y=list(map(int,input().split()))\\n  a.append(x+y)\\n  b.append(x-y)\\nprint((max(max(a)-min(a),max(b)-min(b))))\\n\", \"N = int(input())\\na = []\\nb = []\\nfor i in range(N):\\n  x,y = map(int, input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\n\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"n = int(input())\\na = [0] * n\\nb = [0] * n\\nfor i in range(n):\\n    x, y = list(map(int, input().split()))\\n    a[i] = x + y\\n    b[i] = x - y\\nprint((max(max(a) - min(a), max(b) - min(b))))\\n\", \"N=int(input())\\n\\na,b=[],[]\\n\\nfor i in range(N):\\n  x,y=map(int,input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\na.sort()\\nb.sort()\\n\\nans=max(a[-1]-a[0],b[-1]-b[0])\\nprint(ans)\", \"n=int(input())\\na=[]\\nj=k=0\\ndef s(a):\\n    return a[0]+a[1]\\ndef ss(a):\\n    return a[0]-a[1]\\nfor i in range(n):\\n    f=list(map(int,input().split()))\\n    a.append(f)\\naa=min(map(s,a))\\nb=max(map(s,a))\\nc=min(map(ss,a))\\nd=max(map(ss,a))\\nprint(max(abs(d-c),abs(b-aa)))\", \"n = int(input())\\na, b = [], []\\nfor _ in range(n):\\n    x, y = map(int, input().split())\\n    a.append(x+y)\\n    b.append(x-y)\\n \\na.sort()\\nb.sort()\\n \\nans = max(a[-1]-a[0], b[-1]-b[0])\\nprint(ans)\", \"n=int(input())\\nl=[]\\nar=[]\\nbr=[]\\nfor i in range(n):\\n  l.append(list(map(int,input().split())))\\n  ar.append(l[-1][0]+l[-1][1])\\n  br.append(l[-1][0]-l[-1][1])\\nar.sort()\\nbr.sort()\\nan=max(abs(ar[-1]-ar[0]),abs(br[-1]-br[0]))\\nprint(an)\", \"N = int(input())\\nXY = [list(map(int, input().split())) for _ in range(N)]\\n\\nz = []\\nw = []\\nfor x, y in XY:\\n    z.append(x + y)\\n    w.append(x - y)\\n\\nprint(max(max(z) - min(z), max(w) - min(w)))\", \"n=int(input())\\nmaxa=maxb=-2e9\\nmina=minb=2e9\\nfor i in range(n):\\n  x,y=list(map(int,input().split()))\\n  maxa=max(maxa,x+y)\\n  mina=min(mina,x+y)\\n  maxb=max(maxb,x-y)\\n  minb=min(minb,x-y)\\nprint((max(maxa-mina,maxb-minb)))\\n\", \"N = int(input())\\nL = [[int(l) for l in input().split()] for _ in range(N)]\\n\\nL1 = [0]*N\\nL2 = [0]*N\\nfor i in range(N):\\n    L1[i] = L[i][0]+L[i][1]\\n    L2[i] = L[i][0]-L[i][1]\\n\\nL1.sort()\\nL2.sort()\\nprint(max(L1[-1]-L1[0], L2[-1]-L2[0]))\", \"N = int(input())\\nxy = [list(map(int, input().split())) for _ in range(N)]\\n\\nadd = sorted([x+y for x, y in xy])\\nsub = sorted([x-y for x, y in xy])\\n\\nprint(max(add[-1]-add[0], sub[-1]-sub[0]))\", \"n=int(input())\\nlx=[]\\nly=[]\\nfor i in range(n):\\n  x,y=map(int,input().split())\\n  lx.append(x+y)\\n  ly.append(x-y)\\nprint(max(max(lx)-min(lx),max(ly)-min(ly)))\", \"N = int(input())\\nl0 = [[int(i) for i in input().split()] for _ in range(N)]\\nl1 = [0] * N\\nl2 = [0] * N\\nfor cnt, val in enumerate(l0):\\n    l1[cnt] = val[0] + val[1]\\n    l2[cnt] = val[0] - val[1]\\nl1.sort()\\nl2.sort()\\nprint((max(l1[-1] - l1[0], l2[-1] - l2[0])))\\n\", \"def main():\\n    n = int(input())\\n    xym, xyM, x_ym, x_yM = 10**9, -10**9, 10**9, -10**9\\n    for _ in range(n):\\n        x, y = map(int, input().split())\\n        xy, x_y = x+y, x-y\\n        xym, xyM, x_ym, x_yM = min(xym, xy), max(xyM, xy), min(x_ym, x_y), max(x_yM, x_y)\\n    print(max(xyM-xym, x_yM-x_ym))\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N=int(input())\\nA=[0]*(N)\\nB=[0]*(N)\\nfor i in range(N):\\n    x,y=map(int, input().split())\\n    A[i]=x+y\\n    B[i]=x-y\\n\\nA=sorted(A)\\nB=sorted(B)\\n\\nprint(max(A[-1]-A[0],B[-1]-A[0],A[-1]-A[0],B[-1]-B[0]))\", \"n = int(input())\\nu = []\\nv = []\\nfor i in range(n):\\n    x, y = map(int, input().split())\\n    u.append(x + y)\\n    v.append(x - y)\\n    \\nu.sort()\\nv.sort()\\nprint(max(u[-1] - u[0], v[-1] - v[0]))\", \"N = int(input())\\nA = []; B = []\\nfor i in range(N):\\n  x,y = map(int,input().split())\\n  a = x+y; A.append(a)\\n  b = x-y; B.append(b)\\nA.sort();B.sort()\\nMax_A = A[-1] - A[0]\\nMax_B = B[-1] - B[0]\\nans = max(Max_A,Max_B)\\nprint(ans)\", \"import sys\\n\\nleft_right_max = 0\\nleft_right_min = float('inf')\\nright_left_max = float('-inf')\\nright_left_min = float('inf')\\nr3_max = float('-inf')\\nr3_min = float('inf')\\n\\nn = int(sys.stdin.readline().strip())\\n\\nfor idx in range(n):\\n    x, y = sys.stdin.readline().strip().split(' ')\\n    x = int(x)\\n    y = int(y)\\n\\n    left_right_tmp = x + y\\n    if left_right_tmp > left_right_max:\\n        left_right_max = left_right_tmp\\n      \\n    if left_right_tmp < left_right_min:\\n        left_right_min = left_right_tmp\\n        #res_lr[2] = (x, y)\\n\\n    right_left_tmp = x - y\\n    if right_left_tmp > right_left_max:\\n        right_left_max = right_left_tmp\\n        #res_rl[1] = (x, y)\\n    if right_left_tmp < right_left_min:\\n        right_left_min = right_left_tmp\\n        #res_rl[2] = (x, y)\\n        \\n    r3_tmp = y - x\\n    if r3_tmp > r3_max:\\n        r3_max = r3_tmp\\n        #res_3[1] = (x, y)\\n    if r3_tmp < r3_min:\\n        r3_min = r3_tmp\\n        #res_3[2] = (x, y)\\n\\nreslr_dist = left_right_max - left_right_min\\nresrl_dist = right_left_max - right_left_min\\nres3_dist = r3_max - r3_min\\n\\nprint((max(resrl_dist, reslr_dist, res3_dist)))\\n\", \"N = int(input())\\nlst = []\\nfor i in range(N):\\n    lst.append(tuple(map(lambda i: int(i), input().split())))\\nlstP = [xy[0]+xy[1] for xy in lst]\\nlstM = [xy[0]-xy[1] for xy in lst]\\nlstP, lstM\\nz = max(lstP) - min(lstP)\\nw = max(lstM) - min(lstM)\\nprint(max(z,w))\", \"import sys\\nfrom operator import itemgetter\\n\\nN = int(input())\\nV = set()\\nfor s in sys.stdin.readlines():\\n    x, y = list(map(int, s.split()))\\n    V.add((x + y, x - y))\\n\\ny_max = max(V, key=itemgetter(1))[1]\\ny_min = min(V, key=itemgetter(1))[1]\\nx_max = max(V, key=itemgetter(0))[0]\\nx_min = min(V, key=itemgetter(0))[0]\\n\\nprint((max(x_max - x_min, y_max - y_min)))\\n\", \"N = int(input())\\na = list()\\nb = list()\\nfor i in range(N):\\n  x,y = map(int, input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"def get_ints():\\n    return list(map(int,input().split()))\\n\\nn = int(input())\\na, b = [], []\\nfor i in range(n):\\n    x, y = get_ints()\\n    a.append(x-y)\\n    b.append(x+y)\\n\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"\\\"\\\"\\\"AtCoder Beginner Contest 178.\\n\\nE\\n\\\"\\\"\\\"\\n\\nimport sys\\n\\n\\ndef input() -> str:  # noqa: A001\\n    \\\"\\\"\\\"Input.\\\"\\\"\\\"\\n    return sys.stdin.readline()[:-1]\\n\\n\\ndef calc(p1: list, p2: list) -> int:\\n    \\\"\\\"\\\"Calc Manhattan Distance.\\\"\\\"\\\"\\n    return abs(p2[1] - p1[1]) + abs(p2[0] - p1[0])\\n\\n\\ndef main():\\n    \\\"\\\"\\\"Run.\\\"\\\"\\\"\\n    n = int(input())\\n\\n    patterns = {\\n        'lt': (1, 1),\\n        'rt': (-1, 1),\\n        'lb': (-1, -1),\\n        'rb': (1, -1),\\n    }\\n\\n    points: dict = {k: None for k in list(patterns.keys())}\\n\\n    for _ in range(n):\\n        p = list(map(int, input().split(' ')))\\n\\n        for k, (x, y) in list(patterns.items()):\\n            max_p = points[k]\\n\\n            if max_p:\\n                max_p_pos = (max_p[0] * x) + (max_p[1] * y)\\n                p_pos = (p[0] * x) + (p[1] * y)\\n                if max_p_pos < p_pos:\\n                    points[k] = p\\n            else:\\n                points[k] = p\\n\\n    ans = 0\\n    for i, p1 in enumerate(points.values()):\\n        for p2 in list(points.values())[i + 1:]:\\n            ans = max(ans, calc(p1, p2))\\n\\n    print(ans)\\n\\n\\nmain()\\n\", \"import sys\\nreadline = sys.stdin.readline\\n\\nN = int(readline())\\nX,Y = [None] * N, [None] * N\\nfor i in range(N):\\n  x,y = list(map(int,readline().split()))\\n  X[i],Y[i] = x + y,x - y\\n\\nprint((max(abs(max(X) - min(X)),abs(max(Y) - min(Y)))))\\n\", \"n = int(input())\\na, b = [], []\\nfor _ in range(n):\\n    x, y = map(int, input().split())\\n    a.append(x+y)\\n    b.append(x-y)\\n\\na.sort()\\nb.sort()\\n\\nans = max(a[-1]-a[0], b[-1]-b[0])\\nprint(ans)\", \"#!/usr/bin/env python3\\n\\n\\ndef get_points_and_convert(pts):\\n    x, y = pts\\n    return x + y, x - y\\n\\n\\ndef main():\\n    n = int(input())\\n    points = [\\n        get_points_and_convert(list(map(int, input().split())))\\n        for _ in range(n)\\n    ]\\n    plus_coords, minus_coords = list(zip(*points))\\n    plus_dist = max(plus_coords) - min(plus_coords)\\n    minus_dist = max(minus_coords) - min(minus_coords)\\n    print((max(plus_dist, minus_dist)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nXY = [[int(_) for _ in input().split()] for _ in range(N)]\\nans = -1\\nfor dx, dy in ((1, 1), (-1, 1), (-1, -1), (1, -1)):\\n    xy2 = [x * dx + y * dy for x, y in XY]\\n    ans = max(ans, max(xy2) - min(xy2))\\nprint(ans)\\n\", \"N = int(input())\\nA = [0]*N\\nB = [0]*N\\nfor i in range(N):\\n  x,y = map(int,input().split())\\n  A[i] = x+y\\n  B[i] = x-y\\na = max(A)-min(A)\\nb = max(B)-min(B)\\nprint(max(a,b))\", \"n = int(input())\\nl = [[] for i in range(4)]\\nfor i in range(n):\\n    x, y = list(map(int, input().split()))\\n    l[0].append(x+y)\\n    l[1].append(x-y)\\n    l[2].append(-x+y)\\n    l[3].append(-x-y)\\nfor i in range(4):\\n    l[i].sort()\\nans = 0\\nfor i in range(4):\\n    ans = max(ans, l[i][-1] - l[i][0])\\nprint(ans)\\n\", \"N = int(input())\\na = []\\nb = []\\nfor i in range(N):\\n  x,y = map(int,input().split())\\n  a.append(x-y)\\n  b.append(x+y)\\n  \\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"N=int(input())\\nzls=[0 for _ in range(N)]\\nwls=[0 for _ in range(N)]\\nfor i in range(N):\\n  x,y=[int(s) for s in input().split()]\\n  zls[i]=x+y\\n  wls[i]=x-y\\nprint(max([max(zls)-min(zls),max(wls)-min(wls)]))\", \"n=int(input())\\na=[]\\nb=[]\\nfor i in range(n):\\n  x,y=map(int,input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\nprint(max(max(a)-min(a),max(b)-min(b)))\", \"import sys\\nimport re\\nimport queue\\nfrom math import ceil, floor, sqrt, pi, factorial, gcd\\nfrom copy import deepcopy\\nfrom collections import Counter, deque\\nfrom heapq import heapify, heappop, heappush\\nfrom itertools import accumulate, product, combinations, combinations_with_replacement\\nfrom bisect import bisect, bisect_left, bisect_right\\nfrom functools import reduce\\nfrom decimal import Decimal, getcontext\\n# input = sys.stdin.readline\\ndef i_input(): return int(input())\\ndef i_map(): return map(int, input().split())\\ndef i_list(): return list(i_map())\\ndef i_row(N): return [i_input() for _ in range(N)]\\ndef i_row_list(N): return [i_list() for _ in range(N)]\\ndef s_input(): return input()\\ndef s_map(): return input().split()\\ndef s_list(): return list(s_map())\\ndef s_row(N): return [s_input for _ in range(N)]\\ndef s_row_str(N): return [s_list() for _ in range(N)]\\ndef s_row_list(N): return [list(s_input()) for _ in range(N)]\\ndef lcm(a, b): return a * b // gcd(a, b)\\nsys.setrecursionlimit(10 ** 6)\\nINF = float('inf')\\nMOD = 10 ** 9 + 7\\nnum_list = []\\nstr_list = []\\n\\n\\n\\ndef main():\\n\\tN = i_input()\\n\\n\\tx_y_list = []\\n\\n\\tfor i in range(0,N):\\n\\t\\ttmpx,tmpy = i_map()\\n\\t\\tx_y_list.append((tmpx,tmpy))\\n\\n\\tz_list = []\\n\\tw_list = []\\n\\tfor i in range(0,N):\\n\\t\\ttmpz = x_y_list[i][0] + x_y_list[i][1]\\n\\t\\ttmpw = x_y_list[i][0] - x_y_list[i][1]\\n\\t\\tz_list.append(tmpz)\\n\\t\\tw_list.append(tmpw)\\n\\n\\tprint(max(max(map(lambda x : (x),z_list))-min(map(lambda x: (x), z_list)),max(map(lambda x : (x),w_list))-min(map(lambda x: (x),w_list))))\\n\\t\\n\\treturn\\n\\n\\ndef __starting_point():\\n\\tmain()\\n__starting_point()\", \"n=int(input())\\na,b,c,d=2*10**9,0,10**9,-10**9\\n\\nfor i in range(n):\\n  x,y=list(map(int,input().split()))\\n  a=a if a<x+y else x+y\\n  b=b if b>x+y else x+y\\n  c=c if c<y-x else y-x\\n  d=d if d>y-x else y-x\\n\\nprint((b-a if b-a>d-c else d-c))\\n\", \"n=int(input())\\np=[]\\nq=[]\\nfor _ in range(n):\\n  x,y=map(int,input().split())\\n  p.append(x+y)\\n  q.append(x-y)\\nprint(max(max(p)-min(p),max(q)-min(q)))\", \"n=int(input())\\nl=[list(map(int,input().split())) for i in range(n)]\\na=10**9\\nz_max=-1*a\\nz_min=a\\nw_max=-1*a\\nw_min=a\\nfor x,y in l: #\\u70b9\\u306ex\\u5ea7\\u6a19\\u3068y\\u5ea7\\u6a19\\u306e\\u548c\\u306e\\u6700\\u5927\\u5024\\u3068\\u6700\\u5c0f\\u5024\\u306e\\u5dee\\u304b\\u5ea7\\u6a19\\u306e\\u5dee\\u306e\\u6700\\u5927\\u5024\\u3068\\u6700\\u5c0f\\u5024\\u306e\\u5dee\\u304c\\u7b54\\u3048\\n  z_max=max(z_max,x+y)\\n  z_min=min(z_min,x+y)\\n  w_max=max(w_max,x-y)\\n  w_min=min(w_min,x-y)\\nprint(max(z_max-z_min,w_max-w_min))\", \"n = int(input())\\nu = []\\nv = []\\nfor i in range(n):\\n    x, y = map(int, input().split())\\n    u.append(x + y)\\n    v.append(x - y)\\n    \\nu.sort()\\nv.sort()\\nprint(max(u[-1] - u[0], v[-1] - v[0]))\", \"n = int(input())\\nxy_array = [list(map(int, input().split())) for _ in range(n)]\\n\\nth = pow(10, 9)\\nz_max = -th\\nz_min = th\\nw_max = -th\\nw_min = th\\n\\nfor x, y in xy_array:\\n    z_max = max(x + y, z_max)\\n    z_min = min(x + y, z_min)\\n    w_max = max(x - y, w_max)\\n    w_min = min(x - y, w_min)\\n\\nans = max(z_max - z_min, w_max - w_min)\\nprint(ans)\", \"n = int(input())\\n\\nxy = []\\nfor index in range(n):\\n  x, y = map(int, input().split())\\n  xy.append([x, y])\\n\\npos_max = xy[0][0]+xy[0][1]\\npos_min = xy[0][0]+xy[0][1]\\nneg_max = xy[0][0]-xy[0][1]\\nneg_min = xy[0][0]-xy[0][1]\\nfor item in xy:\\n  pos_v = item[0] + item[1]\\n  neg_v = item[0] - item[1]\\n  pos_max = pos_v if pos_v > pos_max else pos_max\\n  pos_min = pos_v if pos_v < pos_min else pos_min\\n  neg_max = neg_v if neg_v > neg_max else neg_max\\n  neg_min = neg_v if neg_v < neg_min else neg_min\\n\\npos_result = pos_max - pos_min\\nneg_result = neg_max - neg_min\\nprint(pos_result if pos_result >= neg_result else neg_result)\", \"n = int(input())\\nu = []\\nv = []\\nfor _ in range(n):\\n    x, y = list(map(int, input().split()))\\n    u.append(x + y)\\n    v.append(x - y)\\n\\nans = max(max(u) - min(u), max(v) - min(v))\\nprint(ans)\\n\", \"import numpy as np\\ndef solve(n, x, y):\\n    x = np.asarray(x)\\n    y = np.asarray(y)\\n    z = x + y\\n    w = x - y\\n    return max(np.max(z) - np.min(z), np.max(w) - np.min(w))\\n\\nn = int(input())\\nx, y = list(zip(*[list(map(int, input().split())) for i in range(n)]))\\nprint((solve(n, x, y)))\\n\", \"import sys\\ndef Ii():return int(sys.stdin.readline())\\ndef Mi():return map(int,sys.stdin.readline().split())\\ndef Li():return list(map(int,sys.stdin.readline().split()))\\n\\nn = Ii()\\nans = 0\\npoints = []\\nxymax = 0\\nxymin = 10**11\\ndxymax = -10**11\\ndxymin = 10**11\\nfor i in range(n):\\n  point = Li()\\n  xy = point[0]+point[1]\\n  if xy > xymax:\\n    xymax = xy\\n  if xy < xymin:\\n    xymin = xy\\n  dxy = point[0]-point[1]\\n  if dxy > dxymax:\\n    dxymax = dxy\\n  if dxy < dxymin:\\n    dxymin = dxy\\nans = max(dxymax-dxymin,xymax-xymin)\\nprint(ans)\", \"n = int(input())\\n# n = 2*10**5\\n\\nmin_u = float('inf')\\nmax_u = -float('inf')\\nmin_v = float('inf')\\nmax_v = -float('inf')\\n\\n\\nfor i in range(n):\\n    x, y = list(map(int, input().split()))\\n    # x, y = (10**9 , 10**9)\\n    u, v = (x+y, x-y)\\n    if u <= min_u:\\n        min_u = u\\n    if u >= max_u:\\n        max_u = u\\n    if v <= min_v:\\n        min_v = v\\n    if v >= max_v:\\n        max_v = v\\n\\nprint((max(max_u - min_u, max_v - min_v)))\\n\", \"import numpy as np\\n\\nN = int(input())\\nxy = [list(map(int, input().split())) for _ in range(N)]\\n\\nxy45 = [[xy[i][0] - xy[i][1], xy[i][0] + xy[i][1]] for i in range(N)]\\nxy45 = np.array(xy45)\\n\\nprint((max(max(xy45[:, 0]) - min(xy45[:, 0]), max(xy45[:, 1]) - min(xy45[:, 1]))))\\n\", \"import sys\\n\\n\\ndef input():\\n    return sys.stdin.readline()[:-1]\\n\\n\\nN = int(input())\\n\\nplus = []\\nminus = []\\nfor _ in range(N):\\n    x, y = list(map(int, input().split()))\\n    plus.append(x+y)\\n    minus.append(x-y)\\n\\nprint((max(max(plus)-min(plus), max(minus)-min(minus))))\\n\", \"n = int(input())\\n\\nplus,minus = [],[]\\nfor i in range(n):\\n    a,b = map(int,input().split())\\n    plus.append(a+b)\\n    minus.append(a-b)\\n\\nplus.sort()\\nminus.sort()\\n\\nprint(max(plus[-1]-plus[0],minus[-1]-minus[0]))\", \"def get_ints():\\n  return list(map(int,input().split()))\\n\\nn = int(input())\\na,b = [],[]\\nfor i in range(n):\\n  x,y = get_ints()\\n  a.append(x+y)\\n  b.append(x-y)\\n\\na.sort()\\nb.sort()\\nans = max(a[-1]-a[0], b[-1]-b[0])\\nprint(ans)\\n\\n\\n\\n\", \"n = int(input())\\npoints = [tuple(map(int, input().split())) for _ in range(n)]\\nplus = [p[0] + p[1] for p in points]\\nminus = [p[0] - p[1] for p in points]\\nprint(max(max(plus) - min(plus), max(minus) - min(minus)))\", \"n = int(input())\\na, b = [], []\\n\\nfor _ in range(n):\\n    x, y = list(map(int, input().split()))\\n    a.append(x - y)\\n    b.append(x + y)\\n\\nans = max(max(a) - min(a), max(b) - min(b))\\nprint(ans)\\n\", \"N = int(input())\\nx = [0 for _ in range(N)]\\ny = [0 for _ in range(N)]\\n\\nfor i in range(N):\\n    x[i], y[i] = map(int,input().split())\\n\\nX = [0 for _ in range(N)]\\nY = [0 for _ in range(N)]\\n\\nfor i in range(N):\\n    X[i], Y[i] = x[i] - y[i], x[i] + y[i]\\n\\nans = 0\\nans = max(max(X)-min(X),max(Y)-min(Y))\\n\\nprint(ans)\", \"def main():\\n    n = int(input())\\n    X, Y = [], []\\n    for _ in range(n):\\n        x, y = list(map(int, input().split()))\\n        X.append(x + y)\\n        Y.append(x - y)\\n    X.sort()\\n    Y.sort()\\n    print((max(X[-1] - X[0], Y[-1] - Y[0])))\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"import numpy as np\\nN = int(input())\\n\\nx = []\\ny = []\\nxy1 = []\\nxy2 = []\\n\\nfor i in range(N):\\n    a, b = (int(t) for t in input().split())\\n    x.append(a)\\n    y.append(b)\\n    xy1.append(a + b)\\n    xy2.append(a - b)\\n\\nmax1 = max(xy1) - min(xy1)\\nmax2 = max(xy2) - min(xy2)\\nprint((max((max1, max2))))\\n\", \"def manhattan(n, x, y):\\n    x2 = [0] * n\\n    y2 = [0] * n\\n    for i in range(n):\\n        x2[i] = x[i] - y[i]\\n        y2[i] = x[i] + y[i]\\n    print((max(max(x2) - min(x2), max(y2) - min(y2))))\\n\\nn = int(input())\\nx = [0] * n\\ny = [0] * n\\nfor i in range(n):\\n    x[i] , y[i] = list(map(int, input().split()))\\nmanhattan(n, x, y)\\n\", \"# -*- coding: utf-8 -*-\\n\\nN = int(input())\\n\\nXY = []\\nfor n in range(N):\\n    (x, y) = (int(i) for i in input().split())\\n    XY.append([x, y])\\n\\nplus = []\\nminus = []\\nfor [x, y] in XY:\\n    plus.append(x + y)\\n    minus.append(x - y)\\n\\nprint((max(max(plus)- min(plus), max(minus) - min(minus))))\\n\", \"_,*Z=open(0);A,B=[],[]\\nfor z in Z:x,y=map(int,z.split());A+=[x+y];B+=[x-y]\\nprint(max(max(A)-min(A),max(B)-min(B)))\", \"N=int(input())\\na = []\\nb = []\\nfor i in range(N):\\n  x,y=map(int,input().split())\\n  a.append(x+y)\\n  b.append(x-y)\\nA = max(a)-min(a)\\nB = max(b)-min(b)\\nprint(max(A,B))\", \"n=int(input())\\nzmi=wmi=int(1e+10)\\nzma=wma=int(-1e+10)\\nfor i in range(n):\\n    xi,yi=list(map(int,input().split()))\\n    zma=max(xi+yi,zma)\\n    wma=max(xi-yi,wma)\\n    zmi=min(xi+yi,zmi)\\n    wmi=min(xi-yi,wmi)\\nprint((max(zma-zmi,wma-wmi)))\\n\", \"n = int(input())\\nk = [0] * n\\nl = [0] * n\\nfor i in range(n):\\n  x, y = [int(i) for i in input().split()]\\n  k[i] = x + y\\n  l[i] = x - y\\nprint(max(max(k)-min(k), max(l)-min(l)))\", \"def main():\\n    N = int(input())\\n    x, y = list(map(int, input().split()))\\n    a1 = x + y\\n    a2 = x + y\\n    b1 = y - x\\n    b2 = y - x\\n    N -= 1\\n    while N != 0:\\n        x, y = list(map(int, input().split()))\\n        a1 = max(a1, x + y)\\n        a2 = min(a2, x + y)\\n        b1 = max(b1, y - x)\\n        b2 = min(b2, y - x)\\n        N = N - 1\\n    print((max(a1 - a2, b1 - b2)))\\n\\nmain()\\n\", \"N =  int(input())\\nA =  [list(map(int, (input().split(' ')))) for i in range(N)]\\n\\nhoge = [sum(a) for a in A]\\nfuga = [a[0] - a[1] for a in A]\\nprint((max(max(hoge) - min(hoge), max(fuga) - min(fuga))))\\n\", \"n = int(input())\\n\\np_one = input()\\np_one_list = p_one.split(' ')\\n\\nzmax = int(p_one_list[0]) + int(p_one_list[1])\\nzmin = int(p_one_list[0]) + int(p_one_list[1])\\nwmax = int(p_one_list[0]) - int(p_one_list[1])\\nwmin = int(p_one_list[0]) - int(p_one_list[1])\\n\\n\\nfor i in range(1, n):\\n    line = input()\\n    tmp = line.split(' ')\\n    z = int(tmp[0]) + int(tmp[1])\\n    w = int(tmp[0]) - int(tmp[1])\\n    zmax = max(zmax, z)\\n    wmax = max(wmax, w)\\n    zmin = min(zmin, z)\\n    wmin = min(wmin, w)\\n\\n\\nz_ans = zmax - zmin\\nw_ans = wmax - wmin\\n\\n\\nprint(f'{max(z_ans, w_ans)}')\\n\", \"N=int(input())\\nL=[list(map(int,input().split())) for i in range(N)]\\nzmax=zmin=L[0][0]+L[0][1]\\nwmax=wmin=L[0][0]-L[0][1]\\nfor a,b in L:\\n    z,w=a+b,a-b\\n    zmax=max(zmax,z)\\n    zmin=min(zmin,z)\\n    wmax=max(wmax,w)\\n    wmin=min(wmin,w)\\nprint(max(zmax-zmin,wmax-wmin))\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nimport heapq#.heapify:Priority Queue\\u306b\\u5909\\u63db \\n#.heappop:\\u6700\\u5c0f\\u5024\\u53d6\\u5f97, .heappush:\\u8981\\u7d20\\u633f\\u5165\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\nimport numpy as np  \\nfrom scipy.spatial.distance import euclidean, cityblock  \\n\\nn = k()\\np = 0\\n\\na = []\\nb = []\\nfor i in range(n):\\n    A,B = I()\\n    a.append(A)\\n    b.append(B)\\n\\nz = []\\nw = []\\n\\nfor i in range(n):\\n    z.append(a[i]+b[i])\\n    w.append(a[i]-b[i])\\n\\nprint((max(max(z)-min(z), max(w)-min(w))))\\n\", \"N = int(input())\\na,b = [], []\\nfor i in range(N):\\n  x,y = map(int, input().split())\\n  a.append(x-y)\\n  b.append(x+y)\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\nprint(ans)\", \"n=int(input())\\na,b,c,d=2*10**9,0,10**9,-10**9\\n\\nfor i in range(n):\\n  x,y=list(map(int,input().split()))\\n  a=min(a,x+y)\\n  b=max(b,x+y)\\n  c=min(c,y-x)\\n  d=max(d,y-x)\\n\\nprint((max(b-a,d-c)))\\n\", \"n = int(input())\\nz = []\\nw = []\\nfor i in range(n):\\n    x,y = map(int,input().split())\\n    z.append(x+y)\\n    w.append(x-y)\\nzmax = max(z)-min(z)\\nwmax = max(w)-min(w)\\nprint(max(zmax,wmax))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\nn = int(input())\\nA = [[int(i) for i in input().split()]for j in range(n)]    # n\\u306f\\u884c\\u6570\\n\\ntmp = 0\\nres = 0\\n\\nul = INF\\nur = INF\\nbl = INF\\nbr = INF\\nul_index = 0\\nur_index = 0\\nbl_index = 1\\nbr_index = 1\\nfor i in range(n):\\n    x, y = A[i]\\n    if x + 10e9 - y <= ul:\\n        ul = x + 10e9 - y\\n        ul_index = i\\n    if 10e9 - x + 10e9 - y <= ur:\\n        ur = 10e9 - x + 10e9 - y\\n        ur_index = i\\n    if x + y <= bl:\\n        bl = x + y\\n        bl_index = i\\n    if 10e9 - x + y <= br:\\n        br = 10e9 - x + y\\n        br_index = i\\nres = max(abs(A[ul_index][0] - A[br_index][0]) + abs(A[ul_index][1] - A[br_index][1]), abs(A[ur_index][0] - A[bl_index][0]) + abs(A[ur_index][1] - A[bl_index][1]))\\n\\nprint(res)\\n\", \"n= int(input())\\na = [list(map(int, input().split())) for i in range(n)]\\nb = []\\nc = []\\nfor i in range(n):\\n  b.append(a[i][0]+a[i][1])\\n  c.append(a[i][0]-a[i][1])\\nmaxbc=[max(b)-min(b), max(c)-min(c)]\\nprint(max(maxbc))\", \"def main():\\n    n = int(input())\\n    pt = []\\n    for _ in range(n):\\n        x,y = map(int,input().split())\\n        pt.append([x,y])\\n    a,b,c = [],[],[]\\n    for p in pt:\\n        a.append(p[0]+p[1])\\n        b.append(p[0]-p[1])\\n        c.append(p[1]-p[0])\\n    ans = 0\\n    if max(a)-min(a)>ans:\\n        ans = max(a)-min(a)\\n    if max(b)-min(b)>ans:\\n        ans = max(b)-min(b)\\n    if max(c)-min(c)>ans:\\n        ans = max(c)-min(c)\\n    print(ans)\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"#!/usr/bin/env python3\\n\\n\\ndef main():\\n    n = int(input())\\n\\n    ls = []\\n    for i in range(n):\\n        p = list(map(int, input().split()))\\n        np = (p[0] + p[1], p[0] - p[1])\\n        ls.append(np)\\n\\n    minx = float(\\\"inf\\\")\\n    miny = float(\\\"inf\\\")\\n    maxx = -float(\\\"inf\\\")\\n    maxy = -float(\\\"inf\\\")\\n\\n    for i in range(len(ls)):\\n        x, y = ls[i]\\n        minx = min(minx, x)\\n        miny = min(miny, y)\\n        maxx = max(maxx, x)\\n        maxy = max(maxy, y)\\n\\n    print((max(maxx - minx, maxy - miny)))\\n\\n\\nmain()\\n\\n\", \"N=int(input())\\nz=[]\\nw=[]\\nfor _ in range(N):\\n    x,y=map(int,input().split())\\n    z.append(x+y)\\n    w.append(x-y)\\nz.sort()\\nw.sort()\\nans=max(abs(z[-1]-z[0]),abs(w[-1]-w[0]))\\nprint(ans)\", \"N = int(input())\\n\\nxyp = []\\nxym = []\\n\\nfor _ in range(N):\\n    x, y = map(int, input().split())\\n    xyp.append(x+y)\\n    xym.append(x-y)\\n    \\nxyp.sort()\\nxym.sort()\\n\\nprint(max(xyp[-1] - xyp[0], xym[-1] - xym[0]))\", \"n = int(input())\\nz,w = [],[]\\nfor _ in range(n):\\n  x,y = map(int,input().split())\\n  z.append(x+y)\\n  w.append(x-y)\\nprint(max(max(z)-min(z),max(w)-min(w)))\", \"import sys\\ninput=sys.stdin.readline\\n\\nn=int(input())\\na,b,c,d=-10**9,10**9,-10**9,10**9\\nfor _ in range(n):\\n\\tx,y=map(int,input().split())\\n\\ta=max(a,x+y)\\n\\tb=min(b,x+y)\\n\\tc=max(c,x-y)\\n\\td=min(d,x-y)\\nprint(max(a-b,c-d))\", \"def solve():\\n    n = int(input())\\n    z = [0 for _ in range(n)]\\n    w = [0 for _ in range(n)]\\n    for i in range(n):\\n        a, b = list(map(int, input().split()))\\n        z[i] = a+b\\n        w[i] = a-b\\n    print((max(max(z)-min(z), max(w)-min(w))))\\n\\n\\ndef __starting_point():\\n    solve()\\n\\n__starting_point()\", \"N = int(input())\\na, b = [], []\\nfor i in range(N):\\n    x, y = list(map(int, input().split()))\\n    a.append(x - y)\\n    b.append(x + y)\\n\\na.sort()\\nb.sort()\\nans = max(a[-1] - a[0], b[-1] - b[0])\\n\\nprint(ans)\\n\", \"def ans():\\n    N = int(input())\\n    Z = []  # x + y\\n    W = []  # x - y\\n    for _ in range(N):\\n        x, y = map(int, input().split())\\n        Z.append(x + y)\\n        W.append(x - y)\\n\\n    z_max, z_min = max(Z), min(Z)\\n    w_max, w_min = max(W), min(W)\\n\\n    max_d = max((z_max - z_min, w_max - w_min))\\n    print(max_d)\\n\\n\\ndef __starting_point():\\n    ans()\\n__starting_point()\", \"N = int(input())\\n\\nxpy = []\\nxmy = []\\n\\n\\nfor _ in range(N):\\n    x, y = map(int, input().split())\\n\\n    xpy.append(x + y)\\n    xmy.append(x - y)\\n\\nprint(max(max(xpy) - min(xpy), max(xmy) - min(xmy)))\", \"import sys\\n\\nleft_right_max = 0\\nleft_right_min = float('inf')\\nright_left_max = float('-inf')\\nright_left_min = float('inf')\\nr3_max = float('-inf')\\nr3_min = float('inf')\\n\\nn = int(sys.stdin.readline().strip())\\n\\nfor idx in range(n):\\n    x, y = sys.stdin.readline().strip().split(' ')\\n    x = int(x)\\n    y = int(y)\\n\\n    left_right_tmp = x + y\\n    if left_right_tmp > left_right_max:\\n        left_right_max = left_right_tmp\\n    if left_right_tmp < left_right_min:\\n        left_right_min = left_right_tmp\\n\\n    right_left_tmp = x - y\\n    if right_left_tmp > right_left_max:\\n        right_left_max = right_left_tmp\\n    if right_left_tmp < right_left_min:\\n        right_left_min = right_left_tmp\\n        \\n    r3_tmp = y - x\\n    if r3_tmp > r3_max:\\n        r3_max = r3_tmp\\n    if r3_tmp < r3_min:\\n        r3_min = r3_tmp\\n\\nprint(max(left_right_max - left_right_min, right_left_max - right_left_min, r3_max - r3_min))\"]",
        "difficulty": "interview",
        "input": "2\n1 1\n1 1\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc178/tasks/abc178_e"
    },
    {
        "id": 257,
        "task_id": 3201,
        "test_case_id": 1,
        "question": "You are given an array of integers of length $N$. Let $s_1, s_2, \\ldots , s_ q$ be the lexicographically sorted array of all its non-empty subsequences. A subsequence of the array is an array obtained by removing zero or more elements from the initial array. Notice that some subsequences can be equal and that it holds $q = 2^N - 1$.\n\nAn array $A$ is lexicographically smaller than array $B$ if $A_ i < B_ i$ where $i$ is the first position at which the arrays differ, or if $A$ is a strict prefix of array $B$.\n\nLet us define the hash of an array that consists of values $v_1, v_2, \\ldots , v_ p$ as:\\[ h(s) = (v_1 \\cdot B^{p-1} + v_2 \\cdot B^{p-2} + \\ldots + v_{p-1} \\cdot B + v_ p ) \\bmod M \\]\n\nwhere $B$, $M$ are given integers.\n\nCalculate $h(s_1) h(s_2), \\ldots , h(s_ K)$ for a given $K$.\n\n-----Input-----\nThe first line contains integers $N$, $K$, $B$, $M$ ($1 \\leq N \\leq 100000$, $1 \\leq K \\leq 100000$, $1 \\leq B, M \\leq 1000000$). The second line contains integers $a_1, a_2, a_3, \\ldots , a_ N$ ($1 \\leq a_ i \\leq 100000$). In all test cases, it will hold $K \\leq 2^N - 1$.\n\n-----Output-----\nOutput $K$ lines, the $j$-th line containing $h(s_ j)$.\n\n-----Examples-----\nSample Input 1:\n2 3 1 5\n1 2\nSample Output 1:\n1\n3\n2\n\nSample Input 2:\n3 4 2 3\n1 3 1\nSample Output 2:\n1\n1\n0\n2",
        "solutions": "",
        "difficulty": "competition",
        "input": "2 3 1 5\n1 2\n",
        "output": "1\n3\n2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/podnizovi"
    },
    {
        "id": 258,
        "task_id": 3201,
        "test_case_id": 2,
        "question": "You are given an array of integers of length $N$. Let $s_1, s_2, \\ldots , s_ q$ be the lexicographically sorted array of all its non-empty subsequences. A subsequence of the array is an array obtained by removing zero or more elements from the initial array. Notice that some subsequences can be equal and that it holds $q = 2^N - 1$.\n\nAn array $A$ is lexicographically smaller than array $B$ if $A_ i < B_ i$ where $i$ is the first position at which the arrays differ, or if $A$ is a strict prefix of array $B$.\n\nLet us define the hash of an array that consists of values $v_1, v_2, \\ldots , v_ p$ as:\\[ h(s) = (v_1 \\cdot B^{p-1} + v_2 \\cdot B^{p-2} + \\ldots + v_{p-1} \\cdot B + v_ p ) \\bmod M \\]\n\nwhere $B$, $M$ are given integers.\n\nCalculate $h(s_1) h(s_2), \\ldots , h(s_ K)$ for a given $K$.\n\n-----Input-----\nThe first line contains integers $N$, $K$, $B$, $M$ ($1 \\leq N \\leq 100000$, $1 \\leq K \\leq 100000$, $1 \\leq B, M \\leq 1000000$). The second line contains integers $a_1, a_2, a_3, \\ldots , a_ N$ ($1 \\leq a_ i \\leq 100000$). In all test cases, it will hold $K \\leq 2^N - 1$.\n\n-----Output-----\nOutput $K$ lines, the $j$-th line containing $h(s_ j)$.\n\n-----Examples-----\nSample Input 1:\n2 3 1 5\n1 2\nSample Output 1:\n1\n3\n2\n\nSample Input 2:\n3 4 2 3\n1 3 1\nSample Output 2:\n1\n1\n0\n2",
        "solutions": "",
        "difficulty": "competition",
        "input": "3 4 2 3\n1 3 1\n",
        "output": "1\n1\n0\n2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/podnizovi"
    },
    {
        "id": 259,
        "task_id": 3201,
        "test_case_id": 3,
        "question": "You are given an array of integers of length $N$. Let $s_1, s_2, \\ldots , s_ q$ be the lexicographically sorted array of all its non-empty subsequences. A subsequence of the array is an array obtained by removing zero or more elements from the initial array. Notice that some subsequences can be equal and that it holds $q = 2^N - 1$.\n\nAn array $A$ is lexicographically smaller than array $B$ if $A_ i < B_ i$ where $i$ is the first position at which the arrays differ, or if $A$ is a strict prefix of array $B$.\n\nLet us define the hash of an array that consists of values $v_1, v_2, \\ldots , v_ p$ as:\\[ h(s) = (v_1 \\cdot B^{p-1} + v_2 \\cdot B^{p-2} + \\ldots + v_{p-1} \\cdot B + v_ p ) \\bmod M \\]\n\nwhere $B$, $M$ are given integers.\n\nCalculate $h(s_1) h(s_2), \\ldots , h(s_ K)$ for a given $K$.\n\n-----Input-----\nThe first line contains integers $N$, $K$, $B$, $M$ ($1 \\leq N \\leq 100000$, $1 \\leq K \\leq 100000$, $1 \\leq B, M \\leq 1000000$). The second line contains integers $a_1, a_2, a_3, \\ldots , a_ N$ ($1 \\leq a_ i \\leq 100000$). In all test cases, it will hold $K \\leq 2^N - 1$.\n\n-----Output-----\nOutput $K$ lines, the $j$-th line containing $h(s_ j)$.\n\n-----Examples-----\nSample Input 1:\n2 3 1 5\n1 2\nSample Output 1:\n1\n3\n2\n\nSample Input 2:\n3 4 2 3\n1 3 1\nSample Output 2:\n1\n1\n0\n2",
        "solutions": "",
        "difficulty": "competition",
        "input": "5 6 23 1000\n1 2 4 2 3\n",
        "output": "1\n25\n25\n577\n274\n578\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/podnizovi"
    },
    {
        "id": 260,
        "task_id": 3423,
        "test_case_id": 1,
        "question": "Modern operating system distributions have tools to manage installed software, making it easy to keep the software up-to-date. Putting different pieces of software into ‘packages’ that can be installed separately keeps things simple and avoids duplicate effort and code. But this means that a package may depend on other packages, requiring their installation before that package can be installed. For example, many programs need to use ‘libc,’ which contains standard C-library functions. To keep track of these dependencies, many distributions use some sort of package manager.\n\nWhen a user wants to install a new package (or set of packages), a package manager takes care of the headache of tracking down which packages are required to install the desired package. Of course, those may also depend on other packages.\n\nFor this problem, determine an order (if one exists) that allows a given list of packages to be installed. No package should be installed before all the packages it depends on are installed. You may assume that, at the beginning, no packages have been installed.\n\n-----Input-----\nInput consists of up to $10$ test cases. Each test case start with a number $1 \\le n \\le 1000$, which is the number of packages the user wants to install. This is followed by $n$ lines which describe $n$ packages. Each package description starts with the name of the package and is followed by a space-separated list of the package’s unique dependencies. Each package has at most $20$ dependencies, and each is one of the other $n-1$ packages. Each package name is a string of up to $40$ non-whitespace characters using the English alphabet (a-z, A-Z), digits (0-9), as well as the characters _, -, ., and + (i.e. underscore, minus, period, and plus). Input ends when $n$ is zero.\n\n-----Output-----\nFor each test case, output the order of package installation that allow them all to be installed after their respective dependencies. If there are multiple possible orderings, then give the ordering that is lexicographically first (using ASCII values for string ordering). If there is some group of packages that are not able to be ordered within the list, output ‘cannot be ordered’ instead of ordering the packages. Put a blank line between each pair of test cases.\n\n-----Examples-----\nSample Input:\n14\nlibattr\nvim-X11 vim-common gtk2 libattr\nvim-common\ngtk2 libtiff atk pango glib2\nlibtiff zlib libjpeg\natk\npango xorg-x11-libs freetype glib2\nglib2\nzlib\nlibjpeg\nxorg-x11-libs grep freetype\ngrep pcre\npcre\nfreetype\n3\nemacs xorg-x11 lisp\nxorg-x11\nlisp emacs\n0\nSample Output:\natk\nfreetype\nglib2\nlibattr\nlibjpeg\npcre\ngrep\nvim-common\nxorg-x11-libs\npango\nzlib\nlibtiff\ngtk2\nvim-X11\n\ncannot be ordered",
        "solutions": "",
        "difficulty": "competition",
        "input": "14\nlibattr\nvim-X11 vim-common gtk2 libattr\nvim-common\ngtk2 libtiff atk pango glib2\nlibtiff zlib libjpeg\natk\npango xorg-x11-libs freetype glib2\nglib2\nzlib\nlibjpeg\nxorg-x11-libs grep freetype\ngrep pcre\npcre\nfreetype\n3\nemacs xorg-x11 lisp\nxorg-x11\nlisp emacs\n0\n",
        "output": "atk\nfreetype\nglib2\nlibattr\nlibjpeg\npcre\ngrep\nvim-common\nxorg-x11-libs\npango\nzlib\nlibtiff\ngtk2\nvim-X11\n\ncannot be ordered\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/managingpackaging"
    },
    {
        "id": 261,
        "task_id": 3423,
        "test_case_id": 2,
        "question": "Modern operating system distributions have tools to manage installed software, making it easy to keep the software up-to-date. Putting different pieces of software into ‘packages’ that can be installed separately keeps things simple and avoids duplicate effort and code. But this means that a package may depend on other packages, requiring their installation before that package can be installed. For example, many programs need to use ‘libc,’ which contains standard C-library functions. To keep track of these dependencies, many distributions use some sort of package manager.\n\nWhen a user wants to install a new package (or set of packages), a package manager takes care of the headache of tracking down which packages are required to install the desired package. Of course, those may also depend on other packages.\n\nFor this problem, determine an order (if one exists) that allows a given list of packages to be installed. No package should be installed before all the packages it depends on are installed. You may assume that, at the beginning, no packages have been installed.\n\n-----Input-----\nInput consists of up to $10$ test cases. Each test case start with a number $1 \\le n \\le 1000$, which is the number of packages the user wants to install. This is followed by $n$ lines which describe $n$ packages. Each package description starts with the name of the package and is followed by a space-separated list of the package’s unique dependencies. Each package has at most $20$ dependencies, and each is one of the other $n-1$ packages. Each package name is a string of up to $40$ non-whitespace characters using the English alphabet (a-z, A-Z), digits (0-9), as well as the characters _, -, ., and + (i.e. underscore, minus, period, and plus). Input ends when $n$ is zero.\n\n-----Output-----\nFor each test case, output the order of package installation that allow them all to be installed after their respective dependencies. If there are multiple possible orderings, then give the ordering that is lexicographically first (using ASCII values for string ordering). If there is some group of packages that are not able to be ordered within the list, output ‘cannot be ordered’ instead of ordering the packages. Put a blank line between each pair of test cases.\n\n-----Examples-----\nSample Input:\n14\nlibattr\nvim-X11 vim-common gtk2 libattr\nvim-common\ngtk2 libtiff atk pango glib2\nlibtiff zlib libjpeg\natk\npango xorg-x11-libs freetype glib2\nglib2\nzlib\nlibjpeg\nxorg-x11-libs grep freetype\ngrep pcre\npcre\nfreetype\n3\nemacs xorg-x11 lisp\nxorg-x11\nlisp emacs\n0\nSample Output:\natk\nfreetype\nglib2\nlibattr\nlibjpeg\npcre\ngrep\nvim-common\nxorg-x11-libs\npango\nzlib\nlibtiff\ngtk2\nvim-X11\n\ncannot be ordered",
        "solutions": "",
        "difficulty": "competition",
        "input": "4\natk pango\nglib2 pango\ngrep atk\npango\n0\n",
        "output": "pango\natk\nglib2\ngrep\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/managingpackaging"
    },
    {
        "id": 262,
        "task_id": 3531,
        "test_case_id": 1,
        "question": "Your state has just purchased a large, unspoiled tract of land, and wishes to turn it into a nature park with hiking trails. The land has $n$ places of interest to which guests may wish to hike, and of these, $k$ are very special. The state wishes to connect these places with hiking trails. There are $m$ candidate hiking trails to choose from that directly connect two places of interest with various costs. There are some constraints for choosing the trails. First, there must be exactly one way to hike from any place to any other place. Second, exactly $w$ of the trails must directly connect a special place with a regular place. Of course, the state wishes to minimize the cost of blazing these trails.\n\n-----Input-----\nEach input will consist of a single test case. Note that your program may be run multiple times on different inputs. The first line of input will contain four integers $n$, $m$, $k$ and $w$, where $n$ ($2 \\le n \\le 2 \\cdot 10^5$) is the number of places, $m$ ($1 \\le m \\le 5 \\cdot 10^5$) is the number of potential direct trails between places, $k$ ($1 \\le k < n$) is the number of special places, and $w$ ($1 \\le w \\le n-1$) is the number of special-nonspecial direct trails the state wishes to blaze. The places are numbered $1$ to $n$.\n\nEach of the next $k$ lines holds a single integer $s$ ($1 \\le s \\le n$) indicating the special places. These values will be unique and will be in ascending order.\n\nEach of the next $m$ lines will describe a potential trail that the state could blaze. Each of these lines will consist of three integers, $a$, $b$ and $c$, where the trail would go between places $a$ and $b$ ($1 \\le a,b \\le n, a \\ne b$) and would cost $c$ ($1 \\le c \\le 10^5$). No two places will have more than one potential trail between them, and a trail from $a$ to $b$ is the same as a trail from $b$ to $a$.\n\n-----Output-----\nOutput a single integer, which is the minimum total cost for the state to blaze trails in their new park subject to their constraints, or $-1$ if it isn’t possible.\n\n-----Examples-----\nSample Input:\n3 3 1 2\n2\n1 2 2\n1 3 1\n2 3 3\nSample Output:\n5",
        "solutions": "",
        "difficulty": "competition",
        "input": "3 3 1 2\n2\n1 2 2\n1 3 1\n2 3 3\n",
        "output": "5\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/blazingnewtrails"
    },
    {
        "id": 263,
        "task_id": 3531,
        "test_case_id": 2,
        "question": "Your state has just purchased a large, unspoiled tract of land, and wishes to turn it into a nature park with hiking trails. The land has $n$ places of interest to which guests may wish to hike, and of these, $k$ are very special. The state wishes to connect these places with hiking trails. There are $m$ candidate hiking trails to choose from that directly connect two places of interest with various costs. There are some constraints for choosing the trails. First, there must be exactly one way to hike from any place to any other place. Second, exactly $w$ of the trails must directly connect a special place with a regular place. Of course, the state wishes to minimize the cost of blazing these trails.\n\n-----Input-----\nEach input will consist of a single test case. Note that your program may be run multiple times on different inputs. The first line of input will contain four integers $n$, $m$, $k$ and $w$, where $n$ ($2 \\le n \\le 2 \\cdot 10^5$) is the number of places, $m$ ($1 \\le m \\le 5 \\cdot 10^5$) is the number of potential direct trails between places, $k$ ($1 \\le k < n$) is the number of special places, and $w$ ($1 \\le w \\le n-1$) is the number of special-nonspecial direct trails the state wishes to blaze. The places are numbered $1$ to $n$.\n\nEach of the next $k$ lines holds a single integer $s$ ($1 \\le s \\le n$) indicating the special places. These values will be unique and will be in ascending order.\n\nEach of the next $m$ lines will describe a potential trail that the state could blaze. Each of these lines will consist of three integers, $a$, $b$ and $c$, where the trail would go between places $a$ and $b$ ($1 \\le a,b \\le n, a \\ne b$) and would cost $c$ ($1 \\le c \\le 10^5$). No two places will have more than one potential trail between them, and a trail from $a$ to $b$ is the same as a trail from $b$ to $a$.\n\n-----Output-----\nOutput a single integer, which is the minimum total cost for the state to blaze trails in their new park subject to their constraints, or $-1$ if it isn’t possible.\n\n-----Examples-----\nSample Input:\n3 3 1 2\n2\n1 2 2\n1 3 1\n2 3 3\nSample Output:\n5",
        "solutions": "",
        "difficulty": "competition",
        "input": "3 1 1 1\n2\n1 2 2\n",
        "output": "-1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/blazingnewtrails"
    },
    {
        "id": 264,
        "task_id": 3549,
        "test_case_id": 1,
        "question": "After your boat ran out of fuel in the middle of the ocean, you have been following the currents for 80 days. Today, you finally got your radar equipment working. And it’s receiving signals!\n\nAlas, the signals come from the “radar” station owned by the eccentric lighthouse keeper Hasse. Hasse’s radar station (which does not work quite like other radar stations) emits continuous signals of three different wave-lengths. Therefore, the only interesting thing you can measure is the phase of a signal as it reaches you. For example, if the signal you tuned on to has a wave-length of $100$ meters and you are $1456$ meters from the station, your equipment can only tell you that you are either $56$, or $156$, or $256$, or $\\dots $ meters away from the lighthouse.\n\nSo you reach for your last piece of paper to start calculating – but wait, there’s a catch! On the display you read: “ACCURACY: 3 METERS”. So, in fact, the information you get from this signal is that your distance from Hasse’s radar station is in the union of intervals $[53,59] \\cup [153, 159] \\cup [253, 259] \\cup \\dots $.\n\nWhat to do? Since the key to surviving at sea is to be optimistic, you are interested in what the smallest possible distance to the lighthouse could be, given the wavelengths, measurements and accuracies corresponding to the three signals.\n\n-----Task-----\nGiven three positive prime numbers $m_1$, $m_2$, $m_3$ (the wavelengths), three nonnegative integers $x_1$, $x_2$, $x_3$ (the measurements), and three nonnegative integers $y_1$, $y_2$, $y_3$ (the accuracies), find the smallest nonnegative integer $z$ (the smallest possible distance) such that $z$ is within distance $y_ i$ from $x_ i$ modulo $m_ i$ for each $i = 1,2,3$. An integer $x’$ is within distance$y$ from $x$ modulo $m$ if there is some integer $t$ such that $x \\equiv x’ + t \\pmod{m}$ and $|t| \\leq y$.\n\n-----Input-----\nThere are three lines of input. The first line is $m_1$ $m_2$ $m_3$, the second is $x_1$ $x_2$ $x_3$ and the third is $y_1$ $y_2$ $y_3$. You may assume that $0 < m_ i \\leq 10^6$, $0 \\leq x_ i < m_ i$, and $0 \\leq y_ i \\leq 300$ for each $i$. The numbers $m_1$, $m_2$, $m_3$ are all primes and distinct.\n\n-----Output-----\nPrint one line with the answer $z$. Note that the answer might not fit in a 32-bit integer.\n\n-----Examples-----\nSample Input:\n11 13 17\n5 2 4\n0 0 0\nSample Output:\n2095",
        "solutions": "",
        "difficulty": "competition",
        "input": "11 13 17\n5 2 4\n0 0 0\n",
        "output": "2095\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/radar"
    },
    {
        "id": 265,
        "task_id": 3549,
        "test_case_id": 2,
        "question": "After your boat ran out of fuel in the middle of the ocean, you have been following the currents for 80 days. Today, you finally got your radar equipment working. And it’s receiving signals!\n\nAlas, the signals come from the “radar” station owned by the eccentric lighthouse keeper Hasse. Hasse’s radar station (which does not work quite like other radar stations) emits continuous signals of three different wave-lengths. Therefore, the only interesting thing you can measure is the phase of a signal as it reaches you. For example, if the signal you tuned on to has a wave-length of $100$ meters and you are $1456$ meters from the station, your equipment can only tell you that you are either $56$, or $156$, or $256$, or $\\dots $ meters away from the lighthouse.\n\nSo you reach for your last piece of paper to start calculating – but wait, there’s a catch! On the display you read: “ACCURACY: 3 METERS”. So, in fact, the information you get from this signal is that your distance from Hasse’s radar station is in the union of intervals $[53,59] \\cup [153, 159] \\cup [253, 259] \\cup \\dots $.\n\nWhat to do? Since the key to surviving at sea is to be optimistic, you are interested in what the smallest possible distance to the lighthouse could be, given the wavelengths, measurements and accuracies corresponding to the three signals.\n\n-----Task-----\nGiven three positive prime numbers $m_1$, $m_2$, $m_3$ (the wavelengths), three nonnegative integers $x_1$, $x_2$, $x_3$ (the measurements), and three nonnegative integers $y_1$, $y_2$, $y_3$ (the accuracies), find the smallest nonnegative integer $z$ (the smallest possible distance) such that $z$ is within distance $y_ i$ from $x_ i$ modulo $m_ i$ for each $i = 1,2,3$. An integer $x’$ is within distance$y$ from $x$ modulo $m$ if there is some integer $t$ such that $x \\equiv x’ + t \\pmod{m}$ and $|t| \\leq y$.\n\n-----Input-----\nThere are three lines of input. The first line is $m_1$ $m_2$ $m_3$, the second is $x_1$ $x_2$ $x_3$ and the third is $y_1$ $y_2$ $y_3$. You may assume that $0 < m_ i \\leq 10^6$, $0 \\leq x_ i < m_ i$, and $0 \\leq y_ i \\leq 300$ for each $i$. The numbers $m_1$, $m_2$, $m_3$ are all primes and distinct.\n\n-----Output-----\nPrint one line with the answer $z$. Note that the answer might not fit in a 32-bit integer.\n\n-----Examples-----\nSample Input:\n11 13 17\n5 2 4\n0 0 0\nSample Output:\n2095",
        "solutions": "",
        "difficulty": "competition",
        "input": "941 947 977\n142 510 700\n100 100 100\n",
        "output": "60266\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/radar"
    },
    {
        "id": 266,
        "task_id": 3666,
        "test_case_id": 1,
        "question": "The gear ratio designers ate BikeCo need your help! They have designed a new set of gear ratios $n_1/d_1, n_2/d_2, \\cdots , n_{12}/d_{12}$ for a bicycle with front and rear derailleurs having two and six sprockets respectively. Your task is to figure out, if possible, the sprocket sizes needed to achieve the required gear ratios. \n\nThe sprockets of the front derailleur are connected to the pedals and drive the rear sprockets by chain. You recall from Sprocket Science $101$ that a cyclist uses derailleurs to select any combination of front and rear sprocket. The resulting gear ratio is $u/v$ where $u$ is the front sprocket sprocket size and $v$ is the rear sprocket size.\n\nYou are constrained to exactly two sprockets on the front derailleur and six on the rear derailleur, leading to at most $12$ possible gear ratios. Note that the resulting gear ratios are not necessarily unique.\n\n-----Input-----\nTwelve lines with two integers $n_ i, d_ i$ ($1 \\le n_ i, d_ i \\le 100$) separated by forward slash, where $n_ i/d_ i$ is the $i$th gear ratio.\n\n-----Output-----\nIf the specified gear ratios can be achieved, output the required sprocket sizes on two lines with space-separated integers. The first line has the two sprocket sizes for the front derailleur, and the second line gives the six sprocket sizes needed for the rear derailleur. Due to engineering limitations no sprocket size may exceed $10000$. If there are multiple such sets of sprocket sizes that generate the specified gear ratios, output any one of them.\n\nIf no solution exists, print impossible.\n\n-----Examples-----\nSample Input:\n19/13\n10/1\n19/14\n4/3\n20/7\n19/7\n20/13\n19/15\n10/7\n20/17\n19/2\n19/17\nSample Output:\n19 20\n17 15 14 13 7 2",
        "solutions": "",
        "difficulty": "competition",
        "input": "19/13\n10/1\n19/14\n4/3\n20/7\n19/7\n20/13\n19/15\n10/7\n20/17\n19/2\n19/17\n",
        "output": "19 20\n17 15 14 13 7 2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/sprocketscience"
    },
    {
        "id": 267,
        "task_id": 3666,
        "test_case_id": 2,
        "question": "The gear ratio designers ate BikeCo need your help! They have designed a new set of gear ratios $n_1/d_1, n_2/d_2, \\cdots , n_{12}/d_{12}$ for a bicycle with front and rear derailleurs having two and six sprockets respectively. Your task is to figure out, if possible, the sprocket sizes needed to achieve the required gear ratios. \n\nThe sprockets of the front derailleur are connected to the pedals and drive the rear sprockets by chain. You recall from Sprocket Science $101$ that a cyclist uses derailleurs to select any combination of front and rear sprocket. The resulting gear ratio is $u/v$ where $u$ is the front sprocket sprocket size and $v$ is the rear sprocket size.\n\nYou are constrained to exactly two sprockets on the front derailleur and six on the rear derailleur, leading to at most $12$ possible gear ratios. Note that the resulting gear ratios are not necessarily unique.\n\n-----Input-----\nTwelve lines with two integers $n_ i, d_ i$ ($1 \\le n_ i, d_ i \\le 100$) separated by forward slash, where $n_ i/d_ i$ is the $i$th gear ratio.\n\n-----Output-----\nIf the specified gear ratios can be achieved, output the required sprocket sizes on two lines with space-separated integers. The first line has the two sprocket sizes for the front derailleur, and the second line gives the six sprocket sizes needed for the rear derailleur. Due to engineering limitations no sprocket size may exceed $10000$. If there are multiple such sets of sprocket sizes that generate the specified gear ratios, output any one of them.\n\nIf no solution exists, print impossible.\n\n-----Examples-----\nSample Input:\n19/13\n10/1\n19/14\n4/3\n20/7\n19/7\n20/13\n19/15\n10/7\n20/17\n19/2\n19/17\nSample Output:\n19 20\n17 15 14 13 7 2",
        "solutions": "",
        "difficulty": "competition",
        "input": "1/1\n1/1\n1/1\n1/1\n1/1\n1/1\n1/1\n1/1\n1/1\n1/1\n1/1\n1/2\n",
        "output": "impossible\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/sprocketscience"
    },
    {
        "id": 268,
        "task_id": 4604,
        "test_case_id": 1,
        "question": "There are N people, conveniently numbered 1 through N.\nThey were standing in a row yesterday, but now they are unsure of the order in which they were standing.\nHowever, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.\nAccording to their reports, the difference above for person i is A_i.\nBased on these reports, find the number of the possible orders in which they were standing.\nSince it can be extremely large, print the answer modulo 10^9+7.\nNote that the reports may be incorrect and thus there may be no consistent order.\nIn such a case, print 0.\n\n-----Constraints-----\n - 1≦N≦10^5\n - 0≦A_i≦N-1\n\n-----Input-----\nThe input is given from Standard Input in the following format:\nN\nA_1 A_2 ... A_N\n\n-----Output-----\nPrint the number of the possible orders in which they were standing, modulo 10^9+7.\n\n-----Sample Input-----\n5\n2 4 4 0 2\n\n-----Sample Output-----\n4\n\nThere are four possible orders, as follows:\n - 2,1,4,5,3\n - 2,5,4,1,3\n - 3,1,4,5,2\n - 3,5,4,1,2",
        "solutions": "[\"n = int(input())\\na = [int(x) for x in input().split()]\\na.sort()\\nmod = 10 ** 9 + 7\\n\\ndef p(p):\\n  ans = 1\\n  for i in range(p):\\n    ans *= 2\\n    ans %= mod\\n  return ans\\n\\nif n % 2 == 1:\\n  res = True\\n  for i in range(n):\\n    if a[i] != ((i + 1) // 2) * 2:\\n      res = False\\n  if res:\\n    print(p(n // 2))\\n  else:\\n    print(0)\\n    \\nelse:\\n  res = True\\n  for i in range(n):\\n    if a[i] != (i // 2) * 2 + 1:\\n      res = False\\n  if res:\\n    print(p(n // 2))\\n  else:\\n    print(0)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return 0\\n return 1   \\n    \\na=1\\nif N%2==0:a=f(1)\\nelse:\\n if A[0]!=0:a=0\\n else:a=f(2)\\nprint(2**(N//2)%(10**9+7)*a)\", \"import math\\n\\nN = 5\\nARR = [2, 4, 4, 0, 2]\\n\\nN = 7\\nARR = [6, 4, 0, 2, 4, 0, 2]\\n#\\n# N = 8\\n# ARR = [7, 5, 1, 1, 7, 3, 5, 3]\\n#\\nN = int(input())\\nARR = list(map(int, input().split()))\\n\\n\\ndef calculate(n, arr):\\n    if n % 2 == 0:\\n        n = n // 2\\n        start = 1\\n        finalResult = pow(2, n, 1000000000 + 7)\\n    else:\\n        n = n // 2 + 1\\n        start = 0\\n        finalResult = pow(2, (n - 1), 1000000000 + 7)\\n\\n    result = {}\\n    for i in range(n):\\n        index = start + 2 * i\\n        if index == 0:\\n            result.__setitem__(0, 1)\\n        else:\\n            result.__setitem__(index, 2)\\n\\n    isOk = True\\n    for i in range(len(arr)):\\n        if result.get(arr[i]) == None:\\n            isOk = False\\n            break\\n\\n        if result.get(arr[i]) == 0:\\n            isOk = False\\n            break\\n\\n        result.__setitem__(arr[i], result.get(arr[i])-1)\\n\\n    if isOk == False:\\n        print((0))\\n        return\\n\\n    if sum(result.values()) == 0:\\n        print(finalResult)\\n    else:\\n        print((0))\\n\\n\\ncalculate(N, ARR)\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\na.sort()\\nres = True\\nif n % 2 != 0:\\n  if a[0] != 0:\\n    res = False\\n    print(0)\\n  a = a[1:]\\nfor i in range(0, len(a), 2):\\n  if a[i] != a[i+1]:\\n    print(0)\\n    res = False\\n    break\\n\\np = 10**9 + 7\\nif res:\\n  print(pow(2, n//2, p))\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\nans = 1\\n\\nif n%2 == 0:\\n    for i in range(0, n, 2):\\n        if a[i] != i + 1 or a[i + 1] != i + 1:\\n            print(0)\\n            return\\nelse:\\n    if a[0] != 0:\\n        print(0)\\n        return\\n    for i in range(1, n, 2):\\n        if a[i] != i + 1 or a[i + 1] != i + 1:\\n            print(0)\\n            return\\n\\nfor i in range(n//2):\\n    ans = ans*2%(10**9 + 7)\\n\\nprint(ans)\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n%2 == 0: # \\u4eba\\u6570\\u304c\\u5076\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  for i in range(0,n,2):\\n    if a[i] != i+1 or a[i+1] != i+1:\\n      print(0)\\n      return\\nelse: # \\u4eba\\u6570\\u304c\\u5947\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  if a[0] != 0: # \\u5dee\\u5206\\u304c0\\u5b58\\u5728\\u3057\\u3066\\u3044\\u308b\\u3053\\u3068\\u3092\\u78ba\\u8a8d\\n    print(0)\\n    return\\n  else:\\n    for i in range(1,n,2):\\n      if a[i] != i + 1 or a[i+1] != i + 1:\\n        print(0)\\n        return\\n        \\nans = 1        \\nfor i in range(n//2):\\n  ans = ans*2%(10**9+7)\\nprint(ans)\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\nif n % 2 == 0:\\n    b,s = [1,1],3\\nelse:\\n    b,s = [0],2\\nfor i in range(s,n,2):\\n    b += [i,i]\\nif a == b:\\n    print(pow(2,n//2,1000000007))\\nelse:\\n    print(0)\", \"N = int(input())\\nN_List = sorted(list(map(int,input().split())))\\nflg = 0\\nans = 1\\nif N % 2 == 1:\\n    if N_List[0] != 0:\\n        flg = 1\\n    else:\\n        for i in range(2,N,2):\\n            if i*2 != sum(N_List[i-1:i+1]):\\n                flg = 1\\n                break\\n            else:\\n                ans = (ans * 2) % ((10**9) +7)\\n        \\n\\nelse:\\n    for i in range(1,N,2):\\n        if i*2 != sum(N_List[i-1:i+1]):\\n            flg = 1\\n            break\\n        else:\\n            ans = (ans * 2) % ((10**9) +7)\\n\\nif flg == 0:\\n    print(ans)\\nelse:\\n    print((0))\\n\\n                \\n\", \"N = int(input())\\nA = [int(x) for x in input().split()]\\n\\ncnt = {}\\nif N & 1:\\n    bit = 1\\nelse:\\n    bit = 0\\n\\nfor a in A:\\n    if a & bit:\\n        ans = 0\\n        break\\n    if a in cnt:\\n        cnt[a] += 1\\n    else:\\n        cnt[a] = 1\\n\\nfor key in list(cnt.keys()):\\n    if key == 0 and cnt[key] != 1:\\n        ans = 0\\n        break\\n    if key != 0 and cnt[key] != 2:\\n        ans = 0\\n        break\\nelse:\\n    ans = 2**(N//2) %1000000007\\nprint(ans)\\n\", \"n=int(input())\\nfrom collections import Counter as co\\nc=co(map(int,input().split()))\\nans=pow(2,n//2,10**9+7)\\nif n%2 :\\n    if 0 not in c or c[0]>1:ans=0\\n    for i in range(1,n):\\n        if i%2==0 :\\n            if i not in c or c[i]!=2:ans=0;break\\n        else:\\n            if i in c:ans=0;break\\nelse:\\n    if 0 in c:ans=0\\n    for  i in range(1,n):\\n        if i%2:\\n            if i not in c or c[i]!=2:ans=0;break\\n        else:\\n            if i in c:ans=0;break\\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nl = [0] * n\\nfor x in a:\\n    l[x] += 1\\nfor i in range(n):\\n    if l[i] > 2:\\n        print(0)\\n        return\\n    if l[i] > 0 and (i + n) % 2 == 0: \\n        print(0)\\n        return\\nif n % 2 == 1 and l[0] > 1:\\n    print(0)\\n    return\\nprint(pow(2, n // 2, 10 ** 9 + 7))\", \"n = int(input())\\na_list = sorted([int(x) for x in input().split()], reverse=True)\\nm = n\\nif m % 2 == 1:\\n    a_list.append(0)\\n    m += 1\\nfor i in range(0, m, 2):\\n    if not (a_list[i] == a_list[i + 1] == n - (i + 1)):\\n        print(0)\\n        return\\nprint(2 ** (n // 2) % (10 ** 9 + 7))\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nnum_map = [0] * ((n + 2 - 1) // 2)\\nfor i in range(n):\\n    num_map[a[i] // 2] += 1\\n\\nres = 2 - n % 2\\nif num_map[0] != 2 - n % 2:\\n    print((0))\\nelse:\\n    for i in range(1, (n + 2 - 1) // 2):\\n        if num_map[i] != 2:\\n            print((0))\\n            break\\n        else:\\n            res = res * 2 % mod\\n    else:\\n        print(res)\\n\", \"mod = 10**9+7\\nn = int(input())\\na = list(map(int,input().split()))\\nc_dic = dict()\\nif n%2 == 0:\\n  for num in a:\\n    if num%2 == 0 or n < num:\\n      print(0)\\n      return\\n    if num in c_dic:\\n      c_dic[num] += 1\\n      if c_dic[num] > 2:\\n        print(0)\\n        return\\n    else:\\n      c_dic[num] = 1\\n  print(pow(2,n//2,mod))\\nelse:\\n  for num in a:\\n    if num%2 == 1 or n < num:\\n      print(0)\\n      return\\n    if num in c_dic:\\n      c_dic[num] += 1\\n      if c_dic[num] > 2:\\n        print(0)\\n        return\\n    else:\\n      c_dic[num] = 1\\n  if c_dic[0] != 1:\\n    print(0)\\n    return\\n  print(pow(2,n//2,mod))\", \"import sys\\nfrom collections import Counter\\n\\nn = int(input())\\na = list(map(int, input().split()))\\na.sort()\\n\\nl = []\\n\\nfor i in range(n):\\n    li = abs(i - (n-1-i))\\n    l.append(li)\\n    \\nl.sort()\\n\\n\\nfor ai, li in zip(l,a):\\n    if ai != li:\\n        print((0))\\n        return\\n\\nd = Counter(l)\\nmod = 10 ** 9 + 7\\nans = 1\\n\\nfor li in d:\\n    for j in range(1,d[li]+1):\\n        ans *= j\\n        ans %= mod\\n\\nprint(ans)\\n\", \"n=int(input())\\na=[int(i) for i in input().split()]\\n\\ndef somosomo(a):\\n    ans=[]\\n    if n%2==1:\\n        ans.append(0)\\n        for i in range(1,n//2+1):\\n            ans.append(i*2)\\n            ans.append(i*2)\\n        b=sorted(a)\\n        if b==ans:\\n            return True\\n        return False\\n    else:\\n        for i in range(1,n//2+1):\\n            ans.append(i*2-1)\\n            ans.append(i*2-1)\\n        b=sorted(a)\\n        if b==ans:\\n            return True\\n        return False\\n\\ndef two_ride(n):\\n    ans=1\\n    for i in range(n):\\n        ans*=2\\n        ans%=10**9+7\\n    return ans\\n\\nif somosomo(a):\\n    print(two_ride(n//2))\\nelse:\\n    print(0)\", \"n=int(input())\\na=list(map(int,input().split()))\\nl=[0]*n\\nfor i in range(n):\\n    l[a[i]]+=1\\n#print(l)\\nif n%2==1:\\n    if l[0]!=1:\\n        print(0)\\n        return\\nans=1\\nfor i in range(n):\\n    if n%2==0:\\n        if i%2==0:\\n            if l[i]!=0:\\n                print(0)\\n                return\\n    else:\\n        if i%2==1:\\n            if l[i]!=0:\\n                print(0)\\n                return\\n    \\n    if l[i]==2:\\n        ans*=2\\n    elif l[i]>2:\\n        print(0)\\n        return\\n    ans%=(10**9 +7)\\nprint(ans)\", \"N = int(input())\\ncount = [0]*(N+1)\\nmodz = 10**9 + 7\\n\\ndef junretsu(a):\\n    if a <= 0: return 1\\n    if (a & 0x01) == 1:\\n        return 2*junretsu(a-1) % modz\\n    else:\\n        rr = junretsu(a>>1)\\n        return rr*rr % modz\\n\\npos = list(map(int, input().split()))\\nfor i in range(N):\\n    count[pos[i]] += 1\\n\\ndiff = [0]*(N+1)\\nfor i in range(1, N+1):\\n    d = abs((N - i) - (i-1))\\n    diff[d] += 1\\n\\ninvalid = False\\ntotal = 1\\nfor i in range(N):\\n    if count[i] != diff[i]:\\n        invalid = True\\n        break\\n\\nif invalid:\\n    print((0))\\nelse:\\n    print((junretsu(int(N/2))))\\n\", \"num = int(input())\\nt = [int(n) for n in input().split()]\\nt = sorted(t)\\n\\nvalid = True\\n\\nif num % 2 == 1: # odd\\n  check = list(range(0,num+1,2))[1:]\\n  \\n  valid1 = t[0] == 0\\n  valid2 = check == t[2::2] # even, skip first\\n  valid3 = check == t[1::2] # odd\\n  valid = valid1 and valid2 and valid3\\n  \\n  if not valid:\\n    print((0))\\n  else:\\n    ans = 2**((num-1)//2) % (10**9 + 7)\\n    print(ans)\\n  \\nelse: # even \\n  check = list(range(1,num,2))\\n  \\n  valid1 = True\\n  valid2 = check == t[::2] # even\\n  valid3 = check == t[1::2] # odd\\n  valid = valid1 and valid2 and valid3\\n  \\n  if not valid:\\n    print((0))\\n  else:\\n    ans = 2**((num)//2) % (10**9 + 7)\\n    print(ans)\\n\\n\\n  \\n\", \"N = int(input())\\nA = list(map(int,input().split()))\\n   \\nA.sort()\\n\\ncheck=[0]*N\\n\\nfor idx in range(N%2,N,2):\\n    check[idx]=idx+1\\n    check[idx+1]=idx+1\\n\\nans=0\\n\\nif check == A:\\n    if N % 2 == 0:\\n        ans=(2**(N//2))%(10**9+7)\\n    elif N % 2 != 0:\\n        ans=(2**((N-1)//2))%(10**9+7)\\n    \\nprint(ans)\\n\", \"n=int(input())\\nmod=10**9+7\\nA=list(map(int,input().split()))\\n\\nfrom collections import Counter\\nC=Counter(A)\\nif n%2==0:\\n    for i in range(1,n,2):\\n        if C.get(i) != 2:\\n            print(0);return\\nelse:\\n    if C.get(0) !=1:\\n        print(0);return\\n    for i in range(2,n,2):\\n        if C.get(i)!=2:\\n            print(0);return\\n\\nn//=2\\nprint(pow(2,n,mod))\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif len(a)%2==1:\\n    tmp = [0]\\n    for i in range((len(a)-1)//2):\\n        tmp.append((i+1)*2)\\n        tmp.append((i+1)*2)\\n    if a == tmp:\\n        ans = (2**((len(a)-1)//2))%(10**9+7)\\n    else:\\n        ans = 0\\nelse:\\n    tmp = []\\n    for i in range(len(a)//2):\\n        tmp.append(2*i+1)\\n        tmp.append(2*i+1)\\n    if a == tmp:\\n        ans = (2**(len(a)//2))%(10**9+7)\\n    else:\\n        ans = 0\\nprint(ans)\", \"N = int(input())\\nAs = list(map(int, input().split()))\\n# \\u7d76\\u5bfe\\u5024\\u306e\\u5dee\\u306f\\u3001\\n# \\u5947\\u6570\\u306e\\u5834\\u5408\\u306fN+1\\u304b\\u30892\\u305a\\u3064\\u6e1b\\u3089\\u3057\\u3066\\u884c\\u3063\\u305f\\u5206\\u3057\\u304b\\u306a\\u3044\\u3002(N+1)/2\\n# \\u5076\\u6570\\u306e\\u5834\\u5408\\u306fN\\u304b\\u30892\\u305a\\u3064\\u6e1b\\u3089\\u3057\\u3066\\u884c\\u3063\\u305f\\u5206\\u3057\\u304b\\u306a\\u3044\\u3002N/2\\nnums = {}\\nexists = True\\nif N % 2 == 0:\\n    for A in As:\\n        if A in nums:\\n            nums[A] += 1\\n        else:\\n            nums[A] = 1\\n    for key, value in list(nums.items()):\\n        if key == 0:\\n            exists = False\\n        if value != 2:\\n            exists = False\\n\\nelse:\\n    for A in As:\\n        if A in nums:\\n            nums[A] += 1\\n        else:\\n            nums[A] = 1\\n    for key, value in list(nums.items()):\\n        if key == 0:\\n            if value != 1:\\n                exists = False\\n        else:\\n            if value != 2:\\n                exists = False\\nif not exists:\\n    print((0))\\nelse:\\n    ans = 1\\n    if N % 2 == 0:\\n        for i in range(int(N / 2)):\\n            ans = ans * 2\\n            ans %= 10**9 + 7\\n    else:\\n        for i in range(int((N - 1) / 2)):\\n            ans = ans * 2\\n            ans %= 10**9 + 7\\n            # \\u7d76\\u5bfe\\u5024\\u306e\\u5dee\\u306f0\\u306e\\u6642\\u306f1\\u4eba\\u3060\\u3051\\u3002\\u305d\\u306e\\u307b\\u304b\\u306f2\\u4eba\\u3060\\u3051\\u3002\\u3053\\u308c\\u304c\\u6e80\\u305f\\u305b\\u308b\\u306a\\u3089\\n            # (\\u5076\\u6570)2**(N+1/2)\\n            # (\\u5947\\u6570)2**(N/2)\\n    print(ans)\\n\", \"from collections import Counter\\n\\n\\ndef mod_pow(a, n, mod):\\n    \\\"\\\"\\\"\\n    \\u4e8c\\u5206\\u7d2f\\u4e57\\u6cd5\\u306b\\u3088\\u308b a^n (mod m)\\u306e\\u5b9f\\u88c5\\n    :param a: \\u7d2f\\u4e57\\u306e\\u5e95\\n    :param n: \\u7d2f\\u4e57\\u306e\\u6307\\u6570\\n    :param mod: \\u6cd5\\n    :return: a^n (mod m)\\n    \\\"\\\"\\\"\\n\\n    result = 1\\n    a_n = a\\n    while n > 0:\\n        if n & 1:\\n            result = result * a_n % mod\\n        a_n = a_n * a_n % mod\\n        n >>= 1\\n    return result\\n\\n\\nN = int(input())\\nA = Counter(tuple(map(int, input().split(' '))))\\nMOD = 10 ** 9 + 7\\n\\nif A[0] > 1:\\n    print((0))\\nelif sum([key for key, value in list(A.items()) if value == 1]) != 0:\\n    print((0))\\nelse:\\n    print((mod_pow(2, N // 2, MOD)))\\n\", \"N = int(input())\\nA = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nA = sorted(A)\\nans = 1\\nif N % 2 == 0:#[1,1,3,3,5,5,...]\\n  for i in range(N):\\n    xx = int(i / 2)\\n    if A[i] != 2 * xx + 1:\\n      ans = 0\\n    else:\\n      if i % 2 == 1:\\n        ans *= 2\\n        ans %= mod\\nelse:#[0, 2, 2, 4, 4 ...]\\n  for i in range(N):\\n    xx = int((i + 1)/2)\\n    if A[i] != 2 * xx:\\n      ans = 0\\n    else:\\n      if (i % 2 == 0) and (i != 0):\\n        ans *= 2\\n        ans %= mod\\n      \\n      \\n  \\n  \\nprint(ans)\\n\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\na.sort()\\nres = True\\nanse = list(i for i in range(1, n, 2))\\nanso = list(i for i in range(2, n, 2))\\nif n % 2 != 0:\\n  if a[0] != 0:\\n    res = False\\n    print(0)\\n  a = a[1:]\\n  for i in range(0, len(a), 2):\\n    if a[i] != anso[i//2] or a[i+1] != anso[i//2]:\\n        print(0)\\n        res = False\\n        break\\n\\n\\nif n % 2 == 0:\\n    for i in range(0, len(a), 2):\\n        if a[i] != anse[i//2] or a[i+1] != anse[i//2]:\\n            print(0)\\n            res = False\\n            break\\n\\np = 10**9 + 7\\nif res:\\n  print(pow(2, n//2, p))\", \"n=int(input())\\nl=list(map(int,input().split()))\\nmod=10**9+7\\nif n%2==0:\\n    d={i:2 for i in range(1,n,2)}\\nelse:\\n    d={i:2 for i in range(0,n,2)}\\n    d[0]=1\\nfor a in l:\\n    if a in d:\\n        d[a]-=1\\n    else:\\n        print((0))\\n        return\\nfor i in list(d.values()):\\n    if i!=0:\\n        print((0))\\n        return\\nprint(((2**(n//2))%mod))\\n\", \"from collections import Counter\\n\\nn = int(input())\\nA = list(map(int, input().split()))\\ncnt_A = Counter(A)\\n\\nif not all([v == 2 for k, v in cnt_A.items() if k != 0]):\\n    print(0)\\nelse:\\n    print(pow(2, n // 2, 10**9 + 7))\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nans = 0\\nA_test = sorted(list(set(A)))\\n\\nif N % 2 == 1:\\n    judge = [i for i in range(0,N,2)]\\n    if (A_test == judge) and (A.count(0) == 1):\\n        ans = 2**(N//2)\\nelse:\\n    judge = [i for i in range(1,N,2)]\\n    if A_test == judge:\\n        ans = 2**(N//2)\\n\\nans = ans % (10**9 + 7)\\nprint(ans)\\n\", \"import sys\\nfrom collections import Counter\\nN = int(input())\\nA = list(map(int, input().split()))\\nMOD = 10 ** 9 + 7\\n\\nC = Counter(A)\\nC = sorted(C.items(), key=lambda x: x[0])\\nif N % 2 == 0:\\n    s = 1\\n    for k, v in C:\\n        if k != s or v != 2:\\n            print(0)\\n            return\\n        s += 2\\n    print(pow(2, (N // 2), MOD))\\nelse:\\n    s = 0\\n    for k, v in C:\\n        if k == 0:\\n            if k != 0 or v != 1:\\n                print(0)\\n                return\\n            s += 2\\n            continue\\n        if k != s or v != 2:\\n            print(0)\\n            return\\n        s += 2\\n    print(pow(2, (N - 1) // 2, MOD))\", \"from collections import Counter\\nn=int(input())\\na=sorted(list(map(int,input().split())))\\na_count=Counter(a)\\nif n%2==1:\\n    ans=1\\n    for i in a_count:\\n        if i%2!=0:\\n            print(0)\\n            break\\n        else:\\n            if i==0:\\n                if a_count[i]!=1:\\n                    print(0)\\n                    break\\n            \\n            else:\\n                if a_count[i]==2:\\n                     ans=(ans*2)%(10**9+7)\\n                else:\\n                    print(0)\\n                    break\\n    else:\\n      print(ans)\\nelse:\\n    ans=1\\n    for j in a_count:\\n        if j%2!=1:\\n            print(0)\\n            break\\n        else:\\n            if a_count[j]==2:\\n                ans=(ans*2)%(10**9+7)\\n           \\n            else:\\n                print(0)\\n                break\\n    else:\\n      print(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nflg = 0\\n\\na.sort()\\nif n % 2 == 0:\\n  if a[0] == 1 and a[1] == 1:\\n    for i in range(2, n, 2):\\n      if a[i] == a[i + 1] and a[i - 1] + 2 == a[i]:\\n        continue\\n      else:\\n        flg = 1\\n        break\\n  else:\\n    flg = 1\\nelse:\\n  if a[0] == 0:\\n    for i in range(1, n, 2):\\n      if a[i] == a[i + 1] and a[i - 1] + 2 == a[i]:\\n        continue\\n      else:\\n        flg = 1\\n        break\\n  else:\\n    flg = 1\\n\\nif flg == 1:\\n  print(0)\\nelse:\\n  print((2 ** (n // 2)) % (10 ** 9 + 7))\", \"n=int(input())\\nl=list(map(int,input().split()))\\nmod=10**9+7\\nif n%2==0:\\n    d={i:2 for i in range(1,n,2)}\\nelse:\\n    d={i:2 for i in range(0,n,2)}\\n    d[0]=1\\nfor a in l:\\n    if a in d:\\n        d[a]-=1\\n    else:\\n        print(0)\\n        return\\nfor i in d.values():\\n    if i!=0:\\n        print(0)\\n        return\\nprint((2**(n//2))%mod)\", \"def main():\\n  N = int(input())\\n  A = [int(a) for a in input().split(\\\" \\\")]\\n  A.sort()\\n \\n  if N % 2 == 1 and A.count(0) != 1:\\n    print(0)\\n    return 0\\n  elif N % 2 == 0 and A.count(0) > 0:\\n    print(0)\\n    return 0\\n  \\n  if N % 2 == 1:\\n    A.pop(0)\\n  \\n  cnt = 0\\n  while len(A) > 0:\\n    if A[0] != A[1] or (len(A) > 2 and A[0] == A[1] and A[1] == A[2]):\\n      print(0)\\n      return 0\\n    elif A[0] == A[1] == 2 * cnt + (N % 2) + 1:\\n      cnt += 1\\n      A.pop(0)\\n      A.pop(0)\\n    else:\\n      print(0)\\n      return 0\\n \\n  ans = 1\\n  for p in range(cnt):\\n    ans = (ans * 2) % 1000000007\\n  print(ans)\\n\\nmain()\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n == 1:\\n  print(1)\\n  return\\nelif n%2 == 0:\\n  for i in range(0,n-2,2):\\n    if a[i] != a[i+1] or a[i] == a[i+2]:\\n      print(0)\\n      return\\n  if a[-2] != a[-1]:\\n    print(0)\\n    return\\nelse:\\n  if a[0] != 0 or a[1] == 0:\\n    print(0)\\n    return\\n  for i in range(1,n-2,2):\\n    if a[i] != a[i+1] or a[i] == a[i+2]:\\n      print(0)\\n      return\\n  if a[-2] != a[-1]:\\n    print(0)\\n    return\\n\\nmod = 10**9+7\\nif n%2 == 0: print(2**(n//2)%mod)\\nelse: print(2**((n-1)//2)%mod)\", \"N = int(input())\\nA = list(map(int, input().split()))\\nmod = pow(10,9)+7\\nA.sort()\\n\\nif N%2 == 0:\\n    for i in range(N//2):\\n        if A[2*i] != A[2*i+1] or A[2*i] != 2*i+1:\\n            print((0))\\n            return\\n    ans = pow(2,N//2)\\n    print((ans%mod))\\nelse:\\n    if A[0] != 0:\\n        print((0))\\n        return\\n    for i in range(N//2):\\n        if A[2*i+1] != A[2*(i+1)] or A[2*i+1] != 2*(i+1):\\n            print((0))\\n            return\\n    ans = pow(2,N//2)\\n    print((ans%mod))\\n\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n \\na=True\\nif N%2==0:\\n for i in range(1,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    a=False\\n    break\\nelse:\\n if A[0]!=0:a=False\\n else:\\n    for i in range(2,N,2):\\n     if A[i-1]!=i or A[i]!=i:\\n        a=False\\n        break\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"from collections import Counter\\n\\nN = int(input())\\nA = list(map(int, input().split()))\\nMOD = int(1e9) + 7\\n\\n# \\u5076\\u6570\\u306e\\u5834\\u5408\\nif N % 2 == 0:\\n    c = Counter(A)\\n    if all(i == 2 for i in c.values()):\\n        print(pow(2, N//2, MOD))\\n    else:\\n        print(0)\\n# \\u5947\\u6570\\u306e\\u5834\\u5408\\nelse:\\n    A.sort()\\n    A = A[1:]\\n    c = Counter(A)\\n    if all(i == 2 for i in c.values()):\\n        print(pow(2, N//2, MOD))\\n    else:\\n        print(0)\", \"N = int(input())\\na = list(map(int, input().split()))\\nSum = 1\\nmod = 1000000007\\n\\na.sort()\\ndata = []\\nif N % 2 == 0:\\n    for i in range(int(N / 2)):\\n        data.append(1 + i * 2)\\n        data.append(1 + i * 2)\\nelse:\\n    data.append(0)\\n    for i in range(1, N // 2 + 1):\\n        data.append(i * 2)\\n        data.append(i * 2)\\n\\nif a == data:\\n    for i in range(N // 2):\\n        Sum *= 2\\n        Sum %= mod\\n    print(Sum)\\nelse:\\n    print((0))\\n\", \"N=int(input())\\nA=list(map(int,input().split()))\\n\\nA.sort()\\ncheck=[0]*N\\n\\nfor idx in range(N%2,N,2):\\n    check[idx]=idx+1\\n    check[idx+1]=idx+1\\n\\nans=0\\nmod=10**9+7\\nif check==A:\\n    if N%2==0:\\n        ans=(2**(N//2))%mod\\n    else:\\n        ans=(2**((N-1)//2))%mod\\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\nfrom collections import Counter\\nc = Counter(a)\\n\\ncheck_ary = []\\nif n&1:\\n    check_ary.append(0)\\n\\nfor i in range(n//2):\\n    for _ in range(2):\\n        check_ary.append((i+1)*2 if n&1 else i*2+1)\\n\\nc2 = Counter(check_ary)\\n\\nif c != c2:\\n    print(0)\\n    return\\n\\nprint(pow(2, n//2, 10**9+7))\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nB = [0] * N\\n\\nfor a in A:\\n    B[a] += 1\\n\\nok = True\\n\\nif N % 2 == 1:\\n    ok = ok and B[0] == 1\\n    for i in range(1, N):\\n        ok = ok and B[i] == (2 if i % 2 == 0 else 0)\\nelse:\\n    for i in range(N):\\n        ok = ok and B[i] == (0 if i % 2 == 0 else 2)\\n\\nans = 1\\nMOD = int(1e9) + 7\\nfor _ in range(N // 2):\\n    ans *= 2\\n    ans %= MOD\\n\\nprint((ans if ok else 0))\\n\", \"n=int(input())\\nA=list(map(int,input().split()))\\nA.sort()\\njudge=0\\nif n%2==1:\\n    for i in range(n):\\n        if A[i]!=2*((i+1)//2):\\n            judge+=1\\n            break\\nelse:\\n    for i in range(n):\\n        if A[i]!=2*(i//2)+1:\\n            judge+=1\\n            break\\nif judge==1:\\n    print(0)\\nelse:\\n    print((2**(n//2))%(10**9+7))\", \"from collections import Counter\\nn = int(input())\\na = list(map(int, input().split()))\\nc = Counter(a)\\nd = list(c.values())\\nif (n % 2 == 1 and c[0] == 1 and d.count(2) == (n-1)//2) or (n % 2 == 0 and d.count(2) == n//2):\\n    print(pow(2, n//2, 10**9+7))\\nelse:\\n    print(0)\", \"from collections import Counter\\nn = int(input())\\na = list(map(int, input().split()))\\nc = Counter(a)\\nd = list(c.values())\\nif (n % 2 == 1 and c[0] == 1 and d.count(2) == (n-1)//2) or (n % 2 == 0 and d.count(2) == n//2):\\n    print((2**(n//2)) % (10**9+7))\\nelse:\\n    print(0)\", \"N = int(input())\\nK = [0 for i in range(N+1)]\\nA = list(map(int,input().rstrip().split(\\\" \\\")))\\nans = 1\\nfor i in A:\\n    K[i] += 1\\nfor i in range(N):\\n    if i != 0 and K[i] != 0 and K[i] != 2:\\n        ans = 0\\n        break\\n    if K[i] == 2:\\n        ans *= 2\\n        ans %= 10 ** 9 + 7\\nprint(ans)\", \"import collections\\n\\nn = int(input())\\na = list(map(int, input().split()))\\ncnt = collections.Counter(a)\\nmod = 7 + 10**9\\nif n % 2 == 0:\\n    for i in range(1, 1 + n // 2):\\n        if (i * 2 - 1) not in cnt.keys() or cnt[i * 2 - 1] != 2:\\n            print(0)\\n            return\\n\\nelse:\\n    if 0 not in cnt.keys() or cnt[0] != 1:\\n        print(0)\\n        return\\n    for i in range(1, 1 + n // 2):\\n        if i * 2 not in cnt.keys() or cnt[i * 2] != 2:\\n            print(0)\\n            return\\nprint(2 ** (n // 2) % mod)\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\n\\na = sorted(a)\\n\\nnum = 0\\njudge = 0\\n\\nif len(a)%2 == 1:\\n    if a[0] == 0:\\n        for i in range(1, n, 2):\\n            if a[i] == i+1 and a[i+1] == i+1:\\n                num += 1\\n            else:\\n                print(0)\\n                judge = 1\\n                break\\n    else:\\n        print(0)\\n        judge=1\\nelse:\\n    for i in range(0, n, 2):\\n            if a[i] == i+1 and a[i+1] == i+1:\\n                num += 1\\n            else:\\n                print(0)\\n                judge = 1\\n                break\\n        \\nif judge == 0:\\n    result = (2**num)%(10**9+7)\\n    print(result)\", \"from collections import defaultdict\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nL = A[:]\\nL = list(set(L))\\n\\nmod = 10 ** 9 + 7\\n\\nd = defaultdict(int)\\nfor i in range(N):\\n    d[A[i]] += 1\\n\\nif N % 2 == 1:\\n    bfr = 0\\n    for i in L:\\n        if i - bfr != 2 and i != 0:\\n            print((0))\\n            return\\n\\n        if i == 0:\\n            if d[i] != 1:\\n                print((0))\\n                return\\n            else:\\n                continue\\n        if d[i] != 2:\\n            print((0))\\n            return\\n        bfr = i\\n\\n    print(((2 ** (N // 2)) % mod))\\nelse:\\n    bfr = 1\\n    for i in L:\\n        if i - bfr != 2 and i != 1:\\n            print((0))\\n            return\\n\\n        if d[i] != 2:\\n            print((0))\\n            return\\n        bfr = i\\n\\n    print(((2 ** (N // 2)) % mod))\\n\", \"n = int(input())\\na = list(map(int,input().split()))\\nmod = 10**9+7\\n\\na.sort()\\n\\nif n%2 == 1: \\n    if a[0] != 0:\\n        print((0))\\n        return\\n    else:\\n        a.remove(0)\\n        tmp = 2\\nelse:\\n    tmp = 1\\n\\nfor i in range(n//2):\\n    if tmp == a[0] and tmp == a[1]:\\n        a.remove(tmp)\\n        a.remove(tmp)\\n    else:\\n        print((0))\\n        return\\n    tmp += 2\\n\\nif len(a) == 0:\\n    print(((2**(n//2))%mod))\\nelse:\\n    print((0))\\n\\n\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nnum_map = [0] * ((n + 2 - 1) // 2)\\nfor i in range(n):\\n    num_map[a[i] // 2] += 1\\n\\nres = 1\\nif n % 2 == 1:\\n    if num_map[0] != 1:\\n        print((0))\\n    else:\\n        for i in range(1, (n + 2 - 1) // 2):\\n            if num_map[i] != 2:\\n                print((0))\\n                break\\n            else:\\n                res = res * 2 % mod\\n        else:\\n            print(res)\\nelse:\\n    for i in range((n + 2 - 1) // 2):\\n        if num_map[i] != 2:\\n            print((0))\\n            break\\n        else:\\n            res = res * 2 % mod\\n    else:\\n        print(res)\\n\", \"N=int(input())\\nA=list(map(int,input().split()))\\nmod = 10**9+7\\n\\nA=tuple(sorted(A))\\n\\nif N % 2 == 1:\\n  nums=[0]\\n  for i in range(2,N+1,2):\\n    nums.append(i)\\n    nums.append(i)\\nelse:\\n  nums=[]\\n  for i in range(1,N+1,2):\\n    nums.append(i)\\n    nums.append(i)\\n    \\nnums = tuple(nums)\\nif A != nums:\\n  print(0)\\n  return\\n  \\nprint(2**(N//2) % mod)\", \"N = int(input())\\nA = list(map(int,input().split()))\\nA.sort()\\nmod = 10**9 + 7\\nif N%2 == 0:\\n    for i in range(N):\\n        if A[i] != 1+(i//2)*2:\\n            print(0)\\n            break\\n    else:\\n        print(pow(2,N//2,mod))\\nelse:\\n    if A[0] == 0:\\n        for i in range(1,N):\\n            if A[i] != ((i+1)//2)*2:\\n                print(0)\\n                break\\n        else:\\n            print(pow(2,N//2,mod))\", \"n = int(input())\\na = list(map(int,input().split()))\\nmod = 10**9 + 7\\n\\nd = [0]*(n+1)\\nfor x in a:\\n    d[x] += 1\\nans = 1\\nif n%2 == 0:\\n    sw = 1\\n    for i,x in enumerate(d):\\n        if i%2 != 0:\\n            if x == 2:\\n                ans *= 2\\n                ans %= mod\\n            else:\\n                sw = 0\\n                break\\n        else:\\n            if x != 0:\\n                sw = 0\\n                break\\nelse:\\n    sw = 1\\n    for i,x in enumerate(d):\\n        if i%2 == 0:\\n            if i == 0:\\n                if x != 1:\\n                    sw = 0\\n                    break\\n            else:\\n                if x == 2:\\n                    ans *= 2\\n                    ans %= mod\\n                else:\\n                    sw = 0\\n                    break\\n        else:\\n            if x != 0:\\n                sw = 0\\n                break\\nif sw == 0:\\n    ans = 0\\nprint(ans)\\n\", \"N = int(input())\\nA = sorted(list(map(int,input().split())))\\n\\nif N%2==0:\\n  B = [1+2*(n//2) for n in range(N)]\\nelse:\\n  B = [2*(n//2) for n in range(1,1+N)]\\n\\nif A==B:\\n  print(pow(2,N//2,10**9+7))\\nelse:\\n  print(0)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\nMOD = 10 ** 9 + 7\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N = I()\\n    A = LI()\\n\\n    if N % 2 == 0:\\n        if sorted(A) == [i // 2 * 2 + 1 for i in range(N)]:\\n            print((pow(2, N // 2, MOD)))\\n        else:\\n            print((0))\\n    else:\\n        if sorted(A) == [(i // 2 + 1) * 2 for i in range(-1, N - 1)]:\\n            print((pow(2, (N - 1) // 2, MOD)))\\n        else:\\n            print((0))\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"def PowerMod(N,P,Mod):\\n    if N%Mod==0:\\n        return 0\\n    else:\\n        PowM = 1\\n        for TP in range(1,P+1):\\n            PowM = (PowM*N)%Mod\\n        return PowM\\n\\nfrom collections import Counter\\nN = int(input())\\nA = sorted(Counter([int(T) for T in input().split()]).most_common(),key=lambda X:X[0])\\nPassFlag = True\\nif N%2==1:\\n    for TA in range(0,(N+1)//2):\\n        if A[TA][0]!=(2*TA) or A[TA][1]!=(1+(A[TA][0]!=0)):\\n            PassFlag = False\\n            break\\n    print([0,PowerMod(2,(N-1)//2,10**9+7)][PassFlag])\\nelse:\\n    for TA in range(0,N//2):\\n        if A[TA][0]!=(2*TA+1) or A[TA][1]!=2:\\n            PassFlag = False\\n            break\\n    print([0,PowerMod(2,N//2,10**9+7)][PassFlag])\", \"from collections import Counter\\n\\nn = int(input())\\nc = Counter(list(map(int, input().split())))\\n\\nans = 0\\nfor k, v in list(c.items()):\\n    if k == 0:\\n        if n%2==0 and v > 2:\\n            print((0))\\n            return\\n        elif n%2==1 and v > 1:\\n            print((0))\\n            return\\n    else:\\n        ans += 1\\n        if v > 2:\\n            print((0))\\n            return\\n\\nprint((pow(2, ans, 10**9+7)))\\n\", \"from typing import Counter\\n\\n\\nn = int(input())\\nlis = list(map(int, input().split()))\\nmod  =10**9+7\\n\\nans = 0\\nif n % 2 == 0:\\n    b = Counter(lis)\\n    flag = 1\\n    for i in list(b.values()):\\n        if i == 2:\\n            pass\\n        else:\\n            flag = 0\\n            break\\n    if flag:\\n        ans = 2**(n//2)\\n        print((ans % mod))\\n    else:\\n        print((0))\\nelse:\\n    lis = sorted(lis)\\n    lis = lis[1:]\\n    b = Counter(lis)\\n    flag = 1\\n    for i in list(b.values()):\\n        if i == 2:\\n            pass\\n        else:\\n            flag = 0\\n            break\\n    if flag:\\n        ans = 2**(n//2)\\n        print((ans % mod))\\n    else:\\n        print((0))\\n\", \"n=int(input())\\na=list(map(int,input().split()))\\nflag=0\\nA=a.sort()\\nnum=[]\\n\\nif n%2==0:\\n    for i in range(1,n,2):\\n        num.append(i)\\n        num.append(i)\\n\\nif n%2==1:\\n    num=[0]\\n    for i in range(2,n,2):\\n        num.append(i)\\n        num.append(i)\\n\\nif num==a:\\n    print(2**(n//2)%(10**9+7))\\n\\nelse:\\n    print(\\\"0\\\")\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\nf=lambda:2**(N//2)%(10**9+7)\\na=True\\nif N%2==0:\\n    for i in range(1,N,2):\\n        if A[i-1]!=i or A[i]!=i:\\n            # print(i,A[i-1],A[i])\\n            a=False\\n            break\\nelse:\\n    if A[0]!=0:\\n            a=False\\n    else:\\n        for i in range(2,N,2):\\n            if A[i-1]!=i or A[i]!=i:\\n                # print(i,A[i-1],A[i])\\n                a=False\\n                break\\nprint(f() if a else 0)\", \"n = int(input())\\nA = list(map(int, input().split()))\\n\\nd = {}\\nfor a in A:\\n    d[a] = d.get(a, 0)+1\\n\\nzero_cnt = 0\\ntwo = 0\\nno = 0\\nfor i in d:\\n    if i==0:\\n        zero_cnt+=1\\n    elif d[i]==2:\\n        two+=1\\n    else:\\n        no+=1\\n\\nif no!=0 or (n%2==0 and zero_cnt!=0) or (n%2==1 and zero_cnt!=1):\\n    print((0))\\nelse:\\n    ans = 1\\n    mod = 10**9+7\\n    for i in range(two):\\n        ans *= 2\\n        ans %= mod\\n    print((ans%mod))\\n\", \"MOD = 10 ** 9 + 7\\nnum = [0] * (10 ** 5 + 1)\\nN = int(input())\\nA = list(map(int,input().split()))\\nfor i in range(len(A)):\\n\\tnum[A[i]] += 1\\nif N % 2 == 1:\\n\\tfor i in range(0,N,2):\\n\\t\\tcnt = num[i]\\n\\t\\tif i == 0:\\n\\t\\t\\tif cnt != 1:\\n\\t\\t\\t\\tprint(0)\\n\\t\\t\\t\\treturn\\n\\t\\telse:\\n\\t\\t\\tif cnt != 2:\\n\\t\\t\\t\\tprint(0)\\n\\t\\t\\t\\treturn\\n\\tprint(2 ** (N // 2) % MOD)\\nelse:\\n\\tfor i in range(1,N,2):\\n\\t\\tcnt = num[i]\\n\\t\\tif cnt != 2:\\n\\t\\t\\tprint(0)\\n\\t\\t\\treturn\\n\\tprint(2 ** (N // 2) % MOD)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return False\\n return True   \\n    \\na=True\\nif N%2==0:a=f(1)\\nelse:\\n if A[0]!=0:a=False\\n else:a=f(2)\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, *A = list(map(int, read().split()))\\n\\n    A.sort()\\n\\n    ok = True\\n    if len(A) % 2 == 0:\\n        for i in range(N // 2):\\n            if not A[2 * i] == A[2 * i + 1] == 2 * i + 1:\\n                ok = False\\n                break\\n    else:\\n        if A[0] != 0:\\n            ok = False\\n        else:\\n            for i in range(N // 2):\\n                if not A[2 * i + 1] == A[2 * i + 2] == 2 * i + 2:\\n                    ok = False\\n                    break\\n\\n    if ok:\\n        ans = pow(2, N // 2, MOD)\\n    else:\\n        ans = 0\\n\\n    print(ans)\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nm = 1000000007\\n\\nA.sort()\\nif N % 2 == 0:\\n    B = list(range(1, N, 2)) * 2\\nelse:\\n    B = [0] + list(range(2, N, 2)) * 2\\nB.sort()\\n\\nif A != B:\\n    print((0))\\nelse:\\n    result = 1\\n    for i in range(N // 2):\\n        result *= 2\\n        result %= m\\n    print(result)\\n\", \"N = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfrom collections import defaultdict as dd\\nDict = dd(lambda:0)\\nfor a in A:\\n    Dict[a] += 1\\n\\nif N & 1: Dict[0] += 1\\nf = (lambda:(lambda x:0 if x&1 else 2) if N&1 else (lambda x:2 if x&1 else 0))()\\nPossible = {i:f(i) for i in range(N)}\\nfor key,value in list(Dict.items()):\\n    if value != Possible[key]:\\n        print((0))\\n        return\\nelse:\\n    print((2**(N//2)%1000000007))\\n                \\n\\n\", \"import sys\\n\\n# n = 10 ** 5\\n# \\u30c7\\u30fc\\u30bf\\u8aad\\u307f\\u8fbc\\u307f\\u95a2\\u4fc2\\nn = int(input())\\n\\na = list(map(int, input().split(' ')))\\n\\nrecord = {}\\n\\npossible = True\\n\\n# \\u72b6\\u6cc1\\u304c\\u5b9f\\u73fe\\u53ef\\u80fd\\u304b\\u78ba\\u8a8d\\nfor e in a:\\n    if(e in record.keys()):\\n        record[e] += 1\\n        if(record[e] == 2):\\n            if(e == 0):\\n                possible = False\\n                break\\n        if(record[e] == 3):\\n            possible = False\\n            break\\n    else:\\n        record[e] = 1\\n\\nif(possible == False):\\n    print(0)\\n    return\\n\\nmultiCount = int(n / 2)\\n\\nprint(2 ** multiCount % (10 ** 9 + 7))\", \"import collections\\nN = int(input())\\nA = list(map(int,input().split()))\\nans = 1\\nif 0 in A:\\n    A.remove(0)\\nAcounter = collections.Counter(A)\\nfor i in Acounter.values():\\n    if i == 2:\\n        continue\\n    else:\\n        ans = 0\\n        break\\nif ans == 0:\\n    pass\\nif ans != 0:\\n    for i in range(N//2):\\n        ans = (ans * 2) % (10**9 + 7)\\nprint(ans)\", \"import sys\\nsys.setrecursionlimit(10 ** 7)\\ndef input() : return sys.stdin.readline().strip()\\ndef INT()   : return int(input())\\ndef MAP()   : return map(int,input().split())\\ndef LIST()  : return list(MAP())\\ndef NIJIGEN(H): return [list(input()) for i in range(H)]\\nmod=1000000007\\nN=INT()\\nL=LIST()\\nif N%2==0:\\n  A=range(1,N,2)\\n  B=range(1,N,2)\\nelse:\\n  A=range(0,N,2)\\n  B=range(2,N,2)\\nA,B=list(A),list(B)\\nA=A+B\\nif sorted(A)==sorted(L):\\n  print(pow(2,N//2,mod))\\nelse:\\n  print(0)\", \"n=int(input())\\na=list(map(int,input().split()))\\n\\nb=[0 for i in range(10**5+1)]\\nfor i in a:\\n  b[i]+=1\\n\\nif (n%2==0 and b[0]!=0) or (n%2==1 and b[0]!=1):\\n  print(0)\\n  return\\n\\nans=1\\nmod=10**9+7\\nfor i in b:\\n  if i==2:\\n    ans*=2\\n    ans%=mod\\n  if i>=3:\\n    print(0)\\n    return\\n\\nprint(ans)\", \"from collections import Counter\\n\\nn=int(input())\\na=list(map(int,input().split()))\\n\\nc=Counter(a)\\n\\nif (n%2==0 and c[0]!=0) or (n%2==1 and c[0]!=1):\\n  print(0)\\n  return\\n\\nans=1\\nmod=10**9+7\\nfor i in c:\\n  if c[i]==2:\\n    ans*=2\\n    ans%=mod\\n  if c[i]>=3:\\n    print(0)\\n    return\\n\\nprint(ans)\", \"from collections import Counter\\n\\nN = int(input())\\nabs_diffs = list(map(int, input().split()))\\n\\nif N % 2 == 0:\\n    expected = [i // 2 * 2  + 1 for i in range(N)]\\n    dims = N // 2\\nelse:\\n    expected = [(i + 1) // 2 * 2 for i in range(N)]\\n    dims = (N - 1) // 2\\n\\nif sorted(abs_diffs) == expected:\\n    print((2 ** dims % (10 ** 9 + 7)))\\n\\nelse:\\n    print((0))\\n\", \"n = int(input())\\nA = sorted(map(int,input().split()))\\n\\nif n % 2 == 1:\\n    ex = [0]\\n    \\n    for i in range(n//2):\\n        a = 2 * (i+1)\\n        ex += [a,a]\\n        \\nelse:\\n    ex = []\\n    a = 1\\n    \\n    for i in range(n//2):\\n        ex += [a,a]\\n        a += 2\\n        \\nans = 0\\n\\nif A == ex:\\n    ans = 2 ** (n//2) % (10**9 + 7)\\n    \\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nif n % 2 == 0:\\n    b = [2 if i % 2 == 1 else 0 for i in range(n)]\\nelse:\\n    b = [2 if i % 2 == 0 else 0 for i in range(n)]\\n    b[0] = 1\\nc = [0 for i in range(n)]\\nfor i in range(n):\\n    c[a[i]] += 1\\nif b != c:\\n    print(0)\\nelse:\\n    ans = 1\\n    for i in range(n // 2):\\n        ans *= 2\\n        ans %= mod\\n    print(ans)\", \"N = int(input())\\nA = sorted(list(map(int,input().split())))\\n\\nif N%2==0:\\n  B = [2*(n//2)+1 for n in range(N)]\\nelse:\\n  B = [2*(n//2) for n in range(1,N+1)]\\n\\nif A==B:\\n  print(pow(2,N//2,10**9+7))\\nelse:\\n  print(0)\", \"MOD = 10**9+7\\n\\ndef fast_pow(x, n, MOD):\\n    res = 1\\n    while n:\\n        if n & 1:\\n            res = res * x % MOD\\n        x = x * x % MOD\\n        n >>= 1\\n    return res\\n\\n\\nn = int(input())\\na = list(map(int, input().split()))\\n\\nd = {}\\nfor i in a:\\n    if n % 2:\\n        if i > 0 and i % 2:\\n            print((0))\\n            return\\n    else:\\n        if i > 0 and i % 2 == 0:\\n            print((0))\\n            return\\n\\n    if not i in d:\\n        d[i] = 1\\n    elif d[i] == 1:\\n        d[i] += 1\\n    else:\\n        print((0))\\n        return\\n\\nif n % 2:\\n    if d[0] != 1:\\n        print((0))\\n        return\\n    print((fast_pow(2, len(d)-1, MOD)))\\nelse:\\n    if 0 in d:\\n        print((0))\\n        return\\n    print((fast_pow(2, len(d), MOD)))\\n\", \"import math\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nflag = True\\nif N%2 == 0:\\n    if 0 in A or len(set(A)) != N//2:\\n        flag = False\\nelse:\\n    if len([0 for a in A if a == 0]) != 1 or len(set(A)) != N//2 + 1:\\n        flag = False\\n\\nif  flag:\\n    print((2**((N//2))%(10**9+7)))\\nelse:\\n    print((0))\\n\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return 0\\n return 1   \\n    \\na=1\\nif N%2==0:a=f(1)\\nelse: a=A[0]==0 and f(2)\\nprint(2**(N//2)%(10**9+7)*a)\", \"n = int(input())\\nA = tuple(map(int, input().split()))\\nmod = 10**9+7\\n\\nniseven = (n%2 == 0)\\n\\ncd = dict()\\nfor a in (A):\\n    cd.setdefault(a, 0)\\n    cd[a] += 1\\n    if a == 0 and cd[a] > 1:\\n        print((0))\\n        break\\n    if a > 0 and cd[a] > 2:\\n        print((0))\\n        break\\n    if (a%2==0) == niseven:\\n        print((0))\\n        break\\nelse:\\n    print((pow(2, n//2, mod)))\\n\", \"def main():\\n  N=int(input())\\n  A=list(map(int,input().split()))\\n  mod=10**9+7\\n  ans=1\\n  A.sort()\\n  if N%2==0:\\n    for i in range(0,N,2):\\n      if A[i]!=A[i+1] or A[i]!=i+1:\\n        print(0)\\n        return\\n      ans=ans*2%mod\\n    print(ans)\\n  else:\\n    if A[0]!=0:\\n      print(0)\\n      return\\n    ans=1\\n    for i in range(1,N,2):\\n      if A[i]!=A[i+1] or A[i]!=i+1:\\n        print(0)\\n        return\\n      ans=ans*2%mod\\n    print(ans)\\ndef __starting_point():\\n  main()\\n__starting_point()\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\n# \\u77db\\u76fe\\u30c1\\u30a7\\u30c3\\u30af\\nfrom collections import Counter\\nc = Counter(a)\\n\\ndef check():\\n    if n&1:\\n        if c[0]!=1:\\n            return False\\n        for i in range((n-1)//2):\\n            if c[2*(i+1)] != 2:\\n                return False\\n    else:\\n        for i in range(n//2):\\n            if c[2*i+1] != 2:\\n                return False\\n    return True\\n\\nif not check():\\n    print(0)\\n    return\\n\\nprint(pow(2, n//2, 10**9+7))\", \"n = int(input())\\na = list(map(int,input().split()))\\ndic = {}\\nfor i in range(n):\\n    dic.setdefault(a[i],0)\\n    dic[a[i]] += 1\\nans = 1\\nfor key,value in dic.items():\\n    #\\u5076\\u6570\\n    if n%2==0:\\n        if n > key and key%2==1 and value==2:\\n            ans *= 2\\n        else:\\n            ans = 0\\n            break\\n    #\\u5947\\u6570\\n    else:\\n        if n > key and key%2==0:\\n            if key==0 and value==1:\\n                ans *= 1\\n            elif value==2:\\n                ans *= 2\\n            else:\\n                ans = 0\\n                break\\n        else:\\n            ans = 0\\n            break\\nprint(ans%(10**9+7))\", \"N=int(input())\\nMOD=10**9+7\\nA=[int(x) for x in input().split()]\\nflag=1#\\u305d\\u306e\\u4e26\\u3073\\u9806\\u304c\\u3042\\u308a\\u3048\\u308b\\u306a\\u30891\\u3001\\u305d\\u3046\\u3067\\u306a\\u3044\\u306a\\u30890\\nset1=set()\\nset2=set()\\nif N%2==1:\\n    set1.add(0)\\n    for j in range(2,N+1,2):\\n        set1.add(j)\\n        set2.add(j)\\n    for i in range(N):\\n        now=A[i]\\n        if now in set1:\\n            set1.remove(now)\\n        elif now in set2:\\n            set2.remove(now)\\n        else:\\n            flag=0\\n            break\\n    if len(set1)!=0 or len(set2)!=0:\\n        flag=0\\nelse:\\n    for k in range(1,N+1,2):\\n        set1.add(k)\\n        set2.add(k)\\n    for p in range(N):\\n        now=A[p]\\n        if now in set1:\\n            set1.remove(now)\\n        elif now in set2:\\n            set2.remove(now)\\n        else:\\n            flag=0\\n            break\\n    if len(set1)!=0 or len(set2)!=0:\\n        flag=0\\nif flag==0:\\n    print((0))\\nelse:\\n    ans=1\\n    div2=N//2\\n    for q in range(div2):\\n        ans*=2\\n        ans%=MOD\\n    print(ans)\\n\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nm = 1000000007\\n\\nA.sort()\\nif N % 2 == 0:\\n    B = list(range(1, N, 2)) * 2\\nelse:\\n    B = [0] + list(range(2, N, 2)) * 2\\nB.sort()\\n\\nif A != B:\\n    print((0))\\nelse:\\n    result = 1\\n    for i in range(N // 2):\\n        result *= 2\\n        result %= m\\n    print(result)\\n\", \"from collections import Counter\\n\\nN,*A = map(int, open(0).read().split())\\nac = Counter(A)\\nif N % 2 == 0:\\n    for i in range(1,N,2):\\n        if ac[i] != 2:\\n            print(0)\\n            break\\n    else:\\n        print(pow(2,N//2,1000000007))\\nelse:\\n    if ac[0] != 1:\\n        print(0)\\n    else:\\n        for i in range(2,N,2):\\n            if ac[i] != 2:\\n                print(0)\\n                break\\n        else:\\n            print(pow(2,N//2,1000000007))\", \"n=int(input())\\na=list(map(int,input().split()))\\nif n%2==1:\\n    x=[i for i in range(n)]\\n    for i in range(n):\\n        if i%2==1:\\n            x[i]+=1\\nelse:\\n    x=[i for i in range(n)]\\n    for i in range(n):\\n        if i%2==0:\\n            x[i]+=1\\na.sort()\\nif x==a:\\n    print(pow(2,(n//2),10**9+7))\\nelse:\\n    print(0)\", \"import sys\\nfrom collections import deque\\np=10**9+7\\n\\ndef main(n,a):\\n  h=n//2\\n  g=n%2\\n  a.sort()\\n  c=[2*(x//2)+g+1 for x in range(n-g)]\\n  if g==1:\\n    c.insert(0,0)\\n  if a!=c:\\n      return 0\\n  return 2**(h%(p-1)) % p\\n\\ndef __starting_point():\\n  n=int(input())\\n  a=list(map(int,sys.stdin.readline().strip().split()))\\n  print((main(n,a)))\\n\\n__starting_point()\", \"N=int(input())\\nS=list(map(int,input().split()))\\nlenS=len(S)\\nT=[]\\nfor i in range(1,N+1):\\n    T.append(abs(i-(N+1-i)))\\n\\nT.sort()\\nS.sort()\\n\\n\\n\\nfor i in range(N):\\n    if T[i]!=S[i]:\\n        print((0))\\n        return\\n\\n\\nans=1\\nnagasa=lenS//2\\nfor i in range(nagasa):\\n    \\n    ans=(ans*2)%(10**9+7)\\n\\nprint(ans)\\n\\n\\n\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n%2 == 0: # \\u4eba\\u6570\\u304c\\u5076\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  for i in range(0,n,2):\\n    if a[i] != i+1 or a[i] != a[i+1]:\\n      print(0)\\n      return\\nelse: # \\u4eba\\u6570\\u304c\\u5947\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  if a[0] != 0: # \\u5dee\\u5206\\u304c0\\u5b58\\u5728\\u3057\\u3066\\u3044\\u308b\\u3053\\u3068\\u3092\\u78ba\\u8a8d\\n    print(0)\\n    return\\n  else:\\n    for i in range(1,n,2):\\n      if a[i] != i+1 or a[i] != a[i+1]:\\n        print(0)\\n        return\\n\\nans = 1\\nfor i in range(n//2):\\n  ans = ans * 2 % (10**9+7) # \\u7d44\\u307f\\u5408\\u308f\\u305b\\u3068\\u3057\\u3066\\u306f\\u540c\\u3058\\u5dee\\u5206\\u306e\\u5024\\u3092\\u5165\\u308c\\u66ff\\u3048\\u308b2\\u629e\\u306b\\u306a\\u308b\\u306e\\u3067\\u3001\\u7d50\\u679c\\u30922\\u500d\\u306b\\u3059\\u308b\\nprint(ans)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\na=True\\nif N%2==0:\\n for i in range(1,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    a=False\\n    break\\nelse:\\n if A[0]!=0:a=False\\n else:\\n    for i in range(2,N,2):\\n     if A[i-1]!=i or A[i]!=i:\\n        a=False\\n        break\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"import math\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nflag = True\\nif N%2 == 0:\\n    if 0 in A or len(set(A)) != N//2:\\n        flag = False\\nelse:\\n    if len([0 for a in A if a == 0]) != 1 or len(set(A)) != N//2 + 1:\\n        flag = False\\n\\nif  flag:\\n    print((2**(math.floor(N/2))%(10**9+7)))\\nelse:\\n    print((0))\\n\", \"from collections import Counter\\n\\nn = int(input())\\nA = list(map(int, input().split()))\\ncnt_A = Counter(A)\\n\\nif all([v == 2 for k, v in cnt_A.items() if k != 0]):\\n    print(pow(2, n // 2, 10**9 + 7))\\nelse:\\n    print(0)\", \"N=int(input())\\nMOD=1000000007\\nA=list(map(int,input().split()))\\ncnt=[0 for i in range(N)]\\nfor i in range(N):\\n    cnt[A[i]]+=1\\nif N%2==0:\\n    for i in range(1,N,2):\\n        if cnt[i]!=2:\\n            print((0))\\n            break\\n    else:\\n        print((2**(N//2)%MOD))\\nelse:\\n    if cnt[0]!=1:\\n        print((0))\\n    else:\\n        for i in range(2,(N+1)//2,2):\\n            if cnt[i]!=2:\\n                print((0))\\n                break\\n        else:\\n            print((2**((N-1)//2)%MOD))\\n\", \"import collections\\nimport sys\\ninput = sys.stdin.readline\\n\\nN = int(input())\\nA = list(map(int,input().split()))\\nm = 1000000007\\n\\nflag0 = 1\\ncount = 0\\n#\\u5076\\u6570\\u3060\\u3063\\u305f\\u3089\\nif N %2 ==0:\\n    colA = collections.Counter(A)\\n    for key,val in list(colA.items()):\\n        if key%2 != 1 or val != 2:\\n            flag0 = 0\\n            break\\n    for i in range(1,N,2):\\n        if i not in list(colA.keys()):\\n            flag = 0\\n            break\\n        else:\\n            count +=1\\n#\\u5947\\u6570\\u3060\\u3063\\u305f\\u3089\\nelse:\\n    A.append(0)\\n    colA = collections.Counter(A)\\n    for key,val in list(colA.items()):\\n        if key%2 != 0 or val != 2:\\n            flag0 = 0\\n            break\\n    for i in range(0,N,2):\\n        if i not in list(colA.keys()):\\n            flag = 0\\n            break\\n        else:\\n            count +=1\\n    count -=1\\n\\n\\nprint((((2**count)%m)*flag0))\\n    \\n\"]",
        "difficulty": "introductory",
        "input": "5\n2 4 4 0 2\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc050/tasks/arc066_a"
    },
    {
        "id": 269,
        "task_id": 4604,
        "test_case_id": 2,
        "question": "There are N people, conveniently numbered 1 through N.\nThey were standing in a row yesterday, but now they are unsure of the order in which they were standing.\nHowever, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.\nAccording to their reports, the difference above for person i is A_i.\nBased on these reports, find the number of the possible orders in which they were standing.\nSince it can be extremely large, print the answer modulo 10^9+7.\nNote that the reports may be incorrect and thus there may be no consistent order.\nIn such a case, print 0.\n\n-----Constraints-----\n - 1≦N≦10^5\n - 0≦A_i≦N-1\n\n-----Input-----\nThe input is given from Standard Input in the following format:\nN\nA_1 A_2 ... A_N\n\n-----Output-----\nPrint the number of the possible orders in which they were standing, modulo 10^9+7.\n\n-----Sample Input-----\n5\n2 4 4 0 2\n\n-----Sample Output-----\n4\n\nThere are four possible orders, as follows:\n - 2,1,4,5,3\n - 2,5,4,1,3\n - 3,1,4,5,2\n - 3,5,4,1,2",
        "solutions": "[\"n = int(input())\\na = [int(x) for x in input().split()]\\na.sort()\\nmod = 10 ** 9 + 7\\n\\ndef p(p):\\n  ans = 1\\n  for i in range(p):\\n    ans *= 2\\n    ans %= mod\\n  return ans\\n\\nif n % 2 == 1:\\n  res = True\\n  for i in range(n):\\n    if a[i] != ((i + 1) // 2) * 2:\\n      res = False\\n  if res:\\n    print(p(n // 2))\\n  else:\\n    print(0)\\n    \\nelse:\\n  res = True\\n  for i in range(n):\\n    if a[i] != (i // 2) * 2 + 1:\\n      res = False\\n  if res:\\n    print(p(n // 2))\\n  else:\\n    print(0)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return 0\\n return 1   \\n    \\na=1\\nif N%2==0:a=f(1)\\nelse:\\n if A[0]!=0:a=0\\n else:a=f(2)\\nprint(2**(N//2)%(10**9+7)*a)\", \"import math\\n\\nN = 5\\nARR = [2, 4, 4, 0, 2]\\n\\nN = 7\\nARR = [6, 4, 0, 2, 4, 0, 2]\\n#\\n# N = 8\\n# ARR = [7, 5, 1, 1, 7, 3, 5, 3]\\n#\\nN = int(input())\\nARR = list(map(int, input().split()))\\n\\n\\ndef calculate(n, arr):\\n    if n % 2 == 0:\\n        n = n // 2\\n        start = 1\\n        finalResult = pow(2, n, 1000000000 + 7)\\n    else:\\n        n = n // 2 + 1\\n        start = 0\\n        finalResult = pow(2, (n - 1), 1000000000 + 7)\\n\\n    result = {}\\n    for i in range(n):\\n        index = start + 2 * i\\n        if index == 0:\\n            result.__setitem__(0, 1)\\n        else:\\n            result.__setitem__(index, 2)\\n\\n    isOk = True\\n    for i in range(len(arr)):\\n        if result.get(arr[i]) == None:\\n            isOk = False\\n            break\\n\\n        if result.get(arr[i]) == 0:\\n            isOk = False\\n            break\\n\\n        result.__setitem__(arr[i], result.get(arr[i])-1)\\n\\n    if isOk == False:\\n        print((0))\\n        return\\n\\n    if sum(result.values()) == 0:\\n        print(finalResult)\\n    else:\\n        print((0))\\n\\n\\ncalculate(N, ARR)\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\na.sort()\\nres = True\\nif n % 2 != 0:\\n  if a[0] != 0:\\n    res = False\\n    print(0)\\n  a = a[1:]\\nfor i in range(0, len(a), 2):\\n  if a[i] != a[i+1]:\\n    print(0)\\n    res = False\\n    break\\n\\np = 10**9 + 7\\nif res:\\n  print(pow(2, n//2, p))\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\nans = 1\\n\\nif n%2 == 0:\\n    for i in range(0, n, 2):\\n        if a[i] != i + 1 or a[i + 1] != i + 1:\\n            print(0)\\n            return\\nelse:\\n    if a[0] != 0:\\n        print(0)\\n        return\\n    for i in range(1, n, 2):\\n        if a[i] != i + 1 or a[i + 1] != i + 1:\\n            print(0)\\n            return\\n\\nfor i in range(n//2):\\n    ans = ans*2%(10**9 + 7)\\n\\nprint(ans)\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n%2 == 0: # \\u4eba\\u6570\\u304c\\u5076\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  for i in range(0,n,2):\\n    if a[i] != i+1 or a[i+1] != i+1:\\n      print(0)\\n      return\\nelse: # \\u4eba\\u6570\\u304c\\u5947\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  if a[0] != 0: # \\u5dee\\u5206\\u304c0\\u5b58\\u5728\\u3057\\u3066\\u3044\\u308b\\u3053\\u3068\\u3092\\u78ba\\u8a8d\\n    print(0)\\n    return\\n  else:\\n    for i in range(1,n,2):\\n      if a[i] != i + 1 or a[i+1] != i + 1:\\n        print(0)\\n        return\\n        \\nans = 1        \\nfor i in range(n//2):\\n  ans = ans*2%(10**9+7)\\nprint(ans)\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\nif n % 2 == 0:\\n    b,s = [1,1],3\\nelse:\\n    b,s = [0],2\\nfor i in range(s,n,2):\\n    b += [i,i]\\nif a == b:\\n    print(pow(2,n//2,1000000007))\\nelse:\\n    print(0)\", \"N = int(input())\\nN_List = sorted(list(map(int,input().split())))\\nflg = 0\\nans = 1\\nif N % 2 == 1:\\n    if N_List[0] != 0:\\n        flg = 1\\n    else:\\n        for i in range(2,N,2):\\n            if i*2 != sum(N_List[i-1:i+1]):\\n                flg = 1\\n                break\\n            else:\\n                ans = (ans * 2) % ((10**9) +7)\\n        \\n\\nelse:\\n    for i in range(1,N,2):\\n        if i*2 != sum(N_List[i-1:i+1]):\\n            flg = 1\\n            break\\n        else:\\n            ans = (ans * 2) % ((10**9) +7)\\n\\nif flg == 0:\\n    print(ans)\\nelse:\\n    print((0))\\n\\n                \\n\", \"N = int(input())\\nA = [int(x) for x in input().split()]\\n\\ncnt = {}\\nif N & 1:\\n    bit = 1\\nelse:\\n    bit = 0\\n\\nfor a in A:\\n    if a & bit:\\n        ans = 0\\n        break\\n    if a in cnt:\\n        cnt[a] += 1\\n    else:\\n        cnt[a] = 1\\n\\nfor key in list(cnt.keys()):\\n    if key == 0 and cnt[key] != 1:\\n        ans = 0\\n        break\\n    if key != 0 and cnt[key] != 2:\\n        ans = 0\\n        break\\nelse:\\n    ans = 2**(N//2) %1000000007\\nprint(ans)\\n\", \"n=int(input())\\nfrom collections import Counter as co\\nc=co(map(int,input().split()))\\nans=pow(2,n//2,10**9+7)\\nif n%2 :\\n    if 0 not in c or c[0]>1:ans=0\\n    for i in range(1,n):\\n        if i%2==0 :\\n            if i not in c or c[i]!=2:ans=0;break\\n        else:\\n            if i in c:ans=0;break\\nelse:\\n    if 0 in c:ans=0\\n    for  i in range(1,n):\\n        if i%2:\\n            if i not in c or c[i]!=2:ans=0;break\\n        else:\\n            if i in c:ans=0;break\\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nl = [0] * n\\nfor x in a:\\n    l[x] += 1\\nfor i in range(n):\\n    if l[i] > 2:\\n        print(0)\\n        return\\n    if l[i] > 0 and (i + n) % 2 == 0: \\n        print(0)\\n        return\\nif n % 2 == 1 and l[0] > 1:\\n    print(0)\\n    return\\nprint(pow(2, n // 2, 10 ** 9 + 7))\", \"n = int(input())\\na_list = sorted([int(x) for x in input().split()], reverse=True)\\nm = n\\nif m % 2 == 1:\\n    a_list.append(0)\\n    m += 1\\nfor i in range(0, m, 2):\\n    if not (a_list[i] == a_list[i + 1] == n - (i + 1)):\\n        print(0)\\n        return\\nprint(2 ** (n // 2) % (10 ** 9 + 7))\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nnum_map = [0] * ((n + 2 - 1) // 2)\\nfor i in range(n):\\n    num_map[a[i] // 2] += 1\\n\\nres = 2 - n % 2\\nif num_map[0] != 2 - n % 2:\\n    print((0))\\nelse:\\n    for i in range(1, (n + 2 - 1) // 2):\\n        if num_map[i] != 2:\\n            print((0))\\n            break\\n        else:\\n            res = res * 2 % mod\\n    else:\\n        print(res)\\n\", \"mod = 10**9+7\\nn = int(input())\\na = list(map(int,input().split()))\\nc_dic = dict()\\nif n%2 == 0:\\n  for num in a:\\n    if num%2 == 0 or n < num:\\n      print(0)\\n      return\\n    if num in c_dic:\\n      c_dic[num] += 1\\n      if c_dic[num] > 2:\\n        print(0)\\n        return\\n    else:\\n      c_dic[num] = 1\\n  print(pow(2,n//2,mod))\\nelse:\\n  for num in a:\\n    if num%2 == 1 or n < num:\\n      print(0)\\n      return\\n    if num in c_dic:\\n      c_dic[num] += 1\\n      if c_dic[num] > 2:\\n        print(0)\\n        return\\n    else:\\n      c_dic[num] = 1\\n  if c_dic[0] != 1:\\n    print(0)\\n    return\\n  print(pow(2,n//2,mod))\", \"import sys\\nfrom collections import Counter\\n\\nn = int(input())\\na = list(map(int, input().split()))\\na.sort()\\n\\nl = []\\n\\nfor i in range(n):\\n    li = abs(i - (n-1-i))\\n    l.append(li)\\n    \\nl.sort()\\n\\n\\nfor ai, li in zip(l,a):\\n    if ai != li:\\n        print((0))\\n        return\\n\\nd = Counter(l)\\nmod = 10 ** 9 + 7\\nans = 1\\n\\nfor li in d:\\n    for j in range(1,d[li]+1):\\n        ans *= j\\n        ans %= mod\\n\\nprint(ans)\\n\", \"n=int(input())\\na=[int(i) for i in input().split()]\\n\\ndef somosomo(a):\\n    ans=[]\\n    if n%2==1:\\n        ans.append(0)\\n        for i in range(1,n//2+1):\\n            ans.append(i*2)\\n            ans.append(i*2)\\n        b=sorted(a)\\n        if b==ans:\\n            return True\\n        return False\\n    else:\\n        for i in range(1,n//2+1):\\n            ans.append(i*2-1)\\n            ans.append(i*2-1)\\n        b=sorted(a)\\n        if b==ans:\\n            return True\\n        return False\\n\\ndef two_ride(n):\\n    ans=1\\n    for i in range(n):\\n        ans*=2\\n        ans%=10**9+7\\n    return ans\\n\\nif somosomo(a):\\n    print(two_ride(n//2))\\nelse:\\n    print(0)\", \"n=int(input())\\na=list(map(int,input().split()))\\nl=[0]*n\\nfor i in range(n):\\n    l[a[i]]+=1\\n#print(l)\\nif n%2==1:\\n    if l[0]!=1:\\n        print(0)\\n        return\\nans=1\\nfor i in range(n):\\n    if n%2==0:\\n        if i%2==0:\\n            if l[i]!=0:\\n                print(0)\\n                return\\n    else:\\n        if i%2==1:\\n            if l[i]!=0:\\n                print(0)\\n                return\\n    \\n    if l[i]==2:\\n        ans*=2\\n    elif l[i]>2:\\n        print(0)\\n        return\\n    ans%=(10**9 +7)\\nprint(ans)\", \"N = int(input())\\ncount = [0]*(N+1)\\nmodz = 10**9 + 7\\n\\ndef junretsu(a):\\n    if a <= 0: return 1\\n    if (a & 0x01) == 1:\\n        return 2*junretsu(a-1) % modz\\n    else:\\n        rr = junretsu(a>>1)\\n        return rr*rr % modz\\n\\npos = list(map(int, input().split()))\\nfor i in range(N):\\n    count[pos[i]] += 1\\n\\ndiff = [0]*(N+1)\\nfor i in range(1, N+1):\\n    d = abs((N - i) - (i-1))\\n    diff[d] += 1\\n\\ninvalid = False\\ntotal = 1\\nfor i in range(N):\\n    if count[i] != diff[i]:\\n        invalid = True\\n        break\\n\\nif invalid:\\n    print((0))\\nelse:\\n    print((junretsu(int(N/2))))\\n\", \"num = int(input())\\nt = [int(n) for n in input().split()]\\nt = sorted(t)\\n\\nvalid = True\\n\\nif num % 2 == 1: # odd\\n  check = list(range(0,num+1,2))[1:]\\n  \\n  valid1 = t[0] == 0\\n  valid2 = check == t[2::2] # even, skip first\\n  valid3 = check == t[1::2] # odd\\n  valid = valid1 and valid2 and valid3\\n  \\n  if not valid:\\n    print((0))\\n  else:\\n    ans = 2**((num-1)//2) % (10**9 + 7)\\n    print(ans)\\n  \\nelse: # even \\n  check = list(range(1,num,2))\\n  \\n  valid1 = True\\n  valid2 = check == t[::2] # even\\n  valid3 = check == t[1::2] # odd\\n  valid = valid1 and valid2 and valid3\\n  \\n  if not valid:\\n    print((0))\\n  else:\\n    ans = 2**((num)//2) % (10**9 + 7)\\n    print(ans)\\n\\n\\n  \\n\", \"N = int(input())\\nA = list(map(int,input().split()))\\n   \\nA.sort()\\n\\ncheck=[0]*N\\n\\nfor idx in range(N%2,N,2):\\n    check[idx]=idx+1\\n    check[idx+1]=idx+1\\n\\nans=0\\n\\nif check == A:\\n    if N % 2 == 0:\\n        ans=(2**(N//2))%(10**9+7)\\n    elif N % 2 != 0:\\n        ans=(2**((N-1)//2))%(10**9+7)\\n    \\nprint(ans)\\n\", \"n=int(input())\\nmod=10**9+7\\nA=list(map(int,input().split()))\\n\\nfrom collections import Counter\\nC=Counter(A)\\nif n%2==0:\\n    for i in range(1,n,2):\\n        if C.get(i) != 2:\\n            print(0);return\\nelse:\\n    if C.get(0) !=1:\\n        print(0);return\\n    for i in range(2,n,2):\\n        if C.get(i)!=2:\\n            print(0);return\\n\\nn//=2\\nprint(pow(2,n,mod))\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif len(a)%2==1:\\n    tmp = [0]\\n    for i in range((len(a)-1)//2):\\n        tmp.append((i+1)*2)\\n        tmp.append((i+1)*2)\\n    if a == tmp:\\n        ans = (2**((len(a)-1)//2))%(10**9+7)\\n    else:\\n        ans = 0\\nelse:\\n    tmp = []\\n    for i in range(len(a)//2):\\n        tmp.append(2*i+1)\\n        tmp.append(2*i+1)\\n    if a == tmp:\\n        ans = (2**(len(a)//2))%(10**9+7)\\n    else:\\n        ans = 0\\nprint(ans)\", \"N = int(input())\\nAs = list(map(int, input().split()))\\n# \\u7d76\\u5bfe\\u5024\\u306e\\u5dee\\u306f\\u3001\\n# \\u5947\\u6570\\u306e\\u5834\\u5408\\u306fN+1\\u304b\\u30892\\u305a\\u3064\\u6e1b\\u3089\\u3057\\u3066\\u884c\\u3063\\u305f\\u5206\\u3057\\u304b\\u306a\\u3044\\u3002(N+1)/2\\n# \\u5076\\u6570\\u306e\\u5834\\u5408\\u306fN\\u304b\\u30892\\u305a\\u3064\\u6e1b\\u3089\\u3057\\u3066\\u884c\\u3063\\u305f\\u5206\\u3057\\u304b\\u306a\\u3044\\u3002N/2\\nnums = {}\\nexists = True\\nif N % 2 == 0:\\n    for A in As:\\n        if A in nums:\\n            nums[A] += 1\\n        else:\\n            nums[A] = 1\\n    for key, value in list(nums.items()):\\n        if key == 0:\\n            exists = False\\n        if value != 2:\\n            exists = False\\n\\nelse:\\n    for A in As:\\n        if A in nums:\\n            nums[A] += 1\\n        else:\\n            nums[A] = 1\\n    for key, value in list(nums.items()):\\n        if key == 0:\\n            if value != 1:\\n                exists = False\\n        else:\\n            if value != 2:\\n                exists = False\\nif not exists:\\n    print((0))\\nelse:\\n    ans = 1\\n    if N % 2 == 0:\\n        for i in range(int(N / 2)):\\n            ans = ans * 2\\n            ans %= 10**9 + 7\\n    else:\\n        for i in range(int((N - 1) / 2)):\\n            ans = ans * 2\\n            ans %= 10**9 + 7\\n            # \\u7d76\\u5bfe\\u5024\\u306e\\u5dee\\u306f0\\u306e\\u6642\\u306f1\\u4eba\\u3060\\u3051\\u3002\\u305d\\u306e\\u307b\\u304b\\u306f2\\u4eba\\u3060\\u3051\\u3002\\u3053\\u308c\\u304c\\u6e80\\u305f\\u305b\\u308b\\u306a\\u3089\\n            # (\\u5076\\u6570)2**(N+1/2)\\n            # (\\u5947\\u6570)2**(N/2)\\n    print(ans)\\n\", \"from collections import Counter\\n\\n\\ndef mod_pow(a, n, mod):\\n    \\\"\\\"\\\"\\n    \\u4e8c\\u5206\\u7d2f\\u4e57\\u6cd5\\u306b\\u3088\\u308b a^n (mod m)\\u306e\\u5b9f\\u88c5\\n    :param a: \\u7d2f\\u4e57\\u306e\\u5e95\\n    :param n: \\u7d2f\\u4e57\\u306e\\u6307\\u6570\\n    :param mod: \\u6cd5\\n    :return: a^n (mod m)\\n    \\\"\\\"\\\"\\n\\n    result = 1\\n    a_n = a\\n    while n > 0:\\n        if n & 1:\\n            result = result * a_n % mod\\n        a_n = a_n * a_n % mod\\n        n >>= 1\\n    return result\\n\\n\\nN = int(input())\\nA = Counter(tuple(map(int, input().split(' '))))\\nMOD = 10 ** 9 + 7\\n\\nif A[0] > 1:\\n    print((0))\\nelif sum([key for key, value in list(A.items()) if value == 1]) != 0:\\n    print((0))\\nelse:\\n    print((mod_pow(2, N // 2, MOD)))\\n\", \"N = int(input())\\nA = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nA = sorted(A)\\nans = 1\\nif N % 2 == 0:#[1,1,3,3,5,5,...]\\n  for i in range(N):\\n    xx = int(i / 2)\\n    if A[i] != 2 * xx + 1:\\n      ans = 0\\n    else:\\n      if i % 2 == 1:\\n        ans *= 2\\n        ans %= mod\\nelse:#[0, 2, 2, 4, 4 ...]\\n  for i in range(N):\\n    xx = int((i + 1)/2)\\n    if A[i] != 2 * xx:\\n      ans = 0\\n    else:\\n      if (i % 2 == 0) and (i != 0):\\n        ans *= 2\\n        ans %= mod\\n      \\n      \\n  \\n  \\nprint(ans)\\n\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\na.sort()\\nres = True\\nanse = list(i for i in range(1, n, 2))\\nanso = list(i for i in range(2, n, 2))\\nif n % 2 != 0:\\n  if a[0] != 0:\\n    res = False\\n    print(0)\\n  a = a[1:]\\n  for i in range(0, len(a), 2):\\n    if a[i] != anso[i//2] or a[i+1] != anso[i//2]:\\n        print(0)\\n        res = False\\n        break\\n\\n\\nif n % 2 == 0:\\n    for i in range(0, len(a), 2):\\n        if a[i] != anse[i//2] or a[i+1] != anse[i//2]:\\n            print(0)\\n            res = False\\n            break\\n\\np = 10**9 + 7\\nif res:\\n  print(pow(2, n//2, p))\", \"n=int(input())\\nl=list(map(int,input().split()))\\nmod=10**9+7\\nif n%2==0:\\n    d={i:2 for i in range(1,n,2)}\\nelse:\\n    d={i:2 for i in range(0,n,2)}\\n    d[0]=1\\nfor a in l:\\n    if a in d:\\n        d[a]-=1\\n    else:\\n        print((0))\\n        return\\nfor i in list(d.values()):\\n    if i!=0:\\n        print((0))\\n        return\\nprint(((2**(n//2))%mod))\\n\", \"from collections import Counter\\n\\nn = int(input())\\nA = list(map(int, input().split()))\\ncnt_A = Counter(A)\\n\\nif not all([v == 2 for k, v in cnt_A.items() if k != 0]):\\n    print(0)\\nelse:\\n    print(pow(2, n // 2, 10**9 + 7))\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nans = 0\\nA_test = sorted(list(set(A)))\\n\\nif N % 2 == 1:\\n    judge = [i for i in range(0,N,2)]\\n    if (A_test == judge) and (A.count(0) == 1):\\n        ans = 2**(N//2)\\nelse:\\n    judge = [i for i in range(1,N,2)]\\n    if A_test == judge:\\n        ans = 2**(N//2)\\n\\nans = ans % (10**9 + 7)\\nprint(ans)\\n\", \"import sys\\nfrom collections import Counter\\nN = int(input())\\nA = list(map(int, input().split()))\\nMOD = 10 ** 9 + 7\\n\\nC = Counter(A)\\nC = sorted(C.items(), key=lambda x: x[0])\\nif N % 2 == 0:\\n    s = 1\\n    for k, v in C:\\n        if k != s or v != 2:\\n            print(0)\\n            return\\n        s += 2\\n    print(pow(2, (N // 2), MOD))\\nelse:\\n    s = 0\\n    for k, v in C:\\n        if k == 0:\\n            if k != 0 or v != 1:\\n                print(0)\\n                return\\n            s += 2\\n            continue\\n        if k != s or v != 2:\\n            print(0)\\n            return\\n        s += 2\\n    print(pow(2, (N - 1) // 2, MOD))\", \"from collections import Counter\\nn=int(input())\\na=sorted(list(map(int,input().split())))\\na_count=Counter(a)\\nif n%2==1:\\n    ans=1\\n    for i in a_count:\\n        if i%2!=0:\\n            print(0)\\n            break\\n        else:\\n            if i==0:\\n                if a_count[i]!=1:\\n                    print(0)\\n                    break\\n            \\n            else:\\n                if a_count[i]==2:\\n                     ans=(ans*2)%(10**9+7)\\n                else:\\n                    print(0)\\n                    break\\n    else:\\n      print(ans)\\nelse:\\n    ans=1\\n    for j in a_count:\\n        if j%2!=1:\\n            print(0)\\n            break\\n        else:\\n            if a_count[j]==2:\\n                ans=(ans*2)%(10**9+7)\\n           \\n            else:\\n                print(0)\\n                break\\n    else:\\n      print(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nflg = 0\\n\\na.sort()\\nif n % 2 == 0:\\n  if a[0] == 1 and a[1] == 1:\\n    for i in range(2, n, 2):\\n      if a[i] == a[i + 1] and a[i - 1] + 2 == a[i]:\\n        continue\\n      else:\\n        flg = 1\\n        break\\n  else:\\n    flg = 1\\nelse:\\n  if a[0] == 0:\\n    for i in range(1, n, 2):\\n      if a[i] == a[i + 1] and a[i - 1] + 2 == a[i]:\\n        continue\\n      else:\\n        flg = 1\\n        break\\n  else:\\n    flg = 1\\n\\nif flg == 1:\\n  print(0)\\nelse:\\n  print((2 ** (n // 2)) % (10 ** 9 + 7))\", \"n=int(input())\\nl=list(map(int,input().split()))\\nmod=10**9+7\\nif n%2==0:\\n    d={i:2 for i in range(1,n,2)}\\nelse:\\n    d={i:2 for i in range(0,n,2)}\\n    d[0]=1\\nfor a in l:\\n    if a in d:\\n        d[a]-=1\\n    else:\\n        print(0)\\n        return\\nfor i in d.values():\\n    if i!=0:\\n        print(0)\\n        return\\nprint((2**(n//2))%mod)\", \"def main():\\n  N = int(input())\\n  A = [int(a) for a in input().split(\\\" \\\")]\\n  A.sort()\\n \\n  if N % 2 == 1 and A.count(0) != 1:\\n    print(0)\\n    return 0\\n  elif N % 2 == 0 and A.count(0) > 0:\\n    print(0)\\n    return 0\\n  \\n  if N % 2 == 1:\\n    A.pop(0)\\n  \\n  cnt = 0\\n  while len(A) > 0:\\n    if A[0] != A[1] or (len(A) > 2 and A[0] == A[1] and A[1] == A[2]):\\n      print(0)\\n      return 0\\n    elif A[0] == A[1] == 2 * cnt + (N % 2) + 1:\\n      cnt += 1\\n      A.pop(0)\\n      A.pop(0)\\n    else:\\n      print(0)\\n      return 0\\n \\n  ans = 1\\n  for p in range(cnt):\\n    ans = (ans * 2) % 1000000007\\n  print(ans)\\n\\nmain()\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n == 1:\\n  print(1)\\n  return\\nelif n%2 == 0:\\n  for i in range(0,n-2,2):\\n    if a[i] != a[i+1] or a[i] == a[i+2]:\\n      print(0)\\n      return\\n  if a[-2] != a[-1]:\\n    print(0)\\n    return\\nelse:\\n  if a[0] != 0 or a[1] == 0:\\n    print(0)\\n    return\\n  for i in range(1,n-2,2):\\n    if a[i] != a[i+1] or a[i] == a[i+2]:\\n      print(0)\\n      return\\n  if a[-2] != a[-1]:\\n    print(0)\\n    return\\n\\nmod = 10**9+7\\nif n%2 == 0: print(2**(n//2)%mod)\\nelse: print(2**((n-1)//2)%mod)\", \"N = int(input())\\nA = list(map(int, input().split()))\\nmod = pow(10,9)+7\\nA.sort()\\n\\nif N%2 == 0:\\n    for i in range(N//2):\\n        if A[2*i] != A[2*i+1] or A[2*i] != 2*i+1:\\n            print((0))\\n            return\\n    ans = pow(2,N//2)\\n    print((ans%mod))\\nelse:\\n    if A[0] != 0:\\n        print((0))\\n        return\\n    for i in range(N//2):\\n        if A[2*i+1] != A[2*(i+1)] or A[2*i+1] != 2*(i+1):\\n            print((0))\\n            return\\n    ans = pow(2,N//2)\\n    print((ans%mod))\\n\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n \\na=True\\nif N%2==0:\\n for i in range(1,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    a=False\\n    break\\nelse:\\n if A[0]!=0:a=False\\n else:\\n    for i in range(2,N,2):\\n     if A[i-1]!=i or A[i]!=i:\\n        a=False\\n        break\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"from collections import Counter\\n\\nN = int(input())\\nA = list(map(int, input().split()))\\nMOD = int(1e9) + 7\\n\\n# \\u5076\\u6570\\u306e\\u5834\\u5408\\nif N % 2 == 0:\\n    c = Counter(A)\\n    if all(i == 2 for i in c.values()):\\n        print(pow(2, N//2, MOD))\\n    else:\\n        print(0)\\n# \\u5947\\u6570\\u306e\\u5834\\u5408\\nelse:\\n    A.sort()\\n    A = A[1:]\\n    c = Counter(A)\\n    if all(i == 2 for i in c.values()):\\n        print(pow(2, N//2, MOD))\\n    else:\\n        print(0)\", \"N = int(input())\\na = list(map(int, input().split()))\\nSum = 1\\nmod = 1000000007\\n\\na.sort()\\ndata = []\\nif N % 2 == 0:\\n    for i in range(int(N / 2)):\\n        data.append(1 + i * 2)\\n        data.append(1 + i * 2)\\nelse:\\n    data.append(0)\\n    for i in range(1, N // 2 + 1):\\n        data.append(i * 2)\\n        data.append(i * 2)\\n\\nif a == data:\\n    for i in range(N // 2):\\n        Sum *= 2\\n        Sum %= mod\\n    print(Sum)\\nelse:\\n    print((0))\\n\", \"N=int(input())\\nA=list(map(int,input().split()))\\n\\nA.sort()\\ncheck=[0]*N\\n\\nfor idx in range(N%2,N,2):\\n    check[idx]=idx+1\\n    check[idx+1]=idx+1\\n\\nans=0\\nmod=10**9+7\\nif check==A:\\n    if N%2==0:\\n        ans=(2**(N//2))%mod\\n    else:\\n        ans=(2**((N-1)//2))%mod\\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\nfrom collections import Counter\\nc = Counter(a)\\n\\ncheck_ary = []\\nif n&1:\\n    check_ary.append(0)\\n\\nfor i in range(n//2):\\n    for _ in range(2):\\n        check_ary.append((i+1)*2 if n&1 else i*2+1)\\n\\nc2 = Counter(check_ary)\\n\\nif c != c2:\\n    print(0)\\n    return\\n\\nprint(pow(2, n//2, 10**9+7))\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nB = [0] * N\\n\\nfor a in A:\\n    B[a] += 1\\n\\nok = True\\n\\nif N % 2 == 1:\\n    ok = ok and B[0] == 1\\n    for i in range(1, N):\\n        ok = ok and B[i] == (2 if i % 2 == 0 else 0)\\nelse:\\n    for i in range(N):\\n        ok = ok and B[i] == (0 if i % 2 == 0 else 2)\\n\\nans = 1\\nMOD = int(1e9) + 7\\nfor _ in range(N // 2):\\n    ans *= 2\\n    ans %= MOD\\n\\nprint((ans if ok else 0))\\n\", \"n=int(input())\\nA=list(map(int,input().split()))\\nA.sort()\\njudge=0\\nif n%2==1:\\n    for i in range(n):\\n        if A[i]!=2*((i+1)//2):\\n            judge+=1\\n            break\\nelse:\\n    for i in range(n):\\n        if A[i]!=2*(i//2)+1:\\n            judge+=1\\n            break\\nif judge==1:\\n    print(0)\\nelse:\\n    print((2**(n//2))%(10**9+7))\", \"from collections import Counter\\nn = int(input())\\na = list(map(int, input().split()))\\nc = Counter(a)\\nd = list(c.values())\\nif (n % 2 == 1 and c[0] == 1 and d.count(2) == (n-1)//2) or (n % 2 == 0 and d.count(2) == n//2):\\n    print(pow(2, n//2, 10**9+7))\\nelse:\\n    print(0)\", \"from collections import Counter\\nn = int(input())\\na = list(map(int, input().split()))\\nc = Counter(a)\\nd = list(c.values())\\nif (n % 2 == 1 and c[0] == 1 and d.count(2) == (n-1)//2) or (n % 2 == 0 and d.count(2) == n//2):\\n    print((2**(n//2)) % (10**9+7))\\nelse:\\n    print(0)\", \"N = int(input())\\nK = [0 for i in range(N+1)]\\nA = list(map(int,input().rstrip().split(\\\" \\\")))\\nans = 1\\nfor i in A:\\n    K[i] += 1\\nfor i in range(N):\\n    if i != 0 and K[i] != 0 and K[i] != 2:\\n        ans = 0\\n        break\\n    if K[i] == 2:\\n        ans *= 2\\n        ans %= 10 ** 9 + 7\\nprint(ans)\", \"import collections\\n\\nn = int(input())\\na = list(map(int, input().split()))\\ncnt = collections.Counter(a)\\nmod = 7 + 10**9\\nif n % 2 == 0:\\n    for i in range(1, 1 + n // 2):\\n        if (i * 2 - 1) not in cnt.keys() or cnt[i * 2 - 1] != 2:\\n            print(0)\\n            return\\n\\nelse:\\n    if 0 not in cnt.keys() or cnt[0] != 1:\\n        print(0)\\n        return\\n    for i in range(1, 1 + n // 2):\\n        if i * 2 not in cnt.keys() or cnt[i * 2] != 2:\\n            print(0)\\n            return\\nprint(2 ** (n // 2) % mod)\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\n\\na = sorted(a)\\n\\nnum = 0\\njudge = 0\\n\\nif len(a)%2 == 1:\\n    if a[0] == 0:\\n        for i in range(1, n, 2):\\n            if a[i] == i+1 and a[i+1] == i+1:\\n                num += 1\\n            else:\\n                print(0)\\n                judge = 1\\n                break\\n    else:\\n        print(0)\\n        judge=1\\nelse:\\n    for i in range(0, n, 2):\\n            if a[i] == i+1 and a[i+1] == i+1:\\n                num += 1\\n            else:\\n                print(0)\\n                judge = 1\\n                break\\n        \\nif judge == 0:\\n    result = (2**num)%(10**9+7)\\n    print(result)\", \"from collections import defaultdict\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nL = A[:]\\nL = list(set(L))\\n\\nmod = 10 ** 9 + 7\\n\\nd = defaultdict(int)\\nfor i in range(N):\\n    d[A[i]] += 1\\n\\nif N % 2 == 1:\\n    bfr = 0\\n    for i in L:\\n        if i - bfr != 2 and i != 0:\\n            print((0))\\n            return\\n\\n        if i == 0:\\n            if d[i] != 1:\\n                print((0))\\n                return\\n            else:\\n                continue\\n        if d[i] != 2:\\n            print((0))\\n            return\\n        bfr = i\\n\\n    print(((2 ** (N // 2)) % mod))\\nelse:\\n    bfr = 1\\n    for i in L:\\n        if i - bfr != 2 and i != 1:\\n            print((0))\\n            return\\n\\n        if d[i] != 2:\\n            print((0))\\n            return\\n        bfr = i\\n\\n    print(((2 ** (N // 2)) % mod))\\n\", \"n = int(input())\\na = list(map(int,input().split()))\\nmod = 10**9+7\\n\\na.sort()\\n\\nif n%2 == 1: \\n    if a[0] != 0:\\n        print((0))\\n        return\\n    else:\\n        a.remove(0)\\n        tmp = 2\\nelse:\\n    tmp = 1\\n\\nfor i in range(n//2):\\n    if tmp == a[0] and tmp == a[1]:\\n        a.remove(tmp)\\n        a.remove(tmp)\\n    else:\\n        print((0))\\n        return\\n    tmp += 2\\n\\nif len(a) == 0:\\n    print(((2**(n//2))%mod))\\nelse:\\n    print((0))\\n\\n\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nnum_map = [0] * ((n + 2 - 1) // 2)\\nfor i in range(n):\\n    num_map[a[i] // 2] += 1\\n\\nres = 1\\nif n % 2 == 1:\\n    if num_map[0] != 1:\\n        print((0))\\n    else:\\n        for i in range(1, (n + 2 - 1) // 2):\\n            if num_map[i] != 2:\\n                print((0))\\n                break\\n            else:\\n                res = res * 2 % mod\\n        else:\\n            print(res)\\nelse:\\n    for i in range((n + 2 - 1) // 2):\\n        if num_map[i] != 2:\\n            print((0))\\n            break\\n        else:\\n            res = res * 2 % mod\\n    else:\\n        print(res)\\n\", \"N=int(input())\\nA=list(map(int,input().split()))\\nmod = 10**9+7\\n\\nA=tuple(sorted(A))\\n\\nif N % 2 == 1:\\n  nums=[0]\\n  for i in range(2,N+1,2):\\n    nums.append(i)\\n    nums.append(i)\\nelse:\\n  nums=[]\\n  for i in range(1,N+1,2):\\n    nums.append(i)\\n    nums.append(i)\\n    \\nnums = tuple(nums)\\nif A != nums:\\n  print(0)\\n  return\\n  \\nprint(2**(N//2) % mod)\", \"N = int(input())\\nA = list(map(int,input().split()))\\nA.sort()\\nmod = 10**9 + 7\\nif N%2 == 0:\\n    for i in range(N):\\n        if A[i] != 1+(i//2)*2:\\n            print(0)\\n            break\\n    else:\\n        print(pow(2,N//2,mod))\\nelse:\\n    if A[0] == 0:\\n        for i in range(1,N):\\n            if A[i] != ((i+1)//2)*2:\\n                print(0)\\n                break\\n        else:\\n            print(pow(2,N//2,mod))\", \"n = int(input())\\na = list(map(int,input().split()))\\nmod = 10**9 + 7\\n\\nd = [0]*(n+1)\\nfor x in a:\\n    d[x] += 1\\nans = 1\\nif n%2 == 0:\\n    sw = 1\\n    for i,x in enumerate(d):\\n        if i%2 != 0:\\n            if x == 2:\\n                ans *= 2\\n                ans %= mod\\n            else:\\n                sw = 0\\n                break\\n        else:\\n            if x != 0:\\n                sw = 0\\n                break\\nelse:\\n    sw = 1\\n    for i,x in enumerate(d):\\n        if i%2 == 0:\\n            if i == 0:\\n                if x != 1:\\n                    sw = 0\\n                    break\\n            else:\\n                if x == 2:\\n                    ans *= 2\\n                    ans %= mod\\n                else:\\n                    sw = 0\\n                    break\\n        else:\\n            if x != 0:\\n                sw = 0\\n                break\\nif sw == 0:\\n    ans = 0\\nprint(ans)\\n\", \"N = int(input())\\nA = sorted(list(map(int,input().split())))\\n\\nif N%2==0:\\n  B = [1+2*(n//2) for n in range(N)]\\nelse:\\n  B = [2*(n//2) for n in range(1,1+N)]\\n\\nif A==B:\\n  print(pow(2,N//2,10**9+7))\\nelse:\\n  print(0)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\nMOD = 10 ** 9 + 7\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N = I()\\n    A = LI()\\n\\n    if N % 2 == 0:\\n        if sorted(A) == [i // 2 * 2 + 1 for i in range(N)]:\\n            print((pow(2, N // 2, MOD)))\\n        else:\\n            print((0))\\n    else:\\n        if sorted(A) == [(i // 2 + 1) * 2 for i in range(-1, N - 1)]:\\n            print((pow(2, (N - 1) // 2, MOD)))\\n        else:\\n            print((0))\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"def PowerMod(N,P,Mod):\\n    if N%Mod==0:\\n        return 0\\n    else:\\n        PowM = 1\\n        for TP in range(1,P+1):\\n            PowM = (PowM*N)%Mod\\n        return PowM\\n\\nfrom collections import Counter\\nN = int(input())\\nA = sorted(Counter([int(T) for T in input().split()]).most_common(),key=lambda X:X[0])\\nPassFlag = True\\nif N%2==1:\\n    for TA in range(0,(N+1)//2):\\n        if A[TA][0]!=(2*TA) or A[TA][1]!=(1+(A[TA][0]!=0)):\\n            PassFlag = False\\n            break\\n    print([0,PowerMod(2,(N-1)//2,10**9+7)][PassFlag])\\nelse:\\n    for TA in range(0,N//2):\\n        if A[TA][0]!=(2*TA+1) or A[TA][1]!=2:\\n            PassFlag = False\\n            break\\n    print([0,PowerMod(2,N//2,10**9+7)][PassFlag])\", \"from collections import Counter\\n\\nn = int(input())\\nc = Counter(list(map(int, input().split())))\\n\\nans = 0\\nfor k, v in list(c.items()):\\n    if k == 0:\\n        if n%2==0 and v > 2:\\n            print((0))\\n            return\\n        elif n%2==1 and v > 1:\\n            print((0))\\n            return\\n    else:\\n        ans += 1\\n        if v > 2:\\n            print((0))\\n            return\\n\\nprint((pow(2, ans, 10**9+7)))\\n\", \"from typing import Counter\\n\\n\\nn = int(input())\\nlis = list(map(int, input().split()))\\nmod  =10**9+7\\n\\nans = 0\\nif n % 2 == 0:\\n    b = Counter(lis)\\n    flag = 1\\n    for i in list(b.values()):\\n        if i == 2:\\n            pass\\n        else:\\n            flag = 0\\n            break\\n    if flag:\\n        ans = 2**(n//2)\\n        print((ans % mod))\\n    else:\\n        print((0))\\nelse:\\n    lis = sorted(lis)\\n    lis = lis[1:]\\n    b = Counter(lis)\\n    flag = 1\\n    for i in list(b.values()):\\n        if i == 2:\\n            pass\\n        else:\\n            flag = 0\\n            break\\n    if flag:\\n        ans = 2**(n//2)\\n        print((ans % mod))\\n    else:\\n        print((0))\\n\", \"n=int(input())\\na=list(map(int,input().split()))\\nflag=0\\nA=a.sort()\\nnum=[]\\n\\nif n%2==0:\\n    for i in range(1,n,2):\\n        num.append(i)\\n        num.append(i)\\n\\nif n%2==1:\\n    num=[0]\\n    for i in range(2,n,2):\\n        num.append(i)\\n        num.append(i)\\n\\nif num==a:\\n    print(2**(n//2)%(10**9+7))\\n\\nelse:\\n    print(\\\"0\\\")\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\nf=lambda:2**(N//2)%(10**9+7)\\na=True\\nif N%2==0:\\n    for i in range(1,N,2):\\n        if A[i-1]!=i or A[i]!=i:\\n            # print(i,A[i-1],A[i])\\n            a=False\\n            break\\nelse:\\n    if A[0]!=0:\\n            a=False\\n    else:\\n        for i in range(2,N,2):\\n            if A[i-1]!=i or A[i]!=i:\\n                # print(i,A[i-1],A[i])\\n                a=False\\n                break\\nprint(f() if a else 0)\", \"n = int(input())\\nA = list(map(int, input().split()))\\n\\nd = {}\\nfor a in A:\\n    d[a] = d.get(a, 0)+1\\n\\nzero_cnt = 0\\ntwo = 0\\nno = 0\\nfor i in d:\\n    if i==0:\\n        zero_cnt+=1\\n    elif d[i]==2:\\n        two+=1\\n    else:\\n        no+=1\\n\\nif no!=0 or (n%2==0 and zero_cnt!=0) or (n%2==1 and zero_cnt!=1):\\n    print((0))\\nelse:\\n    ans = 1\\n    mod = 10**9+7\\n    for i in range(two):\\n        ans *= 2\\n        ans %= mod\\n    print((ans%mod))\\n\", \"MOD = 10 ** 9 + 7\\nnum = [0] * (10 ** 5 + 1)\\nN = int(input())\\nA = list(map(int,input().split()))\\nfor i in range(len(A)):\\n\\tnum[A[i]] += 1\\nif N % 2 == 1:\\n\\tfor i in range(0,N,2):\\n\\t\\tcnt = num[i]\\n\\t\\tif i == 0:\\n\\t\\t\\tif cnt != 1:\\n\\t\\t\\t\\tprint(0)\\n\\t\\t\\t\\treturn\\n\\t\\telse:\\n\\t\\t\\tif cnt != 2:\\n\\t\\t\\t\\tprint(0)\\n\\t\\t\\t\\treturn\\n\\tprint(2 ** (N // 2) % MOD)\\nelse:\\n\\tfor i in range(1,N,2):\\n\\t\\tcnt = num[i]\\n\\t\\tif cnt != 2:\\n\\t\\t\\tprint(0)\\n\\t\\t\\treturn\\n\\tprint(2 ** (N // 2) % MOD)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return False\\n return True   \\n    \\na=True\\nif N%2==0:a=f(1)\\nelse:\\n if A[0]!=0:a=False\\n else:a=f(2)\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, *A = list(map(int, read().split()))\\n\\n    A.sort()\\n\\n    ok = True\\n    if len(A) % 2 == 0:\\n        for i in range(N // 2):\\n            if not A[2 * i] == A[2 * i + 1] == 2 * i + 1:\\n                ok = False\\n                break\\n    else:\\n        if A[0] != 0:\\n            ok = False\\n        else:\\n            for i in range(N // 2):\\n                if not A[2 * i + 1] == A[2 * i + 2] == 2 * i + 2:\\n                    ok = False\\n                    break\\n\\n    if ok:\\n        ans = pow(2, N // 2, MOD)\\n    else:\\n        ans = 0\\n\\n    print(ans)\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nm = 1000000007\\n\\nA.sort()\\nif N % 2 == 0:\\n    B = list(range(1, N, 2)) * 2\\nelse:\\n    B = [0] + list(range(2, N, 2)) * 2\\nB.sort()\\n\\nif A != B:\\n    print((0))\\nelse:\\n    result = 1\\n    for i in range(N // 2):\\n        result *= 2\\n        result %= m\\n    print(result)\\n\", \"N = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfrom collections import defaultdict as dd\\nDict = dd(lambda:0)\\nfor a in A:\\n    Dict[a] += 1\\n\\nif N & 1: Dict[0] += 1\\nf = (lambda:(lambda x:0 if x&1 else 2) if N&1 else (lambda x:2 if x&1 else 0))()\\nPossible = {i:f(i) for i in range(N)}\\nfor key,value in list(Dict.items()):\\n    if value != Possible[key]:\\n        print((0))\\n        return\\nelse:\\n    print((2**(N//2)%1000000007))\\n                \\n\\n\", \"import sys\\n\\n# n = 10 ** 5\\n# \\u30c7\\u30fc\\u30bf\\u8aad\\u307f\\u8fbc\\u307f\\u95a2\\u4fc2\\nn = int(input())\\n\\na = list(map(int, input().split(' ')))\\n\\nrecord = {}\\n\\npossible = True\\n\\n# \\u72b6\\u6cc1\\u304c\\u5b9f\\u73fe\\u53ef\\u80fd\\u304b\\u78ba\\u8a8d\\nfor e in a:\\n    if(e in record.keys()):\\n        record[e] += 1\\n        if(record[e] == 2):\\n            if(e == 0):\\n                possible = False\\n                break\\n        if(record[e] == 3):\\n            possible = False\\n            break\\n    else:\\n        record[e] = 1\\n\\nif(possible == False):\\n    print(0)\\n    return\\n\\nmultiCount = int(n / 2)\\n\\nprint(2 ** multiCount % (10 ** 9 + 7))\", \"import collections\\nN = int(input())\\nA = list(map(int,input().split()))\\nans = 1\\nif 0 in A:\\n    A.remove(0)\\nAcounter = collections.Counter(A)\\nfor i in Acounter.values():\\n    if i == 2:\\n        continue\\n    else:\\n        ans = 0\\n        break\\nif ans == 0:\\n    pass\\nif ans != 0:\\n    for i in range(N//2):\\n        ans = (ans * 2) % (10**9 + 7)\\nprint(ans)\", \"import sys\\nsys.setrecursionlimit(10 ** 7)\\ndef input() : return sys.stdin.readline().strip()\\ndef INT()   : return int(input())\\ndef MAP()   : return map(int,input().split())\\ndef LIST()  : return list(MAP())\\ndef NIJIGEN(H): return [list(input()) for i in range(H)]\\nmod=1000000007\\nN=INT()\\nL=LIST()\\nif N%2==0:\\n  A=range(1,N,2)\\n  B=range(1,N,2)\\nelse:\\n  A=range(0,N,2)\\n  B=range(2,N,2)\\nA,B=list(A),list(B)\\nA=A+B\\nif sorted(A)==sorted(L):\\n  print(pow(2,N//2,mod))\\nelse:\\n  print(0)\", \"n=int(input())\\na=list(map(int,input().split()))\\n\\nb=[0 for i in range(10**5+1)]\\nfor i in a:\\n  b[i]+=1\\n\\nif (n%2==0 and b[0]!=0) or (n%2==1 and b[0]!=1):\\n  print(0)\\n  return\\n\\nans=1\\nmod=10**9+7\\nfor i in b:\\n  if i==2:\\n    ans*=2\\n    ans%=mod\\n  if i>=3:\\n    print(0)\\n    return\\n\\nprint(ans)\", \"from collections import Counter\\n\\nn=int(input())\\na=list(map(int,input().split()))\\n\\nc=Counter(a)\\n\\nif (n%2==0 and c[0]!=0) or (n%2==1 and c[0]!=1):\\n  print(0)\\n  return\\n\\nans=1\\nmod=10**9+7\\nfor i in c:\\n  if c[i]==2:\\n    ans*=2\\n    ans%=mod\\n  if c[i]>=3:\\n    print(0)\\n    return\\n\\nprint(ans)\", \"from collections import Counter\\n\\nN = int(input())\\nabs_diffs = list(map(int, input().split()))\\n\\nif N % 2 == 0:\\n    expected = [i // 2 * 2  + 1 for i in range(N)]\\n    dims = N // 2\\nelse:\\n    expected = [(i + 1) // 2 * 2 for i in range(N)]\\n    dims = (N - 1) // 2\\n\\nif sorted(abs_diffs) == expected:\\n    print((2 ** dims % (10 ** 9 + 7)))\\n\\nelse:\\n    print((0))\\n\", \"n = int(input())\\nA = sorted(map(int,input().split()))\\n\\nif n % 2 == 1:\\n    ex = [0]\\n    \\n    for i in range(n//2):\\n        a = 2 * (i+1)\\n        ex += [a,a]\\n        \\nelse:\\n    ex = []\\n    a = 1\\n    \\n    for i in range(n//2):\\n        ex += [a,a]\\n        a += 2\\n        \\nans = 0\\n\\nif A == ex:\\n    ans = 2 ** (n//2) % (10**9 + 7)\\n    \\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nif n % 2 == 0:\\n    b = [2 if i % 2 == 1 else 0 for i in range(n)]\\nelse:\\n    b = [2 if i % 2 == 0 else 0 for i in range(n)]\\n    b[0] = 1\\nc = [0 for i in range(n)]\\nfor i in range(n):\\n    c[a[i]] += 1\\nif b != c:\\n    print(0)\\nelse:\\n    ans = 1\\n    for i in range(n // 2):\\n        ans *= 2\\n        ans %= mod\\n    print(ans)\", \"N = int(input())\\nA = sorted(list(map(int,input().split())))\\n\\nif N%2==0:\\n  B = [2*(n//2)+1 for n in range(N)]\\nelse:\\n  B = [2*(n//2) for n in range(1,N+1)]\\n\\nif A==B:\\n  print(pow(2,N//2,10**9+7))\\nelse:\\n  print(0)\", \"MOD = 10**9+7\\n\\ndef fast_pow(x, n, MOD):\\n    res = 1\\n    while n:\\n        if n & 1:\\n            res = res * x % MOD\\n        x = x * x % MOD\\n        n >>= 1\\n    return res\\n\\n\\nn = int(input())\\na = list(map(int, input().split()))\\n\\nd = {}\\nfor i in a:\\n    if n % 2:\\n        if i > 0 and i % 2:\\n            print((0))\\n            return\\n    else:\\n        if i > 0 and i % 2 == 0:\\n            print((0))\\n            return\\n\\n    if not i in d:\\n        d[i] = 1\\n    elif d[i] == 1:\\n        d[i] += 1\\n    else:\\n        print((0))\\n        return\\n\\nif n % 2:\\n    if d[0] != 1:\\n        print((0))\\n        return\\n    print((fast_pow(2, len(d)-1, MOD)))\\nelse:\\n    if 0 in d:\\n        print((0))\\n        return\\n    print((fast_pow(2, len(d), MOD)))\\n\", \"import math\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nflag = True\\nif N%2 == 0:\\n    if 0 in A or len(set(A)) != N//2:\\n        flag = False\\nelse:\\n    if len([0 for a in A if a == 0]) != 1 or len(set(A)) != N//2 + 1:\\n        flag = False\\n\\nif  flag:\\n    print((2**((N//2))%(10**9+7)))\\nelse:\\n    print((0))\\n\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return 0\\n return 1   \\n    \\na=1\\nif N%2==0:a=f(1)\\nelse: a=A[0]==0 and f(2)\\nprint(2**(N//2)%(10**9+7)*a)\", \"n = int(input())\\nA = tuple(map(int, input().split()))\\nmod = 10**9+7\\n\\nniseven = (n%2 == 0)\\n\\ncd = dict()\\nfor a in (A):\\n    cd.setdefault(a, 0)\\n    cd[a] += 1\\n    if a == 0 and cd[a] > 1:\\n        print((0))\\n        break\\n    if a > 0 and cd[a] > 2:\\n        print((0))\\n        break\\n    if (a%2==0) == niseven:\\n        print((0))\\n        break\\nelse:\\n    print((pow(2, n//2, mod)))\\n\", \"def main():\\n  N=int(input())\\n  A=list(map(int,input().split()))\\n  mod=10**9+7\\n  ans=1\\n  A.sort()\\n  if N%2==0:\\n    for i in range(0,N,2):\\n      if A[i]!=A[i+1] or A[i]!=i+1:\\n        print(0)\\n        return\\n      ans=ans*2%mod\\n    print(ans)\\n  else:\\n    if A[0]!=0:\\n      print(0)\\n      return\\n    ans=1\\n    for i in range(1,N,2):\\n      if A[i]!=A[i+1] or A[i]!=i+1:\\n        print(0)\\n        return\\n      ans=ans*2%mod\\n    print(ans)\\ndef __starting_point():\\n  main()\\n__starting_point()\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\n# \\u77db\\u76fe\\u30c1\\u30a7\\u30c3\\u30af\\nfrom collections import Counter\\nc = Counter(a)\\n\\ndef check():\\n    if n&1:\\n        if c[0]!=1:\\n            return False\\n        for i in range((n-1)//2):\\n            if c[2*(i+1)] != 2:\\n                return False\\n    else:\\n        for i in range(n//2):\\n            if c[2*i+1] != 2:\\n                return False\\n    return True\\n\\nif not check():\\n    print(0)\\n    return\\n\\nprint(pow(2, n//2, 10**9+7))\", \"n = int(input())\\na = list(map(int,input().split()))\\ndic = {}\\nfor i in range(n):\\n    dic.setdefault(a[i],0)\\n    dic[a[i]] += 1\\nans = 1\\nfor key,value in dic.items():\\n    #\\u5076\\u6570\\n    if n%2==0:\\n        if n > key and key%2==1 and value==2:\\n            ans *= 2\\n        else:\\n            ans = 0\\n            break\\n    #\\u5947\\u6570\\n    else:\\n        if n > key and key%2==0:\\n            if key==0 and value==1:\\n                ans *= 1\\n            elif value==2:\\n                ans *= 2\\n            else:\\n                ans = 0\\n                break\\n        else:\\n            ans = 0\\n            break\\nprint(ans%(10**9+7))\", \"N=int(input())\\nMOD=10**9+7\\nA=[int(x) for x in input().split()]\\nflag=1#\\u305d\\u306e\\u4e26\\u3073\\u9806\\u304c\\u3042\\u308a\\u3048\\u308b\\u306a\\u30891\\u3001\\u305d\\u3046\\u3067\\u306a\\u3044\\u306a\\u30890\\nset1=set()\\nset2=set()\\nif N%2==1:\\n    set1.add(0)\\n    for j in range(2,N+1,2):\\n        set1.add(j)\\n        set2.add(j)\\n    for i in range(N):\\n        now=A[i]\\n        if now in set1:\\n            set1.remove(now)\\n        elif now in set2:\\n            set2.remove(now)\\n        else:\\n            flag=0\\n            break\\n    if len(set1)!=0 or len(set2)!=0:\\n        flag=0\\nelse:\\n    for k in range(1,N+1,2):\\n        set1.add(k)\\n        set2.add(k)\\n    for p in range(N):\\n        now=A[p]\\n        if now in set1:\\n            set1.remove(now)\\n        elif now in set2:\\n            set2.remove(now)\\n        else:\\n            flag=0\\n            break\\n    if len(set1)!=0 or len(set2)!=0:\\n        flag=0\\nif flag==0:\\n    print((0))\\nelse:\\n    ans=1\\n    div2=N//2\\n    for q in range(div2):\\n        ans*=2\\n        ans%=MOD\\n    print(ans)\\n\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nm = 1000000007\\n\\nA.sort()\\nif N % 2 == 0:\\n    B = list(range(1, N, 2)) * 2\\nelse:\\n    B = [0] + list(range(2, N, 2)) * 2\\nB.sort()\\n\\nif A != B:\\n    print((0))\\nelse:\\n    result = 1\\n    for i in range(N // 2):\\n        result *= 2\\n        result %= m\\n    print(result)\\n\", \"from collections import Counter\\n\\nN,*A = map(int, open(0).read().split())\\nac = Counter(A)\\nif N % 2 == 0:\\n    for i in range(1,N,2):\\n        if ac[i] != 2:\\n            print(0)\\n            break\\n    else:\\n        print(pow(2,N//2,1000000007))\\nelse:\\n    if ac[0] != 1:\\n        print(0)\\n    else:\\n        for i in range(2,N,2):\\n            if ac[i] != 2:\\n                print(0)\\n                break\\n        else:\\n            print(pow(2,N//2,1000000007))\", \"n=int(input())\\na=list(map(int,input().split()))\\nif n%2==1:\\n    x=[i for i in range(n)]\\n    for i in range(n):\\n        if i%2==1:\\n            x[i]+=1\\nelse:\\n    x=[i for i in range(n)]\\n    for i in range(n):\\n        if i%2==0:\\n            x[i]+=1\\na.sort()\\nif x==a:\\n    print(pow(2,(n//2),10**9+7))\\nelse:\\n    print(0)\", \"import sys\\nfrom collections import deque\\np=10**9+7\\n\\ndef main(n,a):\\n  h=n//2\\n  g=n%2\\n  a.sort()\\n  c=[2*(x//2)+g+1 for x in range(n-g)]\\n  if g==1:\\n    c.insert(0,0)\\n  if a!=c:\\n      return 0\\n  return 2**(h%(p-1)) % p\\n\\ndef __starting_point():\\n  n=int(input())\\n  a=list(map(int,sys.stdin.readline().strip().split()))\\n  print((main(n,a)))\\n\\n__starting_point()\", \"N=int(input())\\nS=list(map(int,input().split()))\\nlenS=len(S)\\nT=[]\\nfor i in range(1,N+1):\\n    T.append(abs(i-(N+1-i)))\\n\\nT.sort()\\nS.sort()\\n\\n\\n\\nfor i in range(N):\\n    if T[i]!=S[i]:\\n        print((0))\\n        return\\n\\n\\nans=1\\nnagasa=lenS//2\\nfor i in range(nagasa):\\n    \\n    ans=(ans*2)%(10**9+7)\\n\\nprint(ans)\\n\\n\\n\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n%2 == 0: # \\u4eba\\u6570\\u304c\\u5076\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  for i in range(0,n,2):\\n    if a[i] != i+1 or a[i] != a[i+1]:\\n      print(0)\\n      return\\nelse: # \\u4eba\\u6570\\u304c\\u5947\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  if a[0] != 0: # \\u5dee\\u5206\\u304c0\\u5b58\\u5728\\u3057\\u3066\\u3044\\u308b\\u3053\\u3068\\u3092\\u78ba\\u8a8d\\n    print(0)\\n    return\\n  else:\\n    for i in range(1,n,2):\\n      if a[i] != i+1 or a[i] != a[i+1]:\\n        print(0)\\n        return\\n\\nans = 1\\nfor i in range(n//2):\\n  ans = ans * 2 % (10**9+7) # \\u7d44\\u307f\\u5408\\u308f\\u305b\\u3068\\u3057\\u3066\\u306f\\u540c\\u3058\\u5dee\\u5206\\u306e\\u5024\\u3092\\u5165\\u308c\\u66ff\\u3048\\u308b2\\u629e\\u306b\\u306a\\u308b\\u306e\\u3067\\u3001\\u7d50\\u679c\\u30922\\u500d\\u306b\\u3059\\u308b\\nprint(ans)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\na=True\\nif N%2==0:\\n for i in range(1,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    a=False\\n    break\\nelse:\\n if A[0]!=0:a=False\\n else:\\n    for i in range(2,N,2):\\n     if A[i-1]!=i or A[i]!=i:\\n        a=False\\n        break\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"import math\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nflag = True\\nif N%2 == 0:\\n    if 0 in A or len(set(A)) != N//2:\\n        flag = False\\nelse:\\n    if len([0 for a in A if a == 0]) != 1 or len(set(A)) != N//2 + 1:\\n        flag = False\\n\\nif  flag:\\n    print((2**(math.floor(N/2))%(10**9+7)))\\nelse:\\n    print((0))\\n\", \"from collections import Counter\\n\\nn = int(input())\\nA = list(map(int, input().split()))\\ncnt_A = Counter(A)\\n\\nif all([v == 2 for k, v in cnt_A.items() if k != 0]):\\n    print(pow(2, n // 2, 10**9 + 7))\\nelse:\\n    print(0)\", \"N=int(input())\\nMOD=1000000007\\nA=list(map(int,input().split()))\\ncnt=[0 for i in range(N)]\\nfor i in range(N):\\n    cnt[A[i]]+=1\\nif N%2==0:\\n    for i in range(1,N,2):\\n        if cnt[i]!=2:\\n            print((0))\\n            break\\n    else:\\n        print((2**(N//2)%MOD))\\nelse:\\n    if cnt[0]!=1:\\n        print((0))\\n    else:\\n        for i in range(2,(N+1)//2,2):\\n            if cnt[i]!=2:\\n                print((0))\\n                break\\n        else:\\n            print((2**((N-1)//2)%MOD))\\n\", \"import collections\\nimport sys\\ninput = sys.stdin.readline\\n\\nN = int(input())\\nA = list(map(int,input().split()))\\nm = 1000000007\\n\\nflag0 = 1\\ncount = 0\\n#\\u5076\\u6570\\u3060\\u3063\\u305f\\u3089\\nif N %2 ==0:\\n    colA = collections.Counter(A)\\n    for key,val in list(colA.items()):\\n        if key%2 != 1 or val != 2:\\n            flag0 = 0\\n            break\\n    for i in range(1,N,2):\\n        if i not in list(colA.keys()):\\n            flag = 0\\n            break\\n        else:\\n            count +=1\\n#\\u5947\\u6570\\u3060\\u3063\\u305f\\u3089\\nelse:\\n    A.append(0)\\n    colA = collections.Counter(A)\\n    for key,val in list(colA.items()):\\n        if key%2 != 0 or val != 2:\\n            flag0 = 0\\n            break\\n    for i in range(0,N,2):\\n        if i not in list(colA.keys()):\\n            flag = 0\\n            break\\n        else:\\n            count +=1\\n    count -=1\\n\\n\\nprint((((2**count)%m)*flag0))\\n    \\n\"]",
        "difficulty": "introductory",
        "input": "7\n6 4 0 2 4 0 2\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc050/tasks/arc066_a"
    },
    {
        "id": 270,
        "task_id": 4604,
        "test_case_id": 3,
        "question": "There are N people, conveniently numbered 1 through N.\nThey were standing in a row yesterday, but now they are unsure of the order in which they were standing.\nHowever, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.\nAccording to their reports, the difference above for person i is A_i.\nBased on these reports, find the number of the possible orders in which they were standing.\nSince it can be extremely large, print the answer modulo 10^9+7.\nNote that the reports may be incorrect and thus there may be no consistent order.\nIn such a case, print 0.\n\n-----Constraints-----\n - 1≦N≦10^5\n - 0≦A_i≦N-1\n\n-----Input-----\nThe input is given from Standard Input in the following format:\nN\nA_1 A_2 ... A_N\n\n-----Output-----\nPrint the number of the possible orders in which they were standing, modulo 10^9+7.\n\n-----Sample Input-----\n5\n2 4 4 0 2\n\n-----Sample Output-----\n4\n\nThere are four possible orders, as follows:\n - 2,1,4,5,3\n - 2,5,4,1,3\n - 3,1,4,5,2\n - 3,5,4,1,2",
        "solutions": "[\"n = int(input())\\na = [int(x) for x in input().split()]\\na.sort()\\nmod = 10 ** 9 + 7\\n\\ndef p(p):\\n  ans = 1\\n  for i in range(p):\\n    ans *= 2\\n    ans %= mod\\n  return ans\\n\\nif n % 2 == 1:\\n  res = True\\n  for i in range(n):\\n    if a[i] != ((i + 1) // 2) * 2:\\n      res = False\\n  if res:\\n    print(p(n // 2))\\n  else:\\n    print(0)\\n    \\nelse:\\n  res = True\\n  for i in range(n):\\n    if a[i] != (i // 2) * 2 + 1:\\n      res = False\\n  if res:\\n    print(p(n // 2))\\n  else:\\n    print(0)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return 0\\n return 1   \\n    \\na=1\\nif N%2==0:a=f(1)\\nelse:\\n if A[0]!=0:a=0\\n else:a=f(2)\\nprint(2**(N//2)%(10**9+7)*a)\", \"import math\\n\\nN = 5\\nARR = [2, 4, 4, 0, 2]\\n\\nN = 7\\nARR = [6, 4, 0, 2, 4, 0, 2]\\n#\\n# N = 8\\n# ARR = [7, 5, 1, 1, 7, 3, 5, 3]\\n#\\nN = int(input())\\nARR = list(map(int, input().split()))\\n\\n\\ndef calculate(n, arr):\\n    if n % 2 == 0:\\n        n = n // 2\\n        start = 1\\n        finalResult = pow(2, n, 1000000000 + 7)\\n    else:\\n        n = n // 2 + 1\\n        start = 0\\n        finalResult = pow(2, (n - 1), 1000000000 + 7)\\n\\n    result = {}\\n    for i in range(n):\\n        index = start + 2 * i\\n        if index == 0:\\n            result.__setitem__(0, 1)\\n        else:\\n            result.__setitem__(index, 2)\\n\\n    isOk = True\\n    for i in range(len(arr)):\\n        if result.get(arr[i]) == None:\\n            isOk = False\\n            break\\n\\n        if result.get(arr[i]) == 0:\\n            isOk = False\\n            break\\n\\n        result.__setitem__(arr[i], result.get(arr[i])-1)\\n\\n    if isOk == False:\\n        print((0))\\n        return\\n\\n    if sum(result.values()) == 0:\\n        print(finalResult)\\n    else:\\n        print((0))\\n\\n\\ncalculate(N, ARR)\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\na.sort()\\nres = True\\nif n % 2 != 0:\\n  if a[0] != 0:\\n    res = False\\n    print(0)\\n  a = a[1:]\\nfor i in range(0, len(a), 2):\\n  if a[i] != a[i+1]:\\n    print(0)\\n    res = False\\n    break\\n\\np = 10**9 + 7\\nif res:\\n  print(pow(2, n//2, p))\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\nans = 1\\n\\nif n%2 == 0:\\n    for i in range(0, n, 2):\\n        if a[i] != i + 1 or a[i + 1] != i + 1:\\n            print(0)\\n            return\\nelse:\\n    if a[0] != 0:\\n        print(0)\\n        return\\n    for i in range(1, n, 2):\\n        if a[i] != i + 1 or a[i + 1] != i + 1:\\n            print(0)\\n            return\\n\\nfor i in range(n//2):\\n    ans = ans*2%(10**9 + 7)\\n\\nprint(ans)\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n%2 == 0: # \\u4eba\\u6570\\u304c\\u5076\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  for i in range(0,n,2):\\n    if a[i] != i+1 or a[i+1] != i+1:\\n      print(0)\\n      return\\nelse: # \\u4eba\\u6570\\u304c\\u5947\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  if a[0] != 0: # \\u5dee\\u5206\\u304c0\\u5b58\\u5728\\u3057\\u3066\\u3044\\u308b\\u3053\\u3068\\u3092\\u78ba\\u8a8d\\n    print(0)\\n    return\\n  else:\\n    for i in range(1,n,2):\\n      if a[i] != i + 1 or a[i+1] != i + 1:\\n        print(0)\\n        return\\n        \\nans = 1        \\nfor i in range(n//2):\\n  ans = ans*2%(10**9+7)\\nprint(ans)\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\nif n % 2 == 0:\\n    b,s = [1,1],3\\nelse:\\n    b,s = [0],2\\nfor i in range(s,n,2):\\n    b += [i,i]\\nif a == b:\\n    print(pow(2,n//2,1000000007))\\nelse:\\n    print(0)\", \"N = int(input())\\nN_List = sorted(list(map(int,input().split())))\\nflg = 0\\nans = 1\\nif N % 2 == 1:\\n    if N_List[0] != 0:\\n        flg = 1\\n    else:\\n        for i in range(2,N,2):\\n            if i*2 != sum(N_List[i-1:i+1]):\\n                flg = 1\\n                break\\n            else:\\n                ans = (ans * 2) % ((10**9) +7)\\n        \\n\\nelse:\\n    for i in range(1,N,2):\\n        if i*2 != sum(N_List[i-1:i+1]):\\n            flg = 1\\n            break\\n        else:\\n            ans = (ans * 2) % ((10**9) +7)\\n\\nif flg == 0:\\n    print(ans)\\nelse:\\n    print((0))\\n\\n                \\n\", \"N = int(input())\\nA = [int(x) for x in input().split()]\\n\\ncnt = {}\\nif N & 1:\\n    bit = 1\\nelse:\\n    bit = 0\\n\\nfor a in A:\\n    if a & bit:\\n        ans = 0\\n        break\\n    if a in cnt:\\n        cnt[a] += 1\\n    else:\\n        cnt[a] = 1\\n\\nfor key in list(cnt.keys()):\\n    if key == 0 and cnt[key] != 1:\\n        ans = 0\\n        break\\n    if key != 0 and cnt[key] != 2:\\n        ans = 0\\n        break\\nelse:\\n    ans = 2**(N//2) %1000000007\\nprint(ans)\\n\", \"n=int(input())\\nfrom collections import Counter as co\\nc=co(map(int,input().split()))\\nans=pow(2,n//2,10**9+7)\\nif n%2 :\\n    if 0 not in c or c[0]>1:ans=0\\n    for i in range(1,n):\\n        if i%2==0 :\\n            if i not in c or c[i]!=2:ans=0;break\\n        else:\\n            if i in c:ans=0;break\\nelse:\\n    if 0 in c:ans=0\\n    for  i in range(1,n):\\n        if i%2:\\n            if i not in c or c[i]!=2:ans=0;break\\n        else:\\n            if i in c:ans=0;break\\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nl = [0] * n\\nfor x in a:\\n    l[x] += 1\\nfor i in range(n):\\n    if l[i] > 2:\\n        print(0)\\n        return\\n    if l[i] > 0 and (i + n) % 2 == 0: \\n        print(0)\\n        return\\nif n % 2 == 1 and l[0] > 1:\\n    print(0)\\n    return\\nprint(pow(2, n // 2, 10 ** 9 + 7))\", \"n = int(input())\\na_list = sorted([int(x) for x in input().split()], reverse=True)\\nm = n\\nif m % 2 == 1:\\n    a_list.append(0)\\n    m += 1\\nfor i in range(0, m, 2):\\n    if not (a_list[i] == a_list[i + 1] == n - (i + 1)):\\n        print(0)\\n        return\\nprint(2 ** (n // 2) % (10 ** 9 + 7))\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nnum_map = [0] * ((n + 2 - 1) // 2)\\nfor i in range(n):\\n    num_map[a[i] // 2] += 1\\n\\nres = 2 - n % 2\\nif num_map[0] != 2 - n % 2:\\n    print((0))\\nelse:\\n    for i in range(1, (n + 2 - 1) // 2):\\n        if num_map[i] != 2:\\n            print((0))\\n            break\\n        else:\\n            res = res * 2 % mod\\n    else:\\n        print(res)\\n\", \"mod = 10**9+7\\nn = int(input())\\na = list(map(int,input().split()))\\nc_dic = dict()\\nif n%2 == 0:\\n  for num in a:\\n    if num%2 == 0 or n < num:\\n      print(0)\\n      return\\n    if num in c_dic:\\n      c_dic[num] += 1\\n      if c_dic[num] > 2:\\n        print(0)\\n        return\\n    else:\\n      c_dic[num] = 1\\n  print(pow(2,n//2,mod))\\nelse:\\n  for num in a:\\n    if num%2 == 1 or n < num:\\n      print(0)\\n      return\\n    if num in c_dic:\\n      c_dic[num] += 1\\n      if c_dic[num] > 2:\\n        print(0)\\n        return\\n    else:\\n      c_dic[num] = 1\\n  if c_dic[0] != 1:\\n    print(0)\\n    return\\n  print(pow(2,n//2,mod))\", \"import sys\\nfrom collections import Counter\\n\\nn = int(input())\\na = list(map(int, input().split()))\\na.sort()\\n\\nl = []\\n\\nfor i in range(n):\\n    li = abs(i - (n-1-i))\\n    l.append(li)\\n    \\nl.sort()\\n\\n\\nfor ai, li in zip(l,a):\\n    if ai != li:\\n        print((0))\\n        return\\n\\nd = Counter(l)\\nmod = 10 ** 9 + 7\\nans = 1\\n\\nfor li in d:\\n    for j in range(1,d[li]+1):\\n        ans *= j\\n        ans %= mod\\n\\nprint(ans)\\n\", \"n=int(input())\\na=[int(i) for i in input().split()]\\n\\ndef somosomo(a):\\n    ans=[]\\n    if n%2==1:\\n        ans.append(0)\\n        for i in range(1,n//2+1):\\n            ans.append(i*2)\\n            ans.append(i*2)\\n        b=sorted(a)\\n        if b==ans:\\n            return True\\n        return False\\n    else:\\n        for i in range(1,n//2+1):\\n            ans.append(i*2-1)\\n            ans.append(i*2-1)\\n        b=sorted(a)\\n        if b==ans:\\n            return True\\n        return False\\n\\ndef two_ride(n):\\n    ans=1\\n    for i in range(n):\\n        ans*=2\\n        ans%=10**9+7\\n    return ans\\n\\nif somosomo(a):\\n    print(two_ride(n//2))\\nelse:\\n    print(0)\", \"n=int(input())\\na=list(map(int,input().split()))\\nl=[0]*n\\nfor i in range(n):\\n    l[a[i]]+=1\\n#print(l)\\nif n%2==1:\\n    if l[0]!=1:\\n        print(0)\\n        return\\nans=1\\nfor i in range(n):\\n    if n%2==0:\\n        if i%2==0:\\n            if l[i]!=0:\\n                print(0)\\n                return\\n    else:\\n        if i%2==1:\\n            if l[i]!=0:\\n                print(0)\\n                return\\n    \\n    if l[i]==2:\\n        ans*=2\\n    elif l[i]>2:\\n        print(0)\\n        return\\n    ans%=(10**9 +7)\\nprint(ans)\", \"N = int(input())\\ncount = [0]*(N+1)\\nmodz = 10**9 + 7\\n\\ndef junretsu(a):\\n    if a <= 0: return 1\\n    if (a & 0x01) == 1:\\n        return 2*junretsu(a-1) % modz\\n    else:\\n        rr = junretsu(a>>1)\\n        return rr*rr % modz\\n\\npos = list(map(int, input().split()))\\nfor i in range(N):\\n    count[pos[i]] += 1\\n\\ndiff = [0]*(N+1)\\nfor i in range(1, N+1):\\n    d = abs((N - i) - (i-1))\\n    diff[d] += 1\\n\\ninvalid = False\\ntotal = 1\\nfor i in range(N):\\n    if count[i] != diff[i]:\\n        invalid = True\\n        break\\n\\nif invalid:\\n    print((0))\\nelse:\\n    print((junretsu(int(N/2))))\\n\", \"num = int(input())\\nt = [int(n) for n in input().split()]\\nt = sorted(t)\\n\\nvalid = True\\n\\nif num % 2 == 1: # odd\\n  check = list(range(0,num+1,2))[1:]\\n  \\n  valid1 = t[0] == 0\\n  valid2 = check == t[2::2] # even, skip first\\n  valid3 = check == t[1::2] # odd\\n  valid = valid1 and valid2 and valid3\\n  \\n  if not valid:\\n    print((0))\\n  else:\\n    ans = 2**((num-1)//2) % (10**9 + 7)\\n    print(ans)\\n  \\nelse: # even \\n  check = list(range(1,num,2))\\n  \\n  valid1 = True\\n  valid2 = check == t[::2] # even\\n  valid3 = check == t[1::2] # odd\\n  valid = valid1 and valid2 and valid3\\n  \\n  if not valid:\\n    print((0))\\n  else:\\n    ans = 2**((num)//2) % (10**9 + 7)\\n    print(ans)\\n\\n\\n  \\n\", \"N = int(input())\\nA = list(map(int,input().split()))\\n   \\nA.sort()\\n\\ncheck=[0]*N\\n\\nfor idx in range(N%2,N,2):\\n    check[idx]=idx+1\\n    check[idx+1]=idx+1\\n\\nans=0\\n\\nif check == A:\\n    if N % 2 == 0:\\n        ans=(2**(N//2))%(10**9+7)\\n    elif N % 2 != 0:\\n        ans=(2**((N-1)//2))%(10**9+7)\\n    \\nprint(ans)\\n\", \"n=int(input())\\nmod=10**9+7\\nA=list(map(int,input().split()))\\n\\nfrom collections import Counter\\nC=Counter(A)\\nif n%2==0:\\n    for i in range(1,n,2):\\n        if C.get(i) != 2:\\n            print(0);return\\nelse:\\n    if C.get(0) !=1:\\n        print(0);return\\n    for i in range(2,n,2):\\n        if C.get(i)!=2:\\n            print(0);return\\n\\nn//=2\\nprint(pow(2,n,mod))\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif len(a)%2==1:\\n    tmp = [0]\\n    for i in range((len(a)-1)//2):\\n        tmp.append((i+1)*2)\\n        tmp.append((i+1)*2)\\n    if a == tmp:\\n        ans = (2**((len(a)-1)//2))%(10**9+7)\\n    else:\\n        ans = 0\\nelse:\\n    tmp = []\\n    for i in range(len(a)//2):\\n        tmp.append(2*i+1)\\n        tmp.append(2*i+1)\\n    if a == tmp:\\n        ans = (2**(len(a)//2))%(10**9+7)\\n    else:\\n        ans = 0\\nprint(ans)\", \"N = int(input())\\nAs = list(map(int, input().split()))\\n# \\u7d76\\u5bfe\\u5024\\u306e\\u5dee\\u306f\\u3001\\n# \\u5947\\u6570\\u306e\\u5834\\u5408\\u306fN+1\\u304b\\u30892\\u305a\\u3064\\u6e1b\\u3089\\u3057\\u3066\\u884c\\u3063\\u305f\\u5206\\u3057\\u304b\\u306a\\u3044\\u3002(N+1)/2\\n# \\u5076\\u6570\\u306e\\u5834\\u5408\\u306fN\\u304b\\u30892\\u305a\\u3064\\u6e1b\\u3089\\u3057\\u3066\\u884c\\u3063\\u305f\\u5206\\u3057\\u304b\\u306a\\u3044\\u3002N/2\\nnums = {}\\nexists = True\\nif N % 2 == 0:\\n    for A in As:\\n        if A in nums:\\n            nums[A] += 1\\n        else:\\n            nums[A] = 1\\n    for key, value in list(nums.items()):\\n        if key == 0:\\n            exists = False\\n        if value != 2:\\n            exists = False\\n\\nelse:\\n    for A in As:\\n        if A in nums:\\n            nums[A] += 1\\n        else:\\n            nums[A] = 1\\n    for key, value in list(nums.items()):\\n        if key == 0:\\n            if value != 1:\\n                exists = False\\n        else:\\n            if value != 2:\\n                exists = False\\nif not exists:\\n    print((0))\\nelse:\\n    ans = 1\\n    if N % 2 == 0:\\n        for i in range(int(N / 2)):\\n            ans = ans * 2\\n            ans %= 10**9 + 7\\n    else:\\n        for i in range(int((N - 1) / 2)):\\n            ans = ans * 2\\n            ans %= 10**9 + 7\\n            # \\u7d76\\u5bfe\\u5024\\u306e\\u5dee\\u306f0\\u306e\\u6642\\u306f1\\u4eba\\u3060\\u3051\\u3002\\u305d\\u306e\\u307b\\u304b\\u306f2\\u4eba\\u3060\\u3051\\u3002\\u3053\\u308c\\u304c\\u6e80\\u305f\\u305b\\u308b\\u306a\\u3089\\n            # (\\u5076\\u6570)2**(N+1/2)\\n            # (\\u5947\\u6570)2**(N/2)\\n    print(ans)\\n\", \"from collections import Counter\\n\\n\\ndef mod_pow(a, n, mod):\\n    \\\"\\\"\\\"\\n    \\u4e8c\\u5206\\u7d2f\\u4e57\\u6cd5\\u306b\\u3088\\u308b a^n (mod m)\\u306e\\u5b9f\\u88c5\\n    :param a: \\u7d2f\\u4e57\\u306e\\u5e95\\n    :param n: \\u7d2f\\u4e57\\u306e\\u6307\\u6570\\n    :param mod: \\u6cd5\\n    :return: a^n (mod m)\\n    \\\"\\\"\\\"\\n\\n    result = 1\\n    a_n = a\\n    while n > 0:\\n        if n & 1:\\n            result = result * a_n % mod\\n        a_n = a_n * a_n % mod\\n        n >>= 1\\n    return result\\n\\n\\nN = int(input())\\nA = Counter(tuple(map(int, input().split(' '))))\\nMOD = 10 ** 9 + 7\\n\\nif A[0] > 1:\\n    print((0))\\nelif sum([key for key, value in list(A.items()) if value == 1]) != 0:\\n    print((0))\\nelse:\\n    print((mod_pow(2, N // 2, MOD)))\\n\", \"N = int(input())\\nA = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\n\\nA = sorted(A)\\nans = 1\\nif N % 2 == 0:#[1,1,3,3,5,5,...]\\n  for i in range(N):\\n    xx = int(i / 2)\\n    if A[i] != 2 * xx + 1:\\n      ans = 0\\n    else:\\n      if i % 2 == 1:\\n        ans *= 2\\n        ans %= mod\\nelse:#[0, 2, 2, 4, 4 ...]\\n  for i in range(N):\\n    xx = int((i + 1)/2)\\n    if A[i] != 2 * xx:\\n      ans = 0\\n    else:\\n      if (i % 2 == 0) and (i != 0):\\n        ans *= 2\\n        ans %= mod\\n      \\n      \\n  \\n  \\nprint(ans)\\n\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\na.sort()\\nres = True\\nanse = list(i for i in range(1, n, 2))\\nanso = list(i for i in range(2, n, 2))\\nif n % 2 != 0:\\n  if a[0] != 0:\\n    res = False\\n    print(0)\\n  a = a[1:]\\n  for i in range(0, len(a), 2):\\n    if a[i] != anso[i//2] or a[i+1] != anso[i//2]:\\n        print(0)\\n        res = False\\n        break\\n\\n\\nif n % 2 == 0:\\n    for i in range(0, len(a), 2):\\n        if a[i] != anse[i//2] or a[i+1] != anse[i//2]:\\n            print(0)\\n            res = False\\n            break\\n\\np = 10**9 + 7\\nif res:\\n  print(pow(2, n//2, p))\", \"n=int(input())\\nl=list(map(int,input().split()))\\nmod=10**9+7\\nif n%2==0:\\n    d={i:2 for i in range(1,n,2)}\\nelse:\\n    d={i:2 for i in range(0,n,2)}\\n    d[0]=1\\nfor a in l:\\n    if a in d:\\n        d[a]-=1\\n    else:\\n        print((0))\\n        return\\nfor i in list(d.values()):\\n    if i!=0:\\n        print((0))\\n        return\\nprint(((2**(n//2))%mod))\\n\", \"from collections import Counter\\n\\nn = int(input())\\nA = list(map(int, input().split()))\\ncnt_A = Counter(A)\\n\\nif not all([v == 2 for k, v in cnt_A.items() if k != 0]):\\n    print(0)\\nelse:\\n    print(pow(2, n // 2, 10**9 + 7))\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nans = 0\\nA_test = sorted(list(set(A)))\\n\\nif N % 2 == 1:\\n    judge = [i for i in range(0,N,2)]\\n    if (A_test == judge) and (A.count(0) == 1):\\n        ans = 2**(N//2)\\nelse:\\n    judge = [i for i in range(1,N,2)]\\n    if A_test == judge:\\n        ans = 2**(N//2)\\n\\nans = ans % (10**9 + 7)\\nprint(ans)\\n\", \"import sys\\nfrom collections import Counter\\nN = int(input())\\nA = list(map(int, input().split()))\\nMOD = 10 ** 9 + 7\\n\\nC = Counter(A)\\nC = sorted(C.items(), key=lambda x: x[0])\\nif N % 2 == 0:\\n    s = 1\\n    for k, v in C:\\n        if k != s or v != 2:\\n            print(0)\\n            return\\n        s += 2\\n    print(pow(2, (N // 2), MOD))\\nelse:\\n    s = 0\\n    for k, v in C:\\n        if k == 0:\\n            if k != 0 or v != 1:\\n                print(0)\\n                return\\n            s += 2\\n            continue\\n        if k != s or v != 2:\\n            print(0)\\n            return\\n        s += 2\\n    print(pow(2, (N - 1) // 2, MOD))\", \"from collections import Counter\\nn=int(input())\\na=sorted(list(map(int,input().split())))\\na_count=Counter(a)\\nif n%2==1:\\n    ans=1\\n    for i in a_count:\\n        if i%2!=0:\\n            print(0)\\n            break\\n        else:\\n            if i==0:\\n                if a_count[i]!=1:\\n                    print(0)\\n                    break\\n            \\n            else:\\n                if a_count[i]==2:\\n                     ans=(ans*2)%(10**9+7)\\n                else:\\n                    print(0)\\n                    break\\n    else:\\n      print(ans)\\nelse:\\n    ans=1\\n    for j in a_count:\\n        if j%2!=1:\\n            print(0)\\n            break\\n        else:\\n            if a_count[j]==2:\\n                ans=(ans*2)%(10**9+7)\\n           \\n            else:\\n                print(0)\\n                break\\n    else:\\n      print(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nflg = 0\\n\\na.sort()\\nif n % 2 == 0:\\n  if a[0] == 1 and a[1] == 1:\\n    for i in range(2, n, 2):\\n      if a[i] == a[i + 1] and a[i - 1] + 2 == a[i]:\\n        continue\\n      else:\\n        flg = 1\\n        break\\n  else:\\n    flg = 1\\nelse:\\n  if a[0] == 0:\\n    for i in range(1, n, 2):\\n      if a[i] == a[i + 1] and a[i - 1] + 2 == a[i]:\\n        continue\\n      else:\\n        flg = 1\\n        break\\n  else:\\n    flg = 1\\n\\nif flg == 1:\\n  print(0)\\nelse:\\n  print((2 ** (n // 2)) % (10 ** 9 + 7))\", \"n=int(input())\\nl=list(map(int,input().split()))\\nmod=10**9+7\\nif n%2==0:\\n    d={i:2 for i in range(1,n,2)}\\nelse:\\n    d={i:2 for i in range(0,n,2)}\\n    d[0]=1\\nfor a in l:\\n    if a in d:\\n        d[a]-=1\\n    else:\\n        print(0)\\n        return\\nfor i in d.values():\\n    if i!=0:\\n        print(0)\\n        return\\nprint((2**(n//2))%mod)\", \"def main():\\n  N = int(input())\\n  A = [int(a) for a in input().split(\\\" \\\")]\\n  A.sort()\\n \\n  if N % 2 == 1 and A.count(0) != 1:\\n    print(0)\\n    return 0\\n  elif N % 2 == 0 and A.count(0) > 0:\\n    print(0)\\n    return 0\\n  \\n  if N % 2 == 1:\\n    A.pop(0)\\n  \\n  cnt = 0\\n  while len(A) > 0:\\n    if A[0] != A[1] or (len(A) > 2 and A[0] == A[1] and A[1] == A[2]):\\n      print(0)\\n      return 0\\n    elif A[0] == A[1] == 2 * cnt + (N % 2) + 1:\\n      cnt += 1\\n      A.pop(0)\\n      A.pop(0)\\n    else:\\n      print(0)\\n      return 0\\n \\n  ans = 1\\n  for p in range(cnt):\\n    ans = (ans * 2) % 1000000007\\n  print(ans)\\n\\nmain()\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n == 1:\\n  print(1)\\n  return\\nelif n%2 == 0:\\n  for i in range(0,n-2,2):\\n    if a[i] != a[i+1] or a[i] == a[i+2]:\\n      print(0)\\n      return\\n  if a[-2] != a[-1]:\\n    print(0)\\n    return\\nelse:\\n  if a[0] != 0 or a[1] == 0:\\n    print(0)\\n    return\\n  for i in range(1,n-2,2):\\n    if a[i] != a[i+1] or a[i] == a[i+2]:\\n      print(0)\\n      return\\n  if a[-2] != a[-1]:\\n    print(0)\\n    return\\n\\nmod = 10**9+7\\nif n%2 == 0: print(2**(n//2)%mod)\\nelse: print(2**((n-1)//2)%mod)\", \"N = int(input())\\nA = list(map(int, input().split()))\\nmod = pow(10,9)+7\\nA.sort()\\n\\nif N%2 == 0:\\n    for i in range(N//2):\\n        if A[2*i] != A[2*i+1] or A[2*i] != 2*i+1:\\n            print((0))\\n            return\\n    ans = pow(2,N//2)\\n    print((ans%mod))\\nelse:\\n    if A[0] != 0:\\n        print((0))\\n        return\\n    for i in range(N//2):\\n        if A[2*i+1] != A[2*(i+1)] or A[2*i+1] != 2*(i+1):\\n            print((0))\\n            return\\n    ans = pow(2,N//2)\\n    print((ans%mod))\\n\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n \\na=True\\nif N%2==0:\\n for i in range(1,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    a=False\\n    break\\nelse:\\n if A[0]!=0:a=False\\n else:\\n    for i in range(2,N,2):\\n     if A[i-1]!=i or A[i]!=i:\\n        a=False\\n        break\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"from collections import Counter\\n\\nN = int(input())\\nA = list(map(int, input().split()))\\nMOD = int(1e9) + 7\\n\\n# \\u5076\\u6570\\u306e\\u5834\\u5408\\nif N % 2 == 0:\\n    c = Counter(A)\\n    if all(i == 2 for i in c.values()):\\n        print(pow(2, N//2, MOD))\\n    else:\\n        print(0)\\n# \\u5947\\u6570\\u306e\\u5834\\u5408\\nelse:\\n    A.sort()\\n    A = A[1:]\\n    c = Counter(A)\\n    if all(i == 2 for i in c.values()):\\n        print(pow(2, N//2, MOD))\\n    else:\\n        print(0)\", \"N = int(input())\\na = list(map(int, input().split()))\\nSum = 1\\nmod = 1000000007\\n\\na.sort()\\ndata = []\\nif N % 2 == 0:\\n    for i in range(int(N / 2)):\\n        data.append(1 + i * 2)\\n        data.append(1 + i * 2)\\nelse:\\n    data.append(0)\\n    for i in range(1, N // 2 + 1):\\n        data.append(i * 2)\\n        data.append(i * 2)\\n\\nif a == data:\\n    for i in range(N // 2):\\n        Sum *= 2\\n        Sum %= mod\\n    print(Sum)\\nelse:\\n    print((0))\\n\", \"N=int(input())\\nA=list(map(int,input().split()))\\n\\nA.sort()\\ncheck=[0]*N\\n\\nfor idx in range(N%2,N,2):\\n    check[idx]=idx+1\\n    check[idx+1]=idx+1\\n\\nans=0\\nmod=10**9+7\\nif check==A:\\n    if N%2==0:\\n        ans=(2**(N//2))%mod\\n    else:\\n        ans=(2**((N-1)//2))%mod\\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\nfrom collections import Counter\\nc = Counter(a)\\n\\ncheck_ary = []\\nif n&1:\\n    check_ary.append(0)\\n\\nfor i in range(n//2):\\n    for _ in range(2):\\n        check_ary.append((i+1)*2 if n&1 else i*2+1)\\n\\nc2 = Counter(check_ary)\\n\\nif c != c2:\\n    print(0)\\n    return\\n\\nprint(pow(2, n//2, 10**9+7))\", \"import sys\\nimport heapq, math\\nfrom itertools import zip_longest, permutations, combinations, combinations_with_replacement\\nfrom itertools import accumulate, dropwhile, takewhile, groupby\\nfrom functools import lru_cache\\nfrom copy import deepcopy\\n\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nB = [0] * N\\n\\nfor a in A:\\n    B[a] += 1\\n\\nok = True\\n\\nif N % 2 == 1:\\n    ok = ok and B[0] == 1\\n    for i in range(1, N):\\n        ok = ok and B[i] == (2 if i % 2 == 0 else 0)\\nelse:\\n    for i in range(N):\\n        ok = ok and B[i] == (0 if i % 2 == 0 else 2)\\n\\nans = 1\\nMOD = int(1e9) + 7\\nfor _ in range(N // 2):\\n    ans *= 2\\n    ans %= MOD\\n\\nprint((ans if ok else 0))\\n\", \"n=int(input())\\nA=list(map(int,input().split()))\\nA.sort()\\njudge=0\\nif n%2==1:\\n    for i in range(n):\\n        if A[i]!=2*((i+1)//2):\\n            judge+=1\\n            break\\nelse:\\n    for i in range(n):\\n        if A[i]!=2*(i//2)+1:\\n            judge+=1\\n            break\\nif judge==1:\\n    print(0)\\nelse:\\n    print((2**(n//2))%(10**9+7))\", \"from collections import Counter\\nn = int(input())\\na = list(map(int, input().split()))\\nc = Counter(a)\\nd = list(c.values())\\nif (n % 2 == 1 and c[0] == 1 and d.count(2) == (n-1)//2) or (n % 2 == 0 and d.count(2) == n//2):\\n    print(pow(2, n//2, 10**9+7))\\nelse:\\n    print(0)\", \"from collections import Counter\\nn = int(input())\\na = list(map(int, input().split()))\\nc = Counter(a)\\nd = list(c.values())\\nif (n % 2 == 1 and c[0] == 1 and d.count(2) == (n-1)//2) or (n % 2 == 0 and d.count(2) == n//2):\\n    print((2**(n//2)) % (10**9+7))\\nelse:\\n    print(0)\", \"N = int(input())\\nK = [0 for i in range(N+1)]\\nA = list(map(int,input().rstrip().split(\\\" \\\")))\\nans = 1\\nfor i in A:\\n    K[i] += 1\\nfor i in range(N):\\n    if i != 0 and K[i] != 0 and K[i] != 2:\\n        ans = 0\\n        break\\n    if K[i] == 2:\\n        ans *= 2\\n        ans %= 10 ** 9 + 7\\nprint(ans)\", \"import collections\\n\\nn = int(input())\\na = list(map(int, input().split()))\\ncnt = collections.Counter(a)\\nmod = 7 + 10**9\\nif n % 2 == 0:\\n    for i in range(1, 1 + n // 2):\\n        if (i * 2 - 1) not in cnt.keys() or cnt[i * 2 - 1] != 2:\\n            print(0)\\n            return\\n\\nelse:\\n    if 0 not in cnt.keys() or cnt[0] != 1:\\n        print(0)\\n        return\\n    for i in range(1, 1 + n // 2):\\n        if i * 2 not in cnt.keys() or cnt[i * 2] != 2:\\n            print(0)\\n            return\\nprint(2 ** (n // 2) % mod)\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\n\\na = sorted(a)\\n\\nnum = 0\\njudge = 0\\n\\nif len(a)%2 == 1:\\n    if a[0] == 0:\\n        for i in range(1, n, 2):\\n            if a[i] == i+1 and a[i+1] == i+1:\\n                num += 1\\n            else:\\n                print(0)\\n                judge = 1\\n                break\\n    else:\\n        print(0)\\n        judge=1\\nelse:\\n    for i in range(0, n, 2):\\n            if a[i] == i+1 and a[i+1] == i+1:\\n                num += 1\\n            else:\\n                print(0)\\n                judge = 1\\n                break\\n        \\nif judge == 0:\\n    result = (2**num)%(10**9+7)\\n    print(result)\", \"from collections import defaultdict\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nL = A[:]\\nL = list(set(L))\\n\\nmod = 10 ** 9 + 7\\n\\nd = defaultdict(int)\\nfor i in range(N):\\n    d[A[i]] += 1\\n\\nif N % 2 == 1:\\n    bfr = 0\\n    for i in L:\\n        if i - bfr != 2 and i != 0:\\n            print((0))\\n            return\\n\\n        if i == 0:\\n            if d[i] != 1:\\n                print((0))\\n                return\\n            else:\\n                continue\\n        if d[i] != 2:\\n            print((0))\\n            return\\n        bfr = i\\n\\n    print(((2 ** (N // 2)) % mod))\\nelse:\\n    bfr = 1\\n    for i in L:\\n        if i - bfr != 2 and i != 1:\\n            print((0))\\n            return\\n\\n        if d[i] != 2:\\n            print((0))\\n            return\\n        bfr = i\\n\\n    print(((2 ** (N // 2)) % mod))\\n\", \"n = int(input())\\na = list(map(int,input().split()))\\nmod = 10**9+7\\n\\na.sort()\\n\\nif n%2 == 1: \\n    if a[0] != 0:\\n        print((0))\\n        return\\n    else:\\n        a.remove(0)\\n        tmp = 2\\nelse:\\n    tmp = 1\\n\\nfor i in range(n//2):\\n    if tmp == a[0] and tmp == a[1]:\\n        a.remove(tmp)\\n        a.remove(tmp)\\n    else:\\n        print((0))\\n        return\\n    tmp += 2\\n\\nif len(a) == 0:\\n    print(((2**(n//2))%mod))\\nelse:\\n    print((0))\\n\\n\\n\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nnum_map = [0] * ((n + 2 - 1) // 2)\\nfor i in range(n):\\n    num_map[a[i] // 2] += 1\\n\\nres = 1\\nif n % 2 == 1:\\n    if num_map[0] != 1:\\n        print((0))\\n    else:\\n        for i in range(1, (n + 2 - 1) // 2):\\n            if num_map[i] != 2:\\n                print((0))\\n                break\\n            else:\\n                res = res * 2 % mod\\n        else:\\n            print(res)\\nelse:\\n    for i in range((n + 2 - 1) // 2):\\n        if num_map[i] != 2:\\n            print((0))\\n            break\\n        else:\\n            res = res * 2 % mod\\n    else:\\n        print(res)\\n\", \"N=int(input())\\nA=list(map(int,input().split()))\\nmod = 10**9+7\\n\\nA=tuple(sorted(A))\\n\\nif N % 2 == 1:\\n  nums=[0]\\n  for i in range(2,N+1,2):\\n    nums.append(i)\\n    nums.append(i)\\nelse:\\n  nums=[]\\n  for i in range(1,N+1,2):\\n    nums.append(i)\\n    nums.append(i)\\n    \\nnums = tuple(nums)\\nif A != nums:\\n  print(0)\\n  return\\n  \\nprint(2**(N//2) % mod)\", \"N = int(input())\\nA = list(map(int,input().split()))\\nA.sort()\\nmod = 10**9 + 7\\nif N%2 == 0:\\n    for i in range(N):\\n        if A[i] != 1+(i//2)*2:\\n            print(0)\\n            break\\n    else:\\n        print(pow(2,N//2,mod))\\nelse:\\n    if A[0] == 0:\\n        for i in range(1,N):\\n            if A[i] != ((i+1)//2)*2:\\n                print(0)\\n                break\\n        else:\\n            print(pow(2,N//2,mod))\", \"n = int(input())\\na = list(map(int,input().split()))\\nmod = 10**9 + 7\\n\\nd = [0]*(n+1)\\nfor x in a:\\n    d[x] += 1\\nans = 1\\nif n%2 == 0:\\n    sw = 1\\n    for i,x in enumerate(d):\\n        if i%2 != 0:\\n            if x == 2:\\n                ans *= 2\\n                ans %= mod\\n            else:\\n                sw = 0\\n                break\\n        else:\\n            if x != 0:\\n                sw = 0\\n                break\\nelse:\\n    sw = 1\\n    for i,x in enumerate(d):\\n        if i%2 == 0:\\n            if i == 0:\\n                if x != 1:\\n                    sw = 0\\n                    break\\n            else:\\n                if x == 2:\\n                    ans *= 2\\n                    ans %= mod\\n                else:\\n                    sw = 0\\n                    break\\n        else:\\n            if x != 0:\\n                sw = 0\\n                break\\nif sw == 0:\\n    ans = 0\\nprint(ans)\\n\", \"N = int(input())\\nA = sorted(list(map(int,input().split())))\\n\\nif N%2==0:\\n  B = [1+2*(n//2) for n in range(N)]\\nelse:\\n  B = [2*(n//2) for n in range(1,1+N)]\\n\\nif A==B:\\n  print(pow(2,N//2,10**9+7))\\nelse:\\n  print(0)\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\nMOD = 10 ** 9 + 7\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    N = I()\\n    A = LI()\\n\\n    if N % 2 == 0:\\n        if sorted(A) == [i // 2 * 2 + 1 for i in range(N)]:\\n            print((pow(2, N // 2, MOD)))\\n        else:\\n            print((0))\\n    else:\\n        if sorted(A) == [(i // 2 + 1) * 2 for i in range(-1, N - 1)]:\\n            print((pow(2, (N - 1) // 2, MOD)))\\n        else:\\n            print((0))\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"def PowerMod(N,P,Mod):\\n    if N%Mod==0:\\n        return 0\\n    else:\\n        PowM = 1\\n        for TP in range(1,P+1):\\n            PowM = (PowM*N)%Mod\\n        return PowM\\n\\nfrom collections import Counter\\nN = int(input())\\nA = sorted(Counter([int(T) for T in input().split()]).most_common(),key=lambda X:X[0])\\nPassFlag = True\\nif N%2==1:\\n    for TA in range(0,(N+1)//2):\\n        if A[TA][0]!=(2*TA) or A[TA][1]!=(1+(A[TA][0]!=0)):\\n            PassFlag = False\\n            break\\n    print([0,PowerMod(2,(N-1)//2,10**9+7)][PassFlag])\\nelse:\\n    for TA in range(0,N//2):\\n        if A[TA][0]!=(2*TA+1) or A[TA][1]!=2:\\n            PassFlag = False\\n            break\\n    print([0,PowerMod(2,N//2,10**9+7)][PassFlag])\", \"from collections import Counter\\n\\nn = int(input())\\nc = Counter(list(map(int, input().split())))\\n\\nans = 0\\nfor k, v in list(c.items()):\\n    if k == 0:\\n        if n%2==0 and v > 2:\\n            print((0))\\n            return\\n        elif n%2==1 and v > 1:\\n            print((0))\\n            return\\n    else:\\n        ans += 1\\n        if v > 2:\\n            print((0))\\n            return\\n\\nprint((pow(2, ans, 10**9+7)))\\n\", \"from typing import Counter\\n\\n\\nn = int(input())\\nlis = list(map(int, input().split()))\\nmod  =10**9+7\\n\\nans = 0\\nif n % 2 == 0:\\n    b = Counter(lis)\\n    flag = 1\\n    for i in list(b.values()):\\n        if i == 2:\\n            pass\\n        else:\\n            flag = 0\\n            break\\n    if flag:\\n        ans = 2**(n//2)\\n        print((ans % mod))\\n    else:\\n        print((0))\\nelse:\\n    lis = sorted(lis)\\n    lis = lis[1:]\\n    b = Counter(lis)\\n    flag = 1\\n    for i in list(b.values()):\\n        if i == 2:\\n            pass\\n        else:\\n            flag = 0\\n            break\\n    if flag:\\n        ans = 2**(n//2)\\n        print((ans % mod))\\n    else:\\n        print((0))\\n\", \"n=int(input())\\na=list(map(int,input().split()))\\nflag=0\\nA=a.sort()\\nnum=[]\\n\\nif n%2==0:\\n    for i in range(1,n,2):\\n        num.append(i)\\n        num.append(i)\\n\\nif n%2==1:\\n    num=[0]\\n    for i in range(2,n,2):\\n        num.append(i)\\n        num.append(i)\\n\\nif num==a:\\n    print(2**(n//2)%(10**9+7))\\n\\nelse:\\n    print(\\\"0\\\")\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\nf=lambda:2**(N//2)%(10**9+7)\\na=True\\nif N%2==0:\\n    for i in range(1,N,2):\\n        if A[i-1]!=i or A[i]!=i:\\n            # print(i,A[i-1],A[i])\\n            a=False\\n            break\\nelse:\\n    if A[0]!=0:\\n            a=False\\n    else:\\n        for i in range(2,N,2):\\n            if A[i-1]!=i or A[i]!=i:\\n                # print(i,A[i-1],A[i])\\n                a=False\\n                break\\nprint(f() if a else 0)\", \"n = int(input())\\nA = list(map(int, input().split()))\\n\\nd = {}\\nfor a in A:\\n    d[a] = d.get(a, 0)+1\\n\\nzero_cnt = 0\\ntwo = 0\\nno = 0\\nfor i in d:\\n    if i==0:\\n        zero_cnt+=1\\n    elif d[i]==2:\\n        two+=1\\n    else:\\n        no+=1\\n\\nif no!=0 or (n%2==0 and zero_cnt!=0) or (n%2==1 and zero_cnt!=1):\\n    print((0))\\nelse:\\n    ans = 1\\n    mod = 10**9+7\\n    for i in range(two):\\n        ans *= 2\\n        ans %= mod\\n    print((ans%mod))\\n\", \"MOD = 10 ** 9 + 7\\nnum = [0] * (10 ** 5 + 1)\\nN = int(input())\\nA = list(map(int,input().split()))\\nfor i in range(len(A)):\\n\\tnum[A[i]] += 1\\nif N % 2 == 1:\\n\\tfor i in range(0,N,2):\\n\\t\\tcnt = num[i]\\n\\t\\tif i == 0:\\n\\t\\t\\tif cnt != 1:\\n\\t\\t\\t\\tprint(0)\\n\\t\\t\\t\\treturn\\n\\t\\telse:\\n\\t\\t\\tif cnt != 2:\\n\\t\\t\\t\\tprint(0)\\n\\t\\t\\t\\treturn\\n\\tprint(2 ** (N // 2) % MOD)\\nelse:\\n\\tfor i in range(1,N,2):\\n\\t\\tcnt = num[i]\\n\\t\\tif cnt != 2:\\n\\t\\t\\tprint(0)\\n\\t\\t\\treturn\\n\\tprint(2 ** (N // 2) % MOD)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return False\\n return True   \\n    \\na=True\\nif N%2==0:a=f(1)\\nelse:\\n if A[0]!=0:a=False\\n else:a=f(2)\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N, *A = list(map(int, read().split()))\\n\\n    A.sort()\\n\\n    ok = True\\n    if len(A) % 2 == 0:\\n        for i in range(N // 2):\\n            if not A[2 * i] == A[2 * i + 1] == 2 * i + 1:\\n                ok = False\\n                break\\n    else:\\n        if A[0] != 0:\\n            ok = False\\n        else:\\n            for i in range(N // 2):\\n                if not A[2 * i + 1] == A[2 * i + 2] == 2 * i + 2:\\n                    ok = False\\n                    break\\n\\n    if ok:\\n        ans = pow(2, N // 2, MOD)\\n    else:\\n        ans = 0\\n\\n    print(ans)\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nm = 1000000007\\n\\nA.sort()\\nif N % 2 == 0:\\n    B = list(range(1, N, 2)) * 2\\nelse:\\n    B = [0] + list(range(2, N, 2)) * 2\\nB.sort()\\n\\nif A != B:\\n    print((0))\\nelse:\\n    result = 1\\n    for i in range(N // 2):\\n        result *= 2\\n        result %= m\\n    print(result)\\n\", \"N = int(input())\\nA = [int(x) for x in input().split()]\\n\\nfrom collections import defaultdict as dd\\nDict = dd(lambda:0)\\nfor a in A:\\n    Dict[a] += 1\\n\\nif N & 1: Dict[0] += 1\\nf = (lambda:(lambda x:0 if x&1 else 2) if N&1 else (lambda x:2 if x&1 else 0))()\\nPossible = {i:f(i) for i in range(N)}\\nfor key,value in list(Dict.items()):\\n    if value != Possible[key]:\\n        print((0))\\n        return\\nelse:\\n    print((2**(N//2)%1000000007))\\n                \\n\\n\", \"import sys\\n\\n# n = 10 ** 5\\n# \\u30c7\\u30fc\\u30bf\\u8aad\\u307f\\u8fbc\\u307f\\u95a2\\u4fc2\\nn = int(input())\\n\\na = list(map(int, input().split(' ')))\\n\\nrecord = {}\\n\\npossible = True\\n\\n# \\u72b6\\u6cc1\\u304c\\u5b9f\\u73fe\\u53ef\\u80fd\\u304b\\u78ba\\u8a8d\\nfor e in a:\\n    if(e in record.keys()):\\n        record[e] += 1\\n        if(record[e] == 2):\\n            if(e == 0):\\n                possible = False\\n                break\\n        if(record[e] == 3):\\n            possible = False\\n            break\\n    else:\\n        record[e] = 1\\n\\nif(possible == False):\\n    print(0)\\n    return\\n\\nmultiCount = int(n / 2)\\n\\nprint(2 ** multiCount % (10 ** 9 + 7))\", \"import collections\\nN = int(input())\\nA = list(map(int,input().split()))\\nans = 1\\nif 0 in A:\\n    A.remove(0)\\nAcounter = collections.Counter(A)\\nfor i in Acounter.values():\\n    if i == 2:\\n        continue\\n    else:\\n        ans = 0\\n        break\\nif ans == 0:\\n    pass\\nif ans != 0:\\n    for i in range(N//2):\\n        ans = (ans * 2) % (10**9 + 7)\\nprint(ans)\", \"import sys\\nsys.setrecursionlimit(10 ** 7)\\ndef input() : return sys.stdin.readline().strip()\\ndef INT()   : return int(input())\\ndef MAP()   : return map(int,input().split())\\ndef LIST()  : return list(MAP())\\ndef NIJIGEN(H): return [list(input()) for i in range(H)]\\nmod=1000000007\\nN=INT()\\nL=LIST()\\nif N%2==0:\\n  A=range(1,N,2)\\n  B=range(1,N,2)\\nelse:\\n  A=range(0,N,2)\\n  B=range(2,N,2)\\nA,B=list(A),list(B)\\nA=A+B\\nif sorted(A)==sorted(L):\\n  print(pow(2,N//2,mod))\\nelse:\\n  print(0)\", \"n=int(input())\\na=list(map(int,input().split()))\\n\\nb=[0 for i in range(10**5+1)]\\nfor i in a:\\n  b[i]+=1\\n\\nif (n%2==0 and b[0]!=0) or (n%2==1 and b[0]!=1):\\n  print(0)\\n  return\\n\\nans=1\\nmod=10**9+7\\nfor i in b:\\n  if i==2:\\n    ans*=2\\n    ans%=mod\\n  if i>=3:\\n    print(0)\\n    return\\n\\nprint(ans)\", \"from collections import Counter\\n\\nn=int(input())\\na=list(map(int,input().split()))\\n\\nc=Counter(a)\\n\\nif (n%2==0 and c[0]!=0) or (n%2==1 and c[0]!=1):\\n  print(0)\\n  return\\n\\nans=1\\nmod=10**9+7\\nfor i in c:\\n  if c[i]==2:\\n    ans*=2\\n    ans%=mod\\n  if c[i]>=3:\\n    print(0)\\n    return\\n\\nprint(ans)\", \"from collections import Counter\\n\\nN = int(input())\\nabs_diffs = list(map(int, input().split()))\\n\\nif N % 2 == 0:\\n    expected = [i // 2 * 2  + 1 for i in range(N)]\\n    dims = N // 2\\nelse:\\n    expected = [(i + 1) // 2 * 2 for i in range(N)]\\n    dims = (N - 1) // 2\\n\\nif sorted(abs_diffs) == expected:\\n    print((2 ** dims % (10 ** 9 + 7)))\\n\\nelse:\\n    print((0))\\n\", \"n = int(input())\\nA = sorted(map(int,input().split()))\\n\\nif n % 2 == 1:\\n    ex = [0]\\n    \\n    for i in range(n//2):\\n        a = 2 * (i+1)\\n        ex += [a,a]\\n        \\nelse:\\n    ex = []\\n    a = 1\\n    \\n    for i in range(n//2):\\n        ex += [a,a]\\n        a += 2\\n        \\nans = 0\\n\\nif A == ex:\\n    ans = 2 ** (n//2) % (10**9 + 7)\\n    \\nprint(ans)\", \"n = int(input())\\na = list(map(int, input().split()))\\nmod = 10 ** 9 + 7\\nif n % 2 == 0:\\n    b = [2 if i % 2 == 1 else 0 for i in range(n)]\\nelse:\\n    b = [2 if i % 2 == 0 else 0 for i in range(n)]\\n    b[0] = 1\\nc = [0 for i in range(n)]\\nfor i in range(n):\\n    c[a[i]] += 1\\nif b != c:\\n    print(0)\\nelse:\\n    ans = 1\\n    for i in range(n // 2):\\n        ans *= 2\\n        ans %= mod\\n    print(ans)\", \"N = int(input())\\nA = sorted(list(map(int,input().split())))\\n\\nif N%2==0:\\n  B = [2*(n//2)+1 for n in range(N)]\\nelse:\\n  B = [2*(n//2) for n in range(1,N+1)]\\n\\nif A==B:\\n  print(pow(2,N//2,10**9+7))\\nelse:\\n  print(0)\", \"MOD = 10**9+7\\n\\ndef fast_pow(x, n, MOD):\\n    res = 1\\n    while n:\\n        if n & 1:\\n            res = res * x % MOD\\n        x = x * x % MOD\\n        n >>= 1\\n    return res\\n\\n\\nn = int(input())\\na = list(map(int, input().split()))\\n\\nd = {}\\nfor i in a:\\n    if n % 2:\\n        if i > 0 and i % 2:\\n            print((0))\\n            return\\n    else:\\n        if i > 0 and i % 2 == 0:\\n            print((0))\\n            return\\n\\n    if not i in d:\\n        d[i] = 1\\n    elif d[i] == 1:\\n        d[i] += 1\\n    else:\\n        print((0))\\n        return\\n\\nif n % 2:\\n    if d[0] != 1:\\n        print((0))\\n        return\\n    print((fast_pow(2, len(d)-1, MOD)))\\nelse:\\n    if 0 in d:\\n        print((0))\\n        return\\n    print((fast_pow(2, len(d), MOD)))\\n\", \"import math\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nflag = True\\nif N%2 == 0:\\n    if 0 in A or len(set(A)) != N//2:\\n        flag = False\\nelse:\\n    if len([0 for a in A if a == 0]) != 1 or len(set(A)) != N//2 + 1:\\n        flag = False\\n\\nif  flag:\\n    print((2**((N//2))%(10**9+7)))\\nelse:\\n    print((0))\\n\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\ndef f(x):\\n for i in range(x,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    return 0\\n return 1   \\n    \\na=1\\nif N%2==0:a=f(1)\\nelse: a=A[0]==0 and f(2)\\nprint(2**(N//2)%(10**9+7)*a)\", \"n = int(input())\\nA = tuple(map(int, input().split()))\\nmod = 10**9+7\\n\\nniseven = (n%2 == 0)\\n\\ncd = dict()\\nfor a in (A):\\n    cd.setdefault(a, 0)\\n    cd[a] += 1\\n    if a == 0 and cd[a] > 1:\\n        print((0))\\n        break\\n    if a > 0 and cd[a] > 2:\\n        print((0))\\n        break\\n    if (a%2==0) == niseven:\\n        print((0))\\n        break\\nelse:\\n    print((pow(2, n//2, mod)))\\n\", \"def main():\\n  N=int(input())\\n  A=list(map(int,input().split()))\\n  mod=10**9+7\\n  ans=1\\n  A.sort()\\n  if N%2==0:\\n    for i in range(0,N,2):\\n      if A[i]!=A[i+1] or A[i]!=i+1:\\n        print(0)\\n        return\\n      ans=ans*2%mod\\n    print(ans)\\n  else:\\n    if A[0]!=0:\\n      print(0)\\n      return\\n    ans=1\\n    for i in range(1,N,2):\\n      if A[i]!=A[i+1] or A[i]!=i+1:\\n        print(0)\\n        return\\n      ans=ans*2%mod\\n    print(ans)\\ndef __starting_point():\\n  main()\\n__starting_point()\", \"n = int(input())\\na = list(map(int, input().split()))\\n\\n# \\u77db\\u76fe\\u30c1\\u30a7\\u30c3\\u30af\\nfrom collections import Counter\\nc = Counter(a)\\n\\ndef check():\\n    if n&1:\\n        if c[0]!=1:\\n            return False\\n        for i in range((n-1)//2):\\n            if c[2*(i+1)] != 2:\\n                return False\\n    else:\\n        for i in range(n//2):\\n            if c[2*i+1] != 2:\\n                return False\\n    return True\\n\\nif not check():\\n    print(0)\\n    return\\n\\nprint(pow(2, n//2, 10**9+7))\", \"n = int(input())\\na = list(map(int,input().split()))\\ndic = {}\\nfor i in range(n):\\n    dic.setdefault(a[i],0)\\n    dic[a[i]] += 1\\nans = 1\\nfor key,value in dic.items():\\n    #\\u5076\\u6570\\n    if n%2==0:\\n        if n > key and key%2==1 and value==2:\\n            ans *= 2\\n        else:\\n            ans = 0\\n            break\\n    #\\u5947\\u6570\\n    else:\\n        if n > key and key%2==0:\\n            if key==0 and value==1:\\n                ans *= 1\\n            elif value==2:\\n                ans *= 2\\n            else:\\n                ans = 0\\n                break\\n        else:\\n            ans = 0\\n            break\\nprint(ans%(10**9+7))\", \"N=int(input())\\nMOD=10**9+7\\nA=[int(x) for x in input().split()]\\nflag=1#\\u305d\\u306e\\u4e26\\u3073\\u9806\\u304c\\u3042\\u308a\\u3048\\u308b\\u306a\\u30891\\u3001\\u305d\\u3046\\u3067\\u306a\\u3044\\u306a\\u30890\\nset1=set()\\nset2=set()\\nif N%2==1:\\n    set1.add(0)\\n    for j in range(2,N+1,2):\\n        set1.add(j)\\n        set2.add(j)\\n    for i in range(N):\\n        now=A[i]\\n        if now in set1:\\n            set1.remove(now)\\n        elif now in set2:\\n            set2.remove(now)\\n        else:\\n            flag=0\\n            break\\n    if len(set1)!=0 or len(set2)!=0:\\n        flag=0\\nelse:\\n    for k in range(1,N+1,2):\\n        set1.add(k)\\n        set2.add(k)\\n    for p in range(N):\\n        now=A[p]\\n        if now in set1:\\n            set1.remove(now)\\n        elif now in set2:\\n            set2.remove(now)\\n        else:\\n            flag=0\\n            break\\n    if len(set1)!=0 or len(set2)!=0:\\n        flag=0\\nif flag==0:\\n    print((0))\\nelse:\\n    ans=1\\n    div2=N//2\\n    for q in range(div2):\\n        ans*=2\\n        ans%=MOD\\n    print(ans)\\n\", \"N = int(input())\\nA = list(map(int, input().split()))\\n\\nm = 1000000007\\n\\nA.sort()\\nif N % 2 == 0:\\n    B = list(range(1, N, 2)) * 2\\nelse:\\n    B = [0] + list(range(2, N, 2)) * 2\\nB.sort()\\n\\nif A != B:\\n    print((0))\\nelse:\\n    result = 1\\n    for i in range(N // 2):\\n        result *= 2\\n        result %= m\\n    print(result)\\n\", \"from collections import Counter\\n\\nN,*A = map(int, open(0).read().split())\\nac = Counter(A)\\nif N % 2 == 0:\\n    for i in range(1,N,2):\\n        if ac[i] != 2:\\n            print(0)\\n            break\\n    else:\\n        print(pow(2,N//2,1000000007))\\nelse:\\n    if ac[0] != 1:\\n        print(0)\\n    else:\\n        for i in range(2,N,2):\\n            if ac[i] != 2:\\n                print(0)\\n                break\\n        else:\\n            print(pow(2,N//2,1000000007))\", \"n=int(input())\\na=list(map(int,input().split()))\\nif n%2==1:\\n    x=[i for i in range(n)]\\n    for i in range(n):\\n        if i%2==1:\\n            x[i]+=1\\nelse:\\n    x=[i for i in range(n)]\\n    for i in range(n):\\n        if i%2==0:\\n            x[i]+=1\\na.sort()\\nif x==a:\\n    print(pow(2,(n//2),10**9+7))\\nelse:\\n    print(0)\", \"import sys\\nfrom collections import deque\\np=10**9+7\\n\\ndef main(n,a):\\n  h=n//2\\n  g=n%2\\n  a.sort()\\n  c=[2*(x//2)+g+1 for x in range(n-g)]\\n  if g==1:\\n    c.insert(0,0)\\n  if a!=c:\\n      return 0\\n  return 2**(h%(p-1)) % p\\n\\ndef __starting_point():\\n  n=int(input())\\n  a=list(map(int,sys.stdin.readline().strip().split()))\\n  print((main(n,a)))\\n\\n__starting_point()\", \"N=int(input())\\nS=list(map(int,input().split()))\\nlenS=len(S)\\nT=[]\\nfor i in range(1,N+1):\\n    T.append(abs(i-(N+1-i)))\\n\\nT.sort()\\nS.sort()\\n\\n\\n\\nfor i in range(N):\\n    if T[i]!=S[i]:\\n        print((0))\\n        return\\n\\n\\nans=1\\nnagasa=lenS//2\\nfor i in range(nagasa):\\n    \\n    ans=(ans*2)%(10**9+7)\\n\\nprint(ans)\\n\\n\\n\", \"n = int(input())\\na = sorted(list(map(int, input().split())))\\n\\nif n%2 == 0: # \\u4eba\\u6570\\u304c\\u5076\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  for i in range(0,n,2):\\n    if a[i] != i+1 or a[i] != a[i+1]:\\n      print(0)\\n      return\\nelse: # \\u4eba\\u6570\\u304c\\u5947\\u6570\\u306e\\u5834\\u5408\\u306b\\u4e0d\\u6574\\u5408\\u304c\\u3042\\u308b\\u304b\\u78ba\\u8a8d\\n  if a[0] != 0: # \\u5dee\\u5206\\u304c0\\u5b58\\u5728\\u3057\\u3066\\u3044\\u308b\\u3053\\u3068\\u3092\\u78ba\\u8a8d\\n    print(0)\\n    return\\n  else:\\n    for i in range(1,n,2):\\n      if a[i] != i+1 or a[i] != a[i+1]:\\n        print(0)\\n        return\\n\\nans = 1\\nfor i in range(n//2):\\n  ans = ans * 2 % (10**9+7) # \\u7d44\\u307f\\u5408\\u308f\\u305b\\u3068\\u3057\\u3066\\u306f\\u540c\\u3058\\u5dee\\u5206\\u306e\\u5024\\u3092\\u5165\\u308c\\u66ff\\u3048\\u308b2\\u629e\\u306b\\u306a\\u308b\\u306e\\u3067\\u3001\\u7d50\\u679c\\u30922\\u500d\\u306b\\u3059\\u308b\\nprint(ans)\", \"N=int(input())\\n*A,=sorted(map(int,input().split()))\\n\\na=True\\nif N%2==0:\\n for i in range(1,N,2):\\n  if A[i-1]!=i or A[i]!=i:\\n    a=False\\n    break\\nelse:\\n if A[0]!=0:a=False\\n else:\\n    for i in range(2,N,2):\\n     if A[i-1]!=i or A[i]!=i:\\n        a=False\\n        break\\nprint(2**(N//2)%(10**9+7) if a else 0)\", \"import math\\nN = int(input())\\nA = list(map(int, input().split()))\\n\\nflag = True\\nif N%2 == 0:\\n    if 0 in A or len(set(A)) != N//2:\\n        flag = False\\nelse:\\n    if len([0 for a in A if a == 0]) != 1 or len(set(A)) != N//2 + 1:\\n        flag = False\\n\\nif  flag:\\n    print((2**(math.floor(N/2))%(10**9+7)))\\nelse:\\n    print((0))\\n\", \"from collections import Counter\\n\\nn = int(input())\\nA = list(map(int, input().split()))\\ncnt_A = Counter(A)\\n\\nif all([v == 2 for k, v in cnt_A.items() if k != 0]):\\n    print(pow(2, n // 2, 10**9 + 7))\\nelse:\\n    print(0)\", \"N=int(input())\\nMOD=1000000007\\nA=list(map(int,input().split()))\\ncnt=[0 for i in range(N)]\\nfor i in range(N):\\n    cnt[A[i]]+=1\\nif N%2==0:\\n    for i in range(1,N,2):\\n        if cnt[i]!=2:\\n            print((0))\\n            break\\n    else:\\n        print((2**(N//2)%MOD))\\nelse:\\n    if cnt[0]!=1:\\n        print((0))\\n    else:\\n        for i in range(2,(N+1)//2,2):\\n            if cnt[i]!=2:\\n                print((0))\\n                break\\n        else:\\n            print((2**((N-1)//2)%MOD))\\n\", \"import collections\\nimport sys\\ninput = sys.stdin.readline\\n\\nN = int(input())\\nA = list(map(int,input().split()))\\nm = 1000000007\\n\\nflag0 = 1\\ncount = 0\\n#\\u5076\\u6570\\u3060\\u3063\\u305f\\u3089\\nif N %2 ==0:\\n    colA = collections.Counter(A)\\n    for key,val in list(colA.items()):\\n        if key%2 != 1 or val != 2:\\n            flag0 = 0\\n            break\\n    for i in range(1,N,2):\\n        if i not in list(colA.keys()):\\n            flag = 0\\n            break\\n        else:\\n            count +=1\\n#\\u5947\\u6570\\u3060\\u3063\\u305f\\u3089\\nelse:\\n    A.append(0)\\n    colA = collections.Counter(A)\\n    for key,val in list(colA.items()):\\n        if key%2 != 0 or val != 2:\\n            flag0 = 0\\n            break\\n    for i in range(0,N,2):\\n        if i not in list(colA.keys()):\\n            flag = 0\\n            break\\n        else:\\n            count +=1\\n    count -=1\\n\\n\\nprint((((2**count)%m)*flag0))\\n    \\n\"]",
        "difficulty": "introductory",
        "input": "8\n7 5 1 1 7 3 5 3\n",
        "output": "16\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc050/tasks/arc066_a"
    },
    {
        "id": 271,
        "task_id": 283,
        "test_case_id": 1,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "3\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 272,
        "task_id": 283,
        "test_case_id": 2,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "4\n",
        "output": "2",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 273,
        "task_id": 283,
        "test_case_id": 3,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "10\n",
        "output": "2",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 274,
        "task_id": 283,
        "test_case_id": 4,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "153\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 275,
        "task_id": 283,
        "test_case_id": 5,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "1000\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 276,
        "task_id": 283,
        "test_case_id": 6,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "1\n",
        "output": "3",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 277,
        "task_id": 283,
        "test_case_id": 7,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "2\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 278,
        "task_id": 283,
        "test_case_id": 8,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "5\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 279,
        "task_id": 283,
        "test_case_id": 9,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "6\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 280,
        "task_id": 283,
        "test_case_id": 10,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "7\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 281,
        "task_id": 283,
        "test_case_id": 11,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "8\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 282,
        "task_id": 283,
        "test_case_id": 12,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "9\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 283,
        "task_id": 283,
        "test_case_id": 13,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "11\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 284,
        "task_id": 283,
        "test_case_id": 14,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "998\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 285,
        "task_id": 283,
        "test_case_id": 15,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "996\n",
        "output": "3",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 286,
        "task_id": 283,
        "test_case_id": 16,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "36\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 287,
        "task_id": 283,
        "test_case_id": 17,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "210\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 288,
        "task_id": 283,
        "test_case_id": 18,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "270\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 289,
        "task_id": 283,
        "test_case_id": 19,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "306\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 290,
        "task_id": 283,
        "test_case_id": 20,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "330\n",
        "output": "5",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 291,
        "task_id": 283,
        "test_case_id": 21,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "336\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 292,
        "task_id": 283,
        "test_case_id": 22,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "600\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 293,
        "task_id": 283,
        "test_case_id": 23,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "726\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 294,
        "task_id": 283,
        "test_case_id": 24,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "988\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 295,
        "task_id": 283,
        "test_case_id": 25,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "12\n",
        "output": "2",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 296,
        "task_id": 283,
        "test_case_id": 26,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "987\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 297,
        "task_id": 283,
        "test_case_id": 27,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "13\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 298,
        "task_id": 283,
        "test_case_id": 28,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "986\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 299,
        "task_id": 283,
        "test_case_id": 29,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "14\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 300,
        "task_id": 283,
        "test_case_id": 30,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "985\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 301,
        "task_id": 283,
        "test_case_id": 31,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "15\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 302,
        "task_id": 283,
        "test_case_id": 32,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "984\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 303,
        "task_id": 283,
        "test_case_id": 33,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "16\n",
        "output": "2",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 304,
        "task_id": 283,
        "test_case_id": 34,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "983\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 305,
        "task_id": 283,
        "test_case_id": 35,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "17\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 306,
        "task_id": 283,
        "test_case_id": 36,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "982\n",
        "output": "2",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 307,
        "task_id": 283,
        "test_case_id": 37,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "18\n",
        "output": "3",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 308,
        "task_id": 283,
        "test_case_id": 38,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "981\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 309,
        "task_id": 283,
        "test_case_id": 39,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "19\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 310,
        "task_id": 283,
        "test_case_id": 40,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "980\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 311,
        "task_id": 283,
        "test_case_id": 41,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "20\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 312,
        "task_id": 283,
        "test_case_id": 42,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "979\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 313,
        "task_id": 283,
        "test_case_id": 43,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "21\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 314,
        "task_id": 283,
        "test_case_id": 44,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "978\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 315,
        "task_id": 283,
        "test_case_id": 45,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "22\n",
        "output": "2",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 316,
        "task_id": 283,
        "test_case_id": 46,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "977\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 317,
        "task_id": 283,
        "test_case_id": 47,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "23\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 318,
        "task_id": 283,
        "test_case_id": 48,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "976\n",
        "output": "2",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 319,
        "task_id": 283,
        "test_case_id": 49,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "24\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 320,
        "task_id": 283,
        "test_case_id": 50,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "975\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 321,
        "task_id": 283,
        "test_case_id": 51,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "25\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 322,
        "task_id": 283,
        "test_case_id": 52,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "2\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 323,
        "task_id": 283,
        "test_case_id": 53,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "6\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 324,
        "task_id": 283,
        "test_case_id": 54,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "996\n",
        "output": "3",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 325,
        "task_id": 283,
        "test_case_id": 55,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "8\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 326,
        "task_id": 283,
        "test_case_id": 56,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "998\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 327,
        "task_id": 283,
        "test_case_id": 57,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "330\n",
        "output": "5",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 328,
        "task_id": 283,
        "test_case_id": 58,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "18\n",
        "output": "3",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 329,
        "task_id": 283,
        "test_case_id": 59,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "12\n",
        "output": "2",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 330,
        "task_id": 283,
        "test_case_id": 60,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "24\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 331,
        "task_id": 283,
        "test_case_id": 61,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "999\n",
        "output": "1",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 332,
        "task_id": 283,
        "test_case_id": 62,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "726\n",
        "output": "4",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 333,
        "task_id": 283,
        "test_case_id": 63,
        "question": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number\".\n\nUnfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.\n\n\n-----Input-----\n\nThe only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis. \n\n\n-----Output-----\n\nOutput such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 10^3. It is guaranteed the the answer exists.\n\n\n-----Examples-----\nInput\n3\n\nOutput\n1\nInput\n4\n\nOutput\n2\n\n\n-----Note-----\n\nA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\nFor the first sample testcase, 3·1 + 1 = 4. We can output 1.\n\nIn the second sample testcase, 4·1 + 1 = 5. We cannot output 1 because 5 is prime. However, m = 2 is okay since 4·2 + 1 = 9, which is not a prime number.",
        "solutions": "[\"def prime(x):\\n    if x < 2:\\n        return False\\n    if x == 2:\\n        return True\\n    if x % 2 == 0:\\n        return False\\n\\n    for d in range(3, x, 2):\\n        if d * d > x:\\n            break\\n        if x % d == 0:\\n            return False\\n\\n    return True\\n\\ndef main():\\n    n = int(input())\\n    for m in range(1, 1001):\\n        if not prime(n * m + 1):\\n            ans = m\\n            break\\n\\n    print(ans)\\n\\nmain()\\n\", \"n = int(input())\\ndef ispr(m):\\n\\ti = 2\\n\\twhile i * i <= m:\\n\\t\\tif m % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\nfor i in range(1, 1001):\\n\\tif not ispr(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\treturn\", \"def not_pr(x):\\n    return sum(x % i == 0 for i in range(2, x)) != 0\\n\\nread = lambda: map(int, input().split())\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not_pr(n * m + 1):\\n        print(m)\\n        return\", \"def is_prime(n):\\n\\ti = 2\\n\\twhile i * i <= n:\\n\\t\\tif n % i == 0:\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\nn = int(input())\\nfor i in range(1, 1001):\\n\\tif not is_prime(n * i + 1):\\n\\t\\tprint(i)\\n\\t\\tbreak\\n\", \"def prime(n):\\n\\ti = 2\\n\\twhile (i * i <= n):\\n\\t\\tif (n % i == 0):\\n\\t\\t\\treturn False\\n\\t\\ti += 1\\n\\treturn True\\n\\ndef main(n):\\n\\tm = 1\\n\\twhile(True):\\n\\t\\tif (not prime(m * n + 1)):\\n\\t\\t\\tprint(m)\\n\\t\\t\\treturn\\n\\t\\tm += 1\\n\\n\\nmain(int(input()))\", \"\\ndef primesSieve(limit):\\n    def internalPrimesSieve(limit):\\n        a = [True] * limit # Initialize the primality list\\n        a[0] = a[1] = False\\n\\n        for (i, isprime) in enumerate(a):\\n            if isprime:\\n                yield i\\n                for n in range(i*i, limit, i): # Mark factors non-prime\\n                    a[n] = False\\n    return [p for p in internalPrimesSieve(limit)]\\n\\nn = int(input())\\nprimes = primesSieve(1000002)\\nfor i in range(1,1001):\\n    if n*i + 1 not in primes:\\n        print(i)\\n        break\\n\", \"3\\n\\ndef is_prime(x):\\n    if x == 1:\\n        return False\\n    i = 2\\n    while i * i <= x:\\n        if x % i == 0:\\n            return False\\n        i += 1\\n    return True\\n\\n\\nn = int(input())\\nm = 1\\nwhile is_prime(n * m + 1):\\n    m += 1\\nprint(m)\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    import itertools\\n\\n    def is_prime(x):\\n        if x == 2:\\n            return True\\n        if x & 0x1 == 0:\\n            return False\\n        i = 3\\n        while i * i <= x:\\n            if x % i == 0:\\n                return False\\n            i += 2\\n        return True\\n\\n    try:\\n        while True:\\n            n = int(input())\\n            for m in itertools.count(1):\\n                if not is_prime(n * m + 1):\\n                    print(m)\\n                    break\\n\\n    except EOFError:\\n        pass\\n\\nmain()\\n\", \"n = int(input())\\n\\ndef yes(x):\\n\\tif (x < 3):\\n\\t\\treturn 0\\n\\telse:\\n\\t\\tfor y in range(2,x):\\n\\t\\t\\tif (x%y == 0):\\n\\t\\t\\t\\treturn 1\\n\\t\\treturn 0\\n\\n\\nfor m in range(1,1001):\\n\\tif yes(n*m+1):\\n\\t\\tprint(m)\\n\\t\\tbreak\", \"n = int(input())\\n\\ndef isPrime(x):\\n    for j in range(2,round(x**0.5)+1):\\n        if not x%j: return False\\n    return True\\n\\nfor m in range(1,1000):\\n    if not isPrime(m*n+1):\\n        print(m)\\n        break\", \"from math import sqrt\\nn=int(input())\\na=0\\nm=0\\nwhile True:\\n    m+=1\\n    a=n*m+1\\n    for i in range(2,int(sqrt(a)+1)):\\n        if a%i==0:\\n            print(m)\\n            return\\n\", \"import math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,100):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"import math\\n\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\n\\nn = int(input())\\nm = 1\\n\\nwhile (is_prime((n*m)+1)):\\n\\tm+=1\\nprint(m)\", \"#autor @ShymCoder\\nimport math\\ndef is_prime(n):\\n    if n % 2 == 0 and n > 2: \\n        return False\\n    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))\\nn=int(input())\\nfor i in range(1,1001):\\n    if not is_prime(n*i+1):\\n        print(i)\\n        break\\n\", \"n=int(input())\\n\\nflag=True\\n\\nm=1\\na=[True]*1000001\\na[1]=False\\n\\nfor i in range(2,len(a)):\\n    if a[i]:\\n        for j in range(2*i,len(a),i):\\n            a[j]=False\\n\\nwhile flag:\\n    if a[m*n+1]==False:\\n        flag=False\\n        print(m)\\n    else:\\n        m+=1\\n\", \"def prime(x):\\n    for i in range(2, 1001):\\n        if x % i == 0 and i != x:\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor m in range(1, 1001):\\n    if not prime(n * m + 1):\\n        print(m)\\n        return\\n\", \"\\n\\nisp = [True]*(10**6+8)\\nisp[0] = isp[1] = False\\n\\ni = 2\\nN = 10**6 + 7\\nwhile i*i <= N :\\n\\tif isp[i] : \\n\\t\\tfor j in range(i*i , N+1 , i  ) : \\n\\t\\t\\tisp[j] = False\\n\\ti += 1\\nn = int(input())\\nfor m in range(1,1001) : \\n\\tif not isp[n*m + 1] :\\n\\t\\tprint(m)\\n\\t\\tbreak\\n\", \"#!/usr/bin/env pypy3\\n# -*- coding: UTF-8 -*-\\nimport sys\\nimport re\\nimport math\\nimport itertools\\nimport collections\\nimport bisect\\n#sys.stdin=file('input.txt')\\n#sys.stdout=file('output.txt','w')\\n#10**9+7\\nmod=1000000007\\n#mod=1777777777\\npi=3.1415926535897932\\nIS=float('inf')\\nxy=[(1,0),(-1,0),(0,1),(0,-1)]\\nbs=[(-1,-1),(-1,1),(1,1),(1,-1)]\\ndef niten(a,b): return abs(a-b) if a>=0 and b>=0 else  a+abs(b) if a>=0 else abs(a)+b if b>=0 else abs(abs(a)-abs(b))\\ndef fib(n): return [(seq.append(seq[i-2] + seq[i-1]), seq[i-2])[1] for seq in [[0, 1]] for i in range(2, n)]\\ndef gcd(a,b): return a if b==0 else gcd(b,a%b)\\ndef lcm(a,b): return a*b/gcd(a,b)\\ndef eucl(x1,y1,x2,y2): return ((x1-x2)**2+(y1-y2)**2)**0.5\\ndef choco(xa,ya,xb,yb,xc,yc,xd,yd): return 1 if abs((yb-ya)*(yd-yc)+(xb-xa)*(xd-xc))<1.e-10 else 0\\ndef pscl(num,l=[1]):\\n    for i in range(num):\\n        l = map(lambda x,y:x+y,[0]+l,l+[0])\\n    return l\\n\\ndef prime_t(t):\\n    i=2\\n    while i**2<=t:\\n        if t%i==0:\\n            return 0\\n        i+=1\\n    return 1\\n\\nl=[]\\nfor i in range(2,10000):\\n    if prime_t(i):\\n        l.append(i)\\n\\nn=int(input())\\nfor i in range(1,1001):\\n    if (n*i+1) not in l:\\n        print(i)\\n        return\", \"import math\\n\\n\\ndef check(n):\\n    q = int(math.sqrt(n))\\n    for i in range(2, q + 1):\\n        if not (n % i):\\n            return False\\n    return True\\n\\n\\nn = int(input())\\nfor i in range(1, 1000):\\n    if not check(n * i + 1):\\n        print(i)\\n        break\"]",
        "difficulty": "interview",
        "input": "876\n",
        "output": "3",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/755/A"
    },
    {
        "id": 334,
        "task_id": 452,
        "test_case_id": 1,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "9 4\n2\n2 4\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 335,
        "task_id": 452,
        "test_case_id": 2,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "9 4\n3\n2 3 1\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 336,
        "task_id": 452,
        "test_case_id": 3,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "9 4\n3\n1 2 4\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 337,
        "task_id": 452,
        "test_case_id": 4,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "39088169 24157817\n36\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 338,
        "task_id": 452,
        "test_case_id": 5,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "39088169 24157817\n36\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 339,
        "task_id": 452,
        "test_case_id": 6,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "61305790721611591 37889062373143906\n80\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 340,
        "task_id": 452,
        "test_case_id": 7,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "61305790721611591 37889062373143906\n80\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 341,
        "task_id": 452,
        "test_case_id": 8,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "565049485241691020 228217260073568804\n40\n2 2 9 1 7 1 2 1 2 1 1 1 9 1 2 1 9 1 3 2 3 10 13 2 1 2 7 1 1 2 2 2 1 1 2 1 6 5 3 2\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 342,
        "task_id": 452,
        "test_case_id": 9,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "2 1\n4\n2 1 1 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 343,
        "task_id": 452,
        "test_case_id": 10,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "4 1\n2\n3 1\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 344,
        "task_id": 452,
        "test_case_id": 11,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "72723460248141 1597\n1\n45537545554\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 345,
        "task_id": 452,
        "test_case_id": 12,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "14930352 13\n6\n1148488 1 1 1 1 2\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 346,
        "task_id": 452,
        "test_case_id": 13,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "86267571272 102334155\n6\n842 1 841 1 842 145\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 347,
        "task_id": 452,
        "test_case_id": 14,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "72723460248141 121393\n7\n599074578 122 1 122 2 1 2\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 348,
        "task_id": 452,
        "test_case_id": 15,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "168455988218483660 53310571951833359\n32\n3 6 3 1 14 1 48 1 3 2 1 1 39 2 1 3 13 23 4 1 11 1 1 23 1 3 3 2 1 1 1 3\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 349,
        "task_id": 452,
        "test_case_id": 16,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "382460255113156464 275525972692563593\n37\n1 2 1 1 2 1 3 4 5 5 1 4 2 1 1 1 4 2 2 1 2 1 1 2 3 3 1 2 2 50 4 1 4 2 5 109 8\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 350,
        "task_id": 452,
        "test_case_id": 17,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "1000000000000000000 1\n1\n1000000000000000000\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 351,
        "task_id": 452,
        "test_case_id": 18,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "362912509915545727 266073193475139553\n30\n1 2 1 2 1 25 75 1 14 6 6 9 1 1 1 1 210 2 2 2 5 2 1 3 1 1 13 3 14 3\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 352,
        "task_id": 452,
        "test_case_id": 19,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "933329105990871495 607249523603826772\n33\n1 1 1 6 3 1 5 24 3 55 1 15 2 2 1 12 2 2 3 109 1 1 4 1 4 1 7 2 4 1 3 3 2\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 353,
        "task_id": 452,
        "test_case_id": 20,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "790637895857383456 679586240913926415\n40\n1 6 8 2 1 2 1 7 2 4 1 1 1 10 1 10 1 4 1 4 41 1 1 7 1 1 2 1 2 4 1 2 1 63 1 2 1 1 4 3\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 354,
        "task_id": 452,
        "test_case_id": 21,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "525403371166594848 423455864168639615\n38\n1 4 6 1 1 32 3 1 14 1 3 1 2 4 5 4 1 2 1 5 8 1 3 1 2 1 46 1 1 1 3 1 4 1 11 1 2 4\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 355,
        "task_id": 452,
        "test_case_id": 22,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "1 1\n1\n1\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 356,
        "task_id": 452,
        "test_case_id": 23,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "2 1\n2\n1 2\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 357,
        "task_id": 452,
        "test_case_id": 24,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "531983955813463755 371380136962341468\n38\n1 2 3 4 1 37 1 12 1 3 2 1 6 3 1 7 3 2 8 1 2 1 1 7 1 1 1 7 1 47 2 1 3 1 1 5 1 2\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 358,
        "task_id": 452,
        "test_case_id": 25,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "32951280099 987\n7\n33385288 1 5 1 5 1 6\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 359,
        "task_id": 452,
        "test_case_id": 26,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "6557470319842 86267571272\n6\n76 76 76 76 76 76\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 360,
        "task_id": 452,
        "test_case_id": 27,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "934648630114363087 6565775686518446\n31\n142 2 1 5 2 2 1 1 3 1 2 8 1 3 12 2 1 23 5 1 10 1 863 1 1 1 2 1 14 2 3\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 361,
        "task_id": 452,
        "test_case_id": 28,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "61305790721611591 37889062373143906\n81\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 362,
        "task_id": 452,
        "test_case_id": 29,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "4 1\n1\n4\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 363,
        "task_id": 452,
        "test_case_id": 30,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "500000000000000001 5\n2\n100000000000000000 5\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 364,
        "task_id": 452,
        "test_case_id": 31,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "1000000000000000000 3\n3\n3 4 5\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 365,
        "task_id": 452,
        "test_case_id": 32,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "822981258385599125 28316248989464296\n39\n29 15 1 1 1 4 4 4 1 3 1 5 12 1 1 1 1 1 6 5 2 1 11 1 1 26 1 2 2 2 14 1 1 1 3 2 4 1 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 366,
        "task_id": 452,
        "test_case_id": 33,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "823443107025550834 331822464812968648\n42\n2 2 13 14 4 4 1 1 1 1 2 1 1 1 1 113 1 1 8 1 1 1 1 2 2 1 15 1 5 1 1 2 1 1 1 14 4 3 1 5 1 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 367,
        "task_id": 452,
        "test_case_id": 34,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "226137305050296073 27076290603746056\n30\n8 2 1 5 3 67 2 1 6 1 2 1 5 1 11 8 43 2 1 7 1 95 2 3 1 11 5 2 1 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 368,
        "task_id": 452,
        "test_case_id": 35,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "524928871965838747 313083111434773473\n35\n1 1 2 10 1 4 12 3 28 1 23 1 1 1 4 1 4 3 1 3 2 3 1 4 3 1 3 2 3 11 21 1 35 1 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 369,
        "task_id": 452,
        "test_case_id": 36,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "633468529243155234 4\n90\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 370,
        "task_id": 452,
        "test_case_id": 37,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "742143496299253703 2\n90\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 371,
        "task_id": 452,
        "test_case_id": 38,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "550736960584023286 3\n90\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 372,
        "task_id": 452,
        "test_case_id": 39,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "2 1\n10\n99999999999999999 99999999999999999 99999999999999999 99999999999999999 99999999999999999 99999999999999999 99999999999999999 99999999999999999 99999999999999999 99999999999999999\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 373,
        "task_id": 452,
        "test_case_id": 40,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "262882295792523313 105000000000078855\n1\n105000000000078855\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 374,
        "task_id": 452,
        "test_case_id": 41,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "990130967049151695 166430169817556175\n1\n564668656008429569\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 375,
        "task_id": 452,
        "test_case_id": 42,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "9 4\n2\n2 3\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 376,
        "task_id": 452,
        "test_case_id": 43,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "529824479480396864 4705882352941177\n2\n80000000000000007 80000000000000009\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 377,
        "task_id": 452,
        "test_case_id": 44,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "985625905209512860 565433601688714177\n10\n6423 24947 27507 13031 16414 29169 901 32592 18763 1656\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 378,
        "task_id": 452,
        "test_case_id": 45,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "913255926290448385 4400000000\n2\n4400000000 4400000000\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 379,
        "task_id": 452,
        "test_case_id": 46,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "7 2\n2\n2 1\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 380,
        "task_id": 452,
        "test_case_id": 47,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "10 3\n1\n3\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 381,
        "task_id": 452,
        "test_case_id": 48,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "4 2\n1\n2\n",
        "output": "YES\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 382,
        "task_id": 452,
        "test_case_id": 49,
        "question": "A continued fraction of height n is a fraction of form $a_{1} + \\frac{1}{a_{2} + \\frac{1}{\\ldots + \\frac{1}{a_{n}}}}$. You are given two rational numbers, one is represented as [Image] and the other one is represented as a finite fraction of height n. Check if they are equal.\n\n\n-----Input-----\n\nThe first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 10^18) — the numerator and the denominator of the first fraction.\n\nThe second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^18) — the continued fraction.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\n\n-----Output-----\n\nPrint \"YES\" if these fractions are equal and \"NO\" otherwise.\n\n\n-----Examples-----\nInput\n9 4\n2\n2 4\n\nOutput\nYES\n\nInput\n9 4\n3\n2 3 1\n\nOutput\nYES\n\nInput\n9 4\n3\n1 2 4\n\nOutput\nNO\n\n\n\n-----Note-----\n\nIn the first sample $2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the second sample $2 + \\frac{1}{3 + \\frac{1}{1}} = 2 + \\frac{1}{4} = \\frac{9}{4}$.\n\nIn the third sample $1 + \\frac{1}{2 + \\frac{1}{4}} = \\frac{13}{9}$.",
        "solutions": "[\"#!/usr/bin/env python3\\n\\nfrom fractions import Fraction\\n\\ndef __starting_point():\\n    p, q = list(map(int, input().split()))\\n    n = int(input())\\n    l = list(map(int, input().split()))\\n\\n    f = Fraction(l[-1], 1)\\n\\n    for x in l[-2::-1]:\\n        f = 1 / f\\n        f += x\\n\\n    print([\\\"NO\\\", \\\"YES\\\"][f == Fraction(p, q)])\\n\\n\\n\\n__starting_point()\", \"from  fractions import *\\np,q  = map(int,input().split())\\na1 = Fraction(p,q)\\nn = int(input())\\naaa = list(map(int,input().split()))\\nd2 = Fraction(aaa[-1],1)\\nfor i in range(2,n+1):\\n    d2 = 1/d2+aaa[-i]\\n#print (d2)\\nprint(\\\"YES\\\" if a1 == d2 else \\\"NO\\\")\", \"from fractions import Fraction\\npq = Fraction(*map(int, input().split()))\\ninput()\\na = list(map(int, input().split()))\\na.reverse()\\nf = Fraction(a[0], 1)\\nfor i in a[1:]:\\n  f = i + Fraction(1, f)\\nif pq == f:\\n  print(\\\"YES\\\")\\nelse:\\n  print(\\\"NO\\\")\", \"from fractions import*\\nfrom sys import*\\nfrom copy import*\\nfrom time import*\\n\\n\\nclass Fraction:\\n    def __init__(self, x = 0, y = 1):\\n        if(type(x) == str):\\n            if x.find('/') != -1:\\n                a = list(map(int, x.split('/')))\\n            else:\\n                a = list(map(int, x.split()))\\n            self.num = a[0]\\n            if len(a) == 1:\\n                self.den = 1\\n            else:\\n                self.den = a[1]\\n        elif(type(x) == Fraction):\\n            self.num, self.den = x.num, x.den\\n        else:\\n            self.num, self.den = x, y\\n        self.reduce()\\n\\n    def __str__(self):\\n        if self.den == 1:\\n            return str(int(self.num))\\n        return str(int(self.num)) + '/' + str(int(self.den))\\n\\n    def reduce(self):\\n        d = gcd(abs(self.num), abs(self.den))\\n        if self.den < 0:\\n            self.den, self.num = -self.den, -self.num\\n        self.num, self.den = self.num // d, self.den // d\\n\\n    def __lt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den < other.num * self.den\\n        else:\\n            return self.num < self.den * other\\n\\n    def __le__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den <= other.num * self.den\\n        else:\\n            return self.num <= self.den * other\\n\\n    def __gt__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den > other.num * self.den\\n        else:\\n            return self.num > self.den * other\\n\\n    def __ge__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den >= other.num * self.den\\n        else:\\n            return self.num >= self.den * other\\n\\n    def __eq__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den == other.num * self.den\\n        else:\\n            return self.num == self.den * other\\n\\n    def __ne__(self, other):\\n        if type(other) == Fraction:\\n            return self.num * other.den != other.num * self.den\\n        else:\\n            return self.num != self.den * other\\n\\n    def __mul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def rmul(self, other):\\n        return other * self\\n\\n    def __rmul__(self, other):\\n        if(type(other) == float):\\n            return (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.num, self.den * other.den)\\n\\n    def __imul__(self, other):\\n        if(type(other) == float):\\n            self = (self.num * other) / self.den\\n        else:\\n            other = Fraction(other)\\n            self.num *= other.num\\n            self.den *= other.den\\n            self.reduce()\\n        return self\\n\\n    def __truediv__(self, other):\\n        if(type(other) == float):\\n            return self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            return self * Fraction(other.den, other.num)\\n\\n    def __rtruediv__(self, other):\\n        if(type(self) == float):\\n            return other.num / (other.den * self)\\n        else:\\n            self = Fraction(self)\\n            return other * Fraction(self.den, self.num)\\n\\n    def __itruediv__(self, other):\\n        if(type(other) == float):\\n            self = self.num / (self.den * other)\\n        else:\\n            other = Fraction(other)\\n            self = self * Fraction(other.den, other.num)\\n            self.reduce()\\n        return self\\n\\n    def __pow__(self, other):\\n        if type(other) == Fraction:\\n            return (self.num / self.den) ** (other.num / other.den)\\n        elif type(other) == int:\\n            if other > 0:\\n                return Fraction(self.num ** other, self.den ** other)\\n            else:\\n                return 1 / Fraction(self.num ** (-other), self.den ** (-other))\\n        else:\\n            return (self.num / self.den) ** other\\n\\n    def __rpow__(self, other):\\n        return other ** (self.num / self.den)\\n\\n    def __ipow__(self, other):\\n        if other > 0:\\n            self.num **= other\\n            self.den **= other\\n        else:\\n            self.num **= (-other)\\n            self.den **= (-other)\\n            self.num, self.den = self.den, self.num\\n        return self\\n\\n    def __add__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den + other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den + other.num * self.den, self.den * other.den)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den + other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den + other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __sub__(self, other):\\n        if type(other) == float:\\n            return self.num / self.den - other\\n        elif type(other) == Poly:\\n            return NotImplemented\\n        else:\\n            other = Fraction(other)\\n            return Fraction(self.num * other.den - other.num * self.den, self.den * other.den)\\n\\n    def __rsub__(self, other):\\n        if(type(self - other) == Fraction):\\n            return Fraction(-(self - other).num, (self - other).den)\\n        else:\\n            return -(self - other)\\n\\n    def __isub__(self, other):\\n        if type(other) == float:\\n            self = self.num / self.den - other\\n        else:\\n            other = Fraction(other)\\n            self.num = self.num * other.den - other.num * self.den\\n            self.den = self.den * other.den\\n            self.reduce()\\n        return self\\n\\n    def __pos__(self):\\n        return self\\n\\n    def __neg__(self):\\n        return Fraction(-self.num, self.den)\\n\\n    def __abs__(self):\\n        return Fraction((-self.num) * int(self.num < 0) + (self.num) * (self.num >= 0), self.den)\\n\\n    def __int__(self):\\n        return self.num // self.den\\n\\n    def __float__(self):\\n        return self.num / self.den\\n\\n    def __round__(self, x = 0):\\n        return round(float(self), x)\\n\\n\\nclass Poly:\\n    def __init__(self, s = 0):\\n        if type(s) in [int, float, Fraction]:\\n            self.list = [s]\\n        elif type(s) == str:\\n            self.list, s = [], s.split()\\n            for elem in S:\\n                self.list += eval(elem)\\n        elif type(s) == Poly:\\n            self.list = s.list\\n        else:\\n            self.list = list(s)\\n\\n    def __str__(self):\\n        P, S, power, first = [chr(8304), chr(185), chr(178), chr(179)] + [chr(i) for i in range(8308, 8314)], \\\"\\\", len(self.list) - 1, True\\n        for i in range(len(self.list) - 1, -1, -1):\\n            current = self.list[i]\\n            if current != 0:\\n                if current > 0:\\n                    S += \\\" + \\\" * int(not first)\\n                else:\\n                    S += \\\" - \\\" * int(not first) + \\\"-\\\" * int(first)\\n                current = abs(current)\\n                if current != 1 or (current == 1 and power == 0):\\n                    if type(current) == Fraction:\\n                        if current.den == 1:\\n                            S += str(int(current.num))\\n                        else:\\n                            S += \\\"(\\\" + str(current) + \\\")\\\"\\n                    elif type(current) == float:\\n                        S += str(round(current, 3))\\n                    else:\\n                        S += str(current)\\n                S += ('x' * (power != 0))\\n                for elem in str(power):\\n                    S += P[int(elem)] * (not(elem in [\\\"0\\\", \\\"1\\\"] and len(str(power)) == 1))\\n                first = len(S) == 0\\n            power -= 1\\n        if S == \\\"\\\":\\n            return \\\"0\\\"\\n        return S\\n\\n    def __neg__(self):\\n        result = []\\n        for elem in self.list:\\n            result.append(-elem)\\n        return Poly(result)\\n\\n    def __add__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] + other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] + other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __radd__(self, other):\\n        return self + other\\n\\n    def __iadd__(self, other):\\n        self.list = (self + other).list\\n        return self\\n\\n    def __sub__(self, other):\\n        result = []\\n        if type(other) == Poly:\\n            for i in range(max(len(self.list), len(other.list))):\\n                if i < len(self.list):\\n                    if i < len(other.list):\\n                        result.append(self.list[i] - other.list[i])\\n                    else:\\n                        result.append(self.list[i])\\n                else:\\n                    if i < len(other.list):\\n                        result.append(-other.list[i])\\n                    else:\\n                        result.append(0)\\n            return Poly(result)\\n        else:\\n            lolka = [self.list[0] - other] + self.list[1:]\\n            return Poly(lolka)\\n\\n    def __rsub__(self, other):\\n        return -(self - other)\\n\\n    def __isub__(self, other):\\n        self.list = (self - other).list\\n        return self\\n\\n    def __or__(self, other):\\n        if len(self.list) == 1:\\n            return self.list[0]\\n        result = self.list[len(self.list) - 1]\\n        for i in range(len(self.list) - 2, -1, -1):\\n            result = result * other + self.list[i]\\n        return result\\n\\n    def __mul__(self, other):\\n        result, p = [], Poly(other)\\n        for i in range(len(self.list)):\\n            for j in range(len(p.list)):\\n                if len(result) > i + j:\\n                    result[i + j] += self.list[i] * p.list[j]\\n                else:\\n                    result += [0] * (i + j - len(result)) + [self.list[i] * p.list[j]]\\n        return Poly(result)\\n\\n    def __rmul__(self, other):\\n        return self * other\\n\\n    def __imul__(self, other):\\n        self.list = (self * other).list\\n        return self\\n\\n    def __pow__(self, other):\\n        if other == 0:\\n            return Poly(1)\\n        if other % 2 == 1:\\n            return Poly((self ** (other - 1)) * self)\\n        else:\\n            lolka = self ** (other // 2)\\n            return Poly(lolka * lolka)\\n\\n    def __ipow__(self, other):\\n        self.list = (self ** other).list\\n        return self\\n\\n    def __divmod__(self, other):\\n        result = [0] * 100\\n        p = deepcopy(self.list)\\n        q = Poly(other).list\\n        power1, power2 = len(p) - 1, len(q) - 1\\n        while(power1 > -1 and p[power1] == 0):\\n            power1 -= 1\\n        while(power2 > -1 and q[power2] == 0):\\n            power2 -= 1\\n        while(power1 > -1 and power2 > -1 and power1 >= power2):\\n            minus = [0] * (power1 - power2)\\n            if type(p[power1]) == int and type(q[power2]) == int:\\n                if p[power1] % q[power2] == 0:\\n                    current = p[power1] // q[power2]\\n                else:\\n                    current = Fraction(p[power1], q[power2])\\n            else:\\n                current = p[power1] / q[power2]\\n            for elem in q:\\n                minus += [elem * current]\\n            for i in range(max(len(p), len(minus))):\\n                if i < len(p):\\n                    if i < len(minus):\\n                        p[i] -= minus[i]\\n                else:\\n                    if i < len(minus):\\n                        p.append(-minus[i])\\n                    else:\\n                        p.append(0)\\n            result[power1 - power2] = current\\n            while(power1 > -1 and p[power1] == 0):\\n                power1 -= 1\\n            while(power2 > -1 and q[power2] == 0):\\n                power2 -= 1\\n            #result += [current]\\n        return (Poly(result), Poly(p))\\n\\n    def __rdivmod__(self, other):\\n        return  divmod(Poly(other), self)\\n\\n    def __floordiv__(self, other):\\n        return divmod(self, other)[0]\\n\\n    def __rfloordiv__(self, other):\\n        return divmod(Poly(other), self)[0]\\n\\n    def __ifloordiv__(self, other):\\n        self.list = (divmod(self, other)[0]).list\\n        return self\\n\\n    def __mod__(self, other):\\n        return divmod(self, other)[1]\\n\\n    def __rmod__(self, other):\\n        return divmod(Poly(other), self)[1]\\n\\n    def __imod__(self, other):\\n        self.list = (divmod(self, other)[1]).list\\n        return self\\n\\n#begin = time()\\np, q = list(map(int, input().split()))\\nlolka = Fraction(p, q)\\nn = int(input())\\nA = list(map(int, input().split()))\\nAnswer = Fraction(A[-1])\\nfor i in range(len(A) - 2, -1, -1):\\n    Answer = 1 / Answer\\n    Answer += A[i]\\nif(Answer == lolka):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n#print(time() - begin)\\n\\n\", \"p,q=tuple(map(int,input().split()))\\nn1=input().split()\\nn=int(n1[0])\\na=list(map(int,input().split()))\\nx=1\\ny=a[n-1]\\nfor i in range (n-2,-1,-1):\\n   x1=a[i]*y+x\\n   x=y\\n   y=x1\\nif p*x==q*y:\\n   print('YES')\\nelse:\\n   print('NO')\\n   \\n\", \"#!/usr/local/bin/python3.3 -tt\\n\\nimport fractions\\nimport sys\\n\\n\\ndef __starting_point():\\n    def _(f):\\n        for l in f:\\n            for i in l.split():\\n                yield int(i)\\n\\n    g = _(sys.stdin)\\n\\n    pq = fractions.Fraction(next(g), next(g))\\n\\n    n, a = next(g), []\\n\\n    for i in range(n):\\n        a.append(next(g))\\n\\n    r = fractions.Fraction(a.pop())\\n\\n    while a:\\n        r = fractions.Fraction(a.pop()) + fractions.Fraction(1, r)\\n\\n    if r == pq:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\n__starting_point()\", \"3\\n\\ndef gcd(a, b):\\n\\tif b == 0:\\n\\t\\treturn a\\n\\treturn gcd(b, a % b)\\n\\ndef red(pr):\\n\\ta, b = pr\\n\\tg = gcd(a, b)\\n\\treturn (a // g, b // g)\\n\\ndef rev(pr):\\n\\ta, b = pr\\n\\treturn (b, a)\\n\\ndef add(pr, i):\\n\\ta, b = pr\\n\\ta += b * i\\n\\treturn red((a, b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nargs = args[2:]\\nn = args[0]\\nargs = args[1:]\\na = args[::-1]\\ns = (a[0], 1)\\na = a[1:]\\nfor i in a:\\n\\ts = add(rev(s), i)\\nif red(s) == red((p, q)):\\n\\tprint(\\\"YES\\\")\\nelse:\\n\\tprint(\\\"NO\\\")\\n\", \"import re\\nimport itertools\\nfrom collections import Counter, deque\\nfrom fractions import gcd\\n\\nclass Task:\\n    p, q = 0, 0\\n    a = []\\n    answer = ''\\n\\t\\n    def getData(self):\\n        self.p, self.q = [int(x) for x in input().split(' ')]\\n        input()\\n        self.a = [int(x) for x in input().split(' ')]\\n        #inFile = open('input.txt', 'r')\\n        #inFile.readline().rstrip()\\n        #self.childs = inFile.readline().rstrip()\\n\\n    def solve(self):\\n        p, q = self.toFraction(self.a)\\n        if self.p * q == self.q * p:\\n            self.answer = 'YES'\\n        else:\\n            self.answer = 'NO'\\n\\n    def toFraction(self, a):\\n        if len(a) == 1:\\n            return a[0], 1\\n        q, p = self.toFraction(a[1 : ])\\n        d = gcd(a[0] * q + p, q)\\n        return (a[0] * q + p) // d, q // d\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #outFile = open('output.txt', 'w')\\n        #outFile.write(self.answer)\\n\\ntask = Task()\\ntask.getData()\\ntask.solve()\\ntask.printAnswer()\\n\", \"3\\n\\np, q = tuple(map(int, input().strip().split()))\\nn = int(input().strip())\\na = list(map(int, input().strip().split()))\\na.reverse()\\n\\ndef gcd(a, b):\\n    while a:\\n        a, b = b % a, a\\n    return b\\n\\ng = gcd(p, q)\\np, q = p // g, q // g\\n\\nu, v = 0, 1;\\n\\nfor i in a:\\n    v, u = v * i + u, v\\n    g = gcd(u, v)\\n    u, v = u // g, v // g\\nif p == v and q == u:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"import math\\nimport sys\\n\\ndef gcd(x, y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y)\\np, q = list(map(int,sys.stdin.readline().split()))\\nn = int(input())\\na = [0] * n;\\nb = list(map(int,sys.stdin.readline().split()))\\nl = 0\\nfor i in b: \\n    a[l] = i\\n    l = l + 1\\nx, y = a[n-1], 1\\nfor i in range(n-2,-1,-1):\\n    x, y = y, x\\n    x = x + y*a[i]\\ng1 = gcd(p,q)\\ng2 = gcd(x,y)\\np = p // g1\\nq = q // g1\\nx = x // g2\\ny = y // g2\\nif(x == p and y == q):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"def gcd(a, b):\\n    if b==0:\\n        return a\\n    return gcd(b,a%b)\\n\\ndef red(frac):\\n    gcdfrac = gcd(frac[0],frac[1])\\n    return (frac[0] // gcdfrac, frac[1] // gcdfrac)\\n\\ndef add(i, frac):\\n    a,b = frac\\n    a += b * i\\n    return red((a,b))\\n\\nimport sys\\nargs = list(map(int, sys.stdin.read().split()))\\np, q = args[0], args[1]\\nn = args[2]\\ns = (args[2+n],1)\\nfor i in range(0,n-1):\\n    s = add(args[1+n-i] , (s[1],s[0]))\\nif(s == red((p,q))):\\n    print('YES')\\nelse:\\n    print('NO')\", \"#!/usr/bin/env python\\n#coding:utf-8\\n\\nfrom fractions import Fraction\\n\\ndef frac(lis,i):\\n    if i == len(lis)-1 :\\n        return lis[i]\\n    else:\\n        return lis[i]+1/frac(lis,i+1)\\n\\ndef main():\\n    linesp = input().split(\\\" \\\")\\n    p,q = int(linesp[0]),int(linesp[1])\\n    one = Fraction(p,q)\\n\\n    n = int(input())\\n\\n    A = []\\n    for s in input().split(\\\" \\\"):\\n        A.append(Fraction(int(s)))\\n\\n    two = frac(A,0)\\n    if one == two:\\n        print(\\\"YES\\\")\\n    else:\\n        print(\\\"NO\\\")\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"\\ndef gcd(a, b):\\n\\tif (b == 0):\\n\\t\\treturn a\\n\\telse:\\n\\t\\treturn gcd(b, a % b)\\n\\np, q = map(int, input().split())\\nn = int(input())\\nA = list(map(int, input().split()))\\ng = gcd(p, q)\\np = p // g\\nq = q // g\\nk = A[n - 1]\\nl = 1\\nfor i in range(n - 2, -1, -1):\\n\\tk, l = l, k\\n\\tk += A[i] * l\\n\\tg = gcd(k, l)\\n\\tk = k // g\\n\\tl = l // g\\nif (k == p and q == l):\\n\\tprint (\\\"YES\\\")\\nelse:\\n\\tprint (\\\"NO\\\")\", \"P, Q = [int(x) for x in input().split()]\\n\\nN = int(input())\\nA = [int(x) for x in input().split()]\\n\\nU, V = 1, 0\\nfor x in A[::-1]:\\n    U, V = V, U\\n    U, V = V * x + U, V\\n\\nif U * Q == P * V:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"from decimal import *\\ngetcontext().prec = 75\\np = input().split()\\n\\nn = int(input())\\n\\nc = input().split()\\n\\n\\n\\n\\n\\na='0'\\nfor i in range(n-1,0,-1):\\n    a=str(Decimal(a)+Decimal(c[i]))\\n    a=str(Decimal('1')/Decimal(str(a)))\\n\\na=str(Decimal(a)+Decimal(c[0]))\\nb=str(Decimal(p[0])/Decimal(p[1]))\\n\\n\\nif(a==b):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input().split(' ')\\n\\np = int(s[0])\\nq = int(s[1])\\n\\ns = input()\\nn = int(s)\\n\\ns = input().split(' ')\\n\\nok = True\\n\\nfor i in range(n):\\n    x = int(s[i])\\n    p = p-q*x\\n    if ok==False:\\n        continue\\n    if p==0 and i!=n-1 :\\n        ok = False\\n    elif p<0:\\n        ok = False\\n    t = p\\n    p = q\\n    q = t\\n\\nif ok and (p==0 or q==0):\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p, q = [int(x) for x in input().split()]\\nn = int(input())\\na = [int(x) for x in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\nif x * q == y * p:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"p,q=[int(x) for x in input().split()]\\nn=int(input())\\na=[int(x) for x in input().split()]\\n\\nx,y,i=1,0,n\\nwhile n>0:\\n    x,y=y,x\\n    n-=1\\n    x+=y*a[n]\\n\\nif x*q==y*p:\\n    print(\\\"YES\\\")\\nelse :\\n    print(\\\"NO\\\")\\n\", \"\\ndef gcd(x,y):\\n    if(y == 0):\\n        return x\\n    else:\\n        return gcd(y,x%y) \\n\\np, q = [int(i) for i in input().split()]\\nn = int(input())\\na = [int(i) for i in input().split()]\\nx, y = 1, 0\\nfor i in a[::-1]:\\n    x, y = y+i*x, x\\na, b = gcd(p,q), gcd(x,y)\\np = p // a;\\nq = q // a\\nx = x // b\\ny = y // b\\nif x == p and y == q:\\n    print(\\\"YES\\\")\\nelse:\\n    print(\\\"NO\\\")\\n\", \"s = input()\\na = s.split()\\np = int(a[0])\\nq = int(a[1])\\nn = input()\\ns = input()\\nse = s.split()\\nfor c in se:\\n    e = int(c)\\n    t1 = p-e*q\\n    t2 = q\\n    p = t2\\n    q = t1\\nif q == 0:\\n    print('YES')\\nelse :\\n    print('NO')\\n\", \"def gcd(a,b):\\n    if(b==0):\\n        return a\\n    return gcd(b,a%b)\\np,q=list(map(int,input().split()))\\nN=int(input())\\nA=list(map(int,input().split()))\\nznam=1\\nchisl=A[N-1]\\n\\nfor i in range (N-1,0,-1):\\n    chisl,znam=znam,chisl\\n    #print(chisl,znam)\\n    chisl += znam*A[i-1]\\n    #print(chisl,znam)\\nif(p*znam==q*chisl):\\n    print('YES')\\nelse:\\n    print('NO')\\n\", \"def gcd (x, y):\\n    while (x > 0) and (y > 0):\\n        if (x > y):\\n            x %= y\\n        else:\\n            y %= x\\n    return x + y\\np, q = map(int, input().split())\\nn = int (input ())\\na = list (map (int, input ().split ()))\\np1 = 1\\nq1 = a[n - 1]\\nfor i in range(n - 2, -1, -1):\\n    p1 += a[i] * q1\\n    z = p1\\n    p1 = q1\\n    q1 = z\\nz = p1\\np1 = q1\\nq1 = z\\ng = gcd (p, q)\\nif (g != 0):\\n    p /= g\\n    q /= g\\ng = gcd (p1, q1)\\nif (g != 0):\\n    p1 /= g\\n    q1 /= g\\nif (p == p1) and (q == q1):\\n    print (\\\"YES\\\")\\nelse:\\n    print (\\\"NO\\\")\", \"from fractions import Fraction\\ndef __starting_point():\\n    p,q=list(map(int, input().split(' ')))\\n    n=int(input())\\n    a=list(map(int,input().split(' ')))\\n    def fract(x):\\n        if x==n-1:\\n            return Fraction(1,a[x])\\n        elif x>=n:\\n            return 0\\n        else:\\n            return Fraction(1,a[x]+fract(x+1))\\n    print('YES' if Fraction(p,q)==a[0]+fract(1) else 'NO')\\n\\n\\n\\n\\n\\n__starting_point()\", \"p, q = list(map(int, input().split()))\\nn = int(input())\\nA = list(map(int, input().split()))\\n\\nfor i in range(n):\\n    p, q = q, p - A[i] * q\\n\\nif p != 0 and q == 0:\\n    print('YES')\\nelse:\\n    print('NO')\\n\"]",
        "difficulty": "interview",
        "input": "1337 42\n1\n31\n",
        "output": "NO\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/305/B"
    },
    {
        "id": 383,
        "task_id": 1686,
        "test_case_id": 1,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n",
        "output": "255.255.254.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 384,
        "task_id": 1686,
        "test_case_id": 2,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n",
        "output": "255.255.0.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 385,
        "task_id": 1686,
        "test_case_id": 3,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "2 1\n255.0.0.1\n0.0.0.2\n",
        "output": "-1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 386,
        "task_id": 1686,
        "test_case_id": 4,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "10 2\n57.11.146.42\n200.130.164.235\n52.119.155.71\n113.10.216.20\n28.23.6.128\n190.112.90.85\n7.37.210.55\n20.190.120.226\n170.124.158.110\n122.157.34.141\n",
        "output": "128.0.0.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 387,
        "task_id": 1686,
        "test_case_id": 5,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "11 4\n30.181.69.132\n170.239.176.11\n229.116.128.161\n9.82.24.38\n53.73.223.74\n168.10.125.208\n4.122.30.206\n139.239.173.235\n101.113.26.160\n216.250.148.119\n142.182.207.78\n",
        "output": "192.0.0.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 388,
        "task_id": 1686,
        "test_case_id": 6,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "12 5\n211.200.83.75\n9.64.213.241\n143.23.121.155\n212.121.142.193\n24.184.86.27\n176.131.70.228\n64.47.67.24\n255.241.229.181\n246.34.183.253\n65.121.116.178\n76.84.75.89\n22.239.28.119\n",
        "output": "-1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 389,
        "task_id": 1686,
        "test_case_id": 7,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "13 6\n137.219.97.18\n104.145.250.214\n57.185.114.149\n158.161.4.92\n252.39.206.236\n184.252.14.247\n124.228.103.97\n114.244.29.127\n135.210.84.91\n169.248.84.237\n9.241.200.99\n90.154.249.89\n15.98.23.33\n",
        "output": "-1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 390,
        "task_id": 1686,
        "test_case_id": 8,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "14 7\n62.238.111.217\n200.225.31.188\n228.91.108.143\n105.200.123.248\n223.149.69.190\n192.117.215.11\n184.153.140.170\n230.246.85.73\n24.131.241.184\n18.119.52.40\n199.143.68.109\n158.69.214.60\n174.25.117.109\n1.204.187.57\n",
        "output": "224.0.0.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 391,
        "task_id": 1686,
        "test_case_id": 9,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "15 8\n244.1.125.160\n39.50.68.162\n142.253.101.137\n52.239.241.147\n194.4.189.143\n200.238.160.30\n245.78.177.243\n89.249.140.19\n169.51.142.22\n123.246.20.99\n133.44.192.119\n226.240.179.30\n76.209.211.184\n98.15.6.117\n227.219.117.153\n",
        "output": "-1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 392,
        "task_id": 1686,
        "test_case_id": 10,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "5 5\n223.122.75.125\n79.30.187.249\n231.244.158.56\n166.205.237.209\n82.85.12.212\n",
        "output": "240.0.0.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 393,
        "task_id": 1686,
        "test_case_id": 11,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "2 1\n0.0.0.0\n0.0.0.1\n",
        "output": "128.0.0.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 394,
        "task_id": 1686,
        "test_case_id": 12,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "2 2\n0.0.0.0\n1.0.0.1\n",
        "output": "255.0.0.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 395,
        "task_id": 1686,
        "test_case_id": 13,
        "question": "The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively.\n\nPolycarpus has found a job, he is a system administrator. One day he came across n IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address.\n\nHaving worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess.\n\nThe subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as \"11...11000..000\". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000.\n\nTo get the network address of the IP address, you need to perform the operation of the bitwise \"and\" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise \"and\" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one.\n\nNow Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly k distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly k distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.\n\n\n-----Input-----\n\nThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 10^5) — the number of IP addresses and networks. The next n lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.\n\n\n-----Output-----\n\nIn a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.\n\n\n-----Examples-----\nInput\n5 3\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.254.0\nInput\n5 2\n0.0.0.1\n0.1.1.2\n0.0.2.1\n0.1.1.0\n0.0.2.3\n\nOutput\n255.255.0.0\nInput\n2 1\n255.0.0.1\n0.0.0.2\n\nOutput\n-1",
        "solutions": "[\"import math\\nimport re\\nfrom fractions import Fraction\\nfrom collections import Counter\\n\\nclass Task:\\n    ips = []\\n    k = 0\\n    answer = ''\\n    \\n    def __init__(self):\\n        n, self.k = [int(x) for x in input().split()]\\n        self.ips = ['' for _ in range(n)]\\n        for i in range(len(self.ips)):\\n            self.ips[i] = input()\\n\\n    def solve(self):\\n        ips, k = self.ips, self.k\\n        ipAsNumbers = []\\n        for currentIp in ips:\\n            number = 0\\n            parts = currentIp.split('.')\\n            for i in range(0, len(parts)):\\n                number += int(parts[i]) * 2**(32 - (i + 1) * 8)\\n            ipAsNumbers += [number]\\n\\n        mask = 0\\n        for i in range(31, -1, -1):\\n            mask += 2**i\\n            netAddresses = set()\\n            for ip in ipAsNumbers:\\n                netAddresses.add(mask & ip)\\n            if len(netAddresses) == k:\\n                mask = bin(mask)[2:]\\n                self.answer = '.'.join([str(int(mask[i : i + 8], 2)) \\\\\\n                    for i in range(0, len(mask), 8)])\\n                return\\n        self.answer = '-1'\\n\\n\\n    def printAnswer(self):\\n        print(self.answer)\\n        #for line in self.answer:\\n        #    print(line)\\n\\ntask = Task()\\ntask.solve()\\ntask.printAnswer()\\n\", \"def f(t):\\n    a, b, c, d = map(int, t.split('.'))\\n    return d + (c << 8) + (b << 16) + (a << 24)\\n\\ndef g(x):\\n    p = [0] * 4\\n    for i in range(4):\\n        p[3 - i] = str(x % 256)\\n        x //= 256\\n    return '.'.join(p)\\n\\nn, k = map(int, input().split())\\nt = [f(input()) for i in range(n)]\\np = [0] * n\\nx = 1 << 31\\nfor i in range(32):\\n    for j, y in enumerate(t):\\n        if y & x: p[j] += x\\n    if len(set(p)) >= k: break\\n    x >>= 1\\nprint(-1 if len(set(p)) != k else g((1 << 32) - x))\", \"def parse(ip_address):\\n    a, b, c, d = [int(x) for x in ip_address.split('.')]\\n    return (a << 24) | (b << 16) | (c << 8) | d\\n\\nn, k = [int(x) for x in input().split()]\\nips = [parse(input()) for i in range(n)]\\nall_ones = (1 << 32) - 1\\neight_ones = (1 << 8) - 1\\nfor n_zeros in range(31, 0, -1):\\n    mask = all_ones << n_zeros\\n    if len(set(mask & ip for ip in ips)) == k:\\n        address = [(mask >> 24) & eight_ones, (mask >> 16) & eight_ones, (mask >> 8) & eight_ones, mask & eight_ones]\\n        print('.'.join(str(x) for x in address))\\n        return\\n\\nprint(-1)\"]",
        "difficulty": "interview",
        "input": "1 1\n0.0.0.0\n",
        "output": "128.0.0.0",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/291/C"
    },
    {
        "id": 396,
        "task_id": 1983,
        "test_case_id": 1,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "2\n3\n3 2 1\n6\n3 1 4 1 5 9\n",
        "output": "3\n5\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 397,
        "task_id": 1983,
        "test_case_id": 2,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "4\n7\n6 6 8 8 6 6 6\n1\n2\n5\n4 5 9 8 7\n7\n1 2 7 1 6 10 2\n",
        "output": "2\n1\n5\n5\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 398,
        "task_id": 1983,
        "test_case_id": 3,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "2\n5\n5 5 5 5 5\n3\n1 2 5\n",
        "output": "1\n3\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 399,
        "task_id": 1983,
        "test_case_id": 4,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "2\n5\n1 2 3 4 5\n4\n2 3 4 5\n",
        "output": "5\n4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 400,
        "task_id": 1983,
        "test_case_id": 5,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "1\n3\n1 1 274005660\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 401,
        "task_id": 1983,
        "test_case_id": 6,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "2\n2\n1 1\n1\n1\n",
        "output": "1\n1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 402,
        "task_id": 1983,
        "test_case_id": 7,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "2\n4\n1 3 3 3\n3\n1 2 3\n",
        "output": "2\n3\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 403,
        "task_id": 1983,
        "test_case_id": 8,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "2\n3\n1 1 1\n2\n1 1\n",
        "output": "1\n1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 404,
        "task_id": 1983,
        "test_case_id": 9,
        "question": "Ehab has an array $a$ of length $n$. He has just enough free time to make a new array consisting of $n$ copies of the old array, written back-to-back. What will be the length of the new array's longest increasing subsequence?\n\nA sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements. The longest increasing subsequence of an array is the longest subsequence such that its elements are ordered in strictly increasing order.\n\n\n-----Input-----\n\nThe first line contains an integer $t$ — the number of test cases you need to solve. The description of the test cases follows.\n\nThe first line of each test case contains an integer $n$ ($1 \\le n \\le 10^5$) — the number of elements in the array $a$.\n\nThe second line contains $n$ space-separated integers $a_1$, $a_2$, $\\ldots$, $a_{n}$ ($1 \\le a_i \\le 10^9$) — the elements of the array $a$.\n\nThe sum of $n$ across the test cases doesn't exceed $10^5$.\n\n\n-----Output-----\n\nFor each testcase, output the length of the longest increasing subsequence of $a$ if you concatenate it to itself $n$ times.\n\n\n-----Example-----\nInput\n2\n3\n3 2 1\n6\n3 1 4 1 5 9\n\nOutput\n3\n5\n\n\n\n-----Note-----\n\nIn the first sample, the new array is $[3,2,\\textbf{1},3,\\textbf{2},1,\\textbf{3},2,1]$. The longest increasing subsequence is marked in bold.\n\nIn the second sample, the longest increasing subsequence will be $[1,3,4,5,9]$.",
        "solutions": "[\"#list(map(int,input().split()))\\nt=int(input())\\nfor _ in range(t):\\n    n=int(input())\\n    it=list(map(int,input().split()))\\n    print(len(set(it)))\\n\", \"for _ in range(int(input())):\\n\\tn = int(input())\\n\\ta = [int(i) for i in input().split()]\\n\\tprint(len(set(a)))\", \"import sys\\ninput = sys.stdin.readline\\n\\nt = int(input())\\nfor _ in range(t):\\n    input()\\n    print(len(set(map(int, input().split()))))\\n\", \"a = int(input())\\nfor i in range(a):\\n    o = int(input())\\n    u = list(map(int, input().split()))\\n    print(len(set(u)))\", \"t = int(input())\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    set_ = set(a)\\n    print(len(set_))\", \"\\n\\nfor _ in range(int(input())):\\n\\tn=int(input())\\n\\ta=list(map(int,input().split()))\\n\\tprint(len(set(a)))\", \"for nt in range(int(input())):\\n\\tn=int(input())\\n\\tl=list(map(int,input().split()))\\n\\tl=set(l)\\n\\tl=list(l)\\n\\tprint (len(l))\", \"#!/usr/bin/env python\\n#-*- coding:utf-8 -*-\\n\\n# Code by H~$~C\\n\\nfrom sys import stdin\\ninput = stdin.readline\\nimport math\\n\\nfor i in range(int(input())):\\n  n = int(input())\\n  arr = sorted(list(map(int, input().split())))\\n  ans = n\\n  for j in range(n - 1):\\n    if (arr[j + 1] == arr[j]):\\n      ans -= 1\\n  print(ans)\", \"t = int(input())\\n\\nfor _ in range(t):\\n    n = int(input())\\n    a = list(map(int, input().strip().split()))\\n\\n    print(len(set(a)))\", \"t = int(input())\\nwhile(t):\\n    t -= 1\\n    n = int(input())\\n    a = set(map(int, input().split()))\\n    print(len(a))\", \"import sys\\nreader = (s.rstrip() for s in sys.stdin)\\ninput = reader.__next__\\n\\ndef solve():\\n    n = int(input())\\n    a = list(map(int, input().split()))\\n    ans = len(set(a))\\n    print(ans)\\n\\nt = int(input())\\nfor i in range(t):\\n    solve()\\n\", \"t = int(input())\\nfor _ in range(t):\\n\\tn = int(input())\\n\\ta = set(map(int, input().split()))\\n\\tprint(len(a))\", \"from bisect import bisect_left as bl, bisect_right as br, insort\\nimport sys\\nimport heapq\\nfrom math import *\\nfrom collections import defaultdict as dd, deque\\ndef data(): return sys.stdin.readline().strip()\\ndef mdata(): return map(int, data().split())\\n#sys.setrecursionlimit(100000)\\n\\nfor i in range(int(data())):\\n    n=int(data())\\n    A=set(mdata())\\n    print(len(A))\", \"from sys import stdin,stdout                           #\\nimport math                                            #\\nimport heapq                                           #\\n                                                       #\\nt = 1                                                  #\\ndef aint():                                            #\\n\\treturn int(input().strip())                        #\\ndef lint():                                            #\\n\\treturn list(map(int,input().split()))              #\\ndef fint():                                            #\\n\\treturn list(map(int,stdin.readline().split()))     #\\n                                                       #\\t\\n########################################################\\n\\ndef main():\\n\\tn=aint()\\n\\tl=lint()\\n\\tprint(len(set(l)))\\n\\t#solve\\n\\nt=int(input())\\n\\n########################################################\\nfor i in range(t):                                     #\\n\\tmain()                                             #\", \"import sys\\ninput = sys.stdin.readline\\n\\nt=int(input())\\nfor tests in range(t):\\n    n=int(input())\\n    A=list(map(int,input().split()))\\n    print(len(set(A)))\\n    \\n\"]",
        "difficulty": "interview",
        "input": "1\n5\n1 3 4 5 2\n",
        "output": "5\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/1325/B"
    },
    {
        "id": 405,
        "task_id": 2681,
        "test_case_id": 1,
        "question": "Write a program to obtain 2 numbers $($ $A$ $and$ $B$ $)$ and an arithmetic operator $(C)$ and then design a $calculator$ depending upon the operator entered by the user.\nSo for example if C=\"+\", you have to sum the two numbers.\nIf C=\"-\", you have to subtract the two numbers.\nIf C=\" * \", you have to print the product.\nIf C=\" / \", you have to divide the two numbers.\n\n-----Input:-----\n- First line will contain the first number $A$.\n- Second line will contain the second number $B$.\n- Third line will contain the operator $C$, that is to be performed on A and B.\n\n-----Output:-----\nOutput a single line containing the answer, obtained by, performing the operator on the numbers. Your output will be considered to be correct if the difference between your output and the actual answer is not more than $10^{-6}$.\n\n-----Constraints-----\n- $-1000 \\leq A \\leq 1000$\n- $-1000 \\leq B \\leq 1000$ $and$ $B \\neq 0$\n- $C$ $can$ $only$ $be$ $one$ $of$ $these$ $4$ $operators$ {\" + \", \" - \", \" * \", \" / \"}\n\n-----Sample Input:-----\n8\n2\n/\n\n-----Sample Output:-----\n4.0\n\n-----Sample Input:-----\n5\n3\n+\n\n-----Sample Output:-----\n8",
        "solutions": "[\"one = int(input())\\ntwo = int(input())\\nelement = input()\\nif element == '/':\\n print(one / two)\\nelif element == '*':\\n print(one * two)\\nelif element == '-':\\n print(one - two)\\nelif element == '+':\\n print(one + two)\", \"a=int(input())\\nb=int(input())\\nch=input()\\nif(ch==\\\"/\\\"):\\n print(a/b)\\nelif(ch==\\\"*\\\"):\\n print(a*b)\\nelif(ch==\\\"-\\\"):\\n print(a-b)\\nelse:\\n print(a+b)\\n\", \"a=int(input())\\nb=int(input())\\nch=input()\\nif(ch==\\\"/\\\"):\\n print(a/b)\\nelif(ch==\\\"*\\\"):\\n print(a*b)\\nelif(ch==\\\"-\\\"):\\n print(a-b)\\nelse:\\n print(a+b)\\n\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c=='+':\\n print(a+b)\\nelif c=='*':\\n print(a*b)\\nelif c=='-':\\n print(a-b)\\nelse:\\n print(a/b)\", \"# cook your dish here\\nx=int(input())\\ny=int(input())\\no=input()\\nif o=='+':\\n print(x+y)\\nelif o=='-':\\n print(x-y)\\nelif o=='/':\\n print(x/y)\\nelif o=='*':\\n print(x*y)\", \"A=int(input())\\nB=int(input())\\nc=input()\\nif c=='+':\\n print(A+B)\\nelif c=='-':\\n print(A-B)\\nelif c=='*':\\n print(A*B)\\nelif c=='/':\\n print(A/B)\\n\\n\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nc=input()\\nif(c=='+'):\\n print(a+b)\\nelif(c=='-'):\\n print(a-b)\\nelif(c=='*'):\\n print(a*b)\\nelse:\\n print(a/b)\", \"# cook your dish here\\nn=int(input())\\nk=int(input())\\ns=input()\\nif s=='+':\\n print(n+k)\\nelif s=='-':\\n print(n-k)\\nelif s=='*':\\n print(n*k)\\nelif s=='/':\\n print(n/k)\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c=='+':\\n print(a+b)\\nelif c=='-':\\n print(a-b)\\nelif c=='*':\\n print(a*b)\\nelif c=='/':\\n print(a/b)\\n\", \"# cook your dish here\\ndef cal (a,b,s):\\n if s=='+':\\n  print(a+b)\\n elif s=='-':\\n  print(a-b)\\n elif s=='*':\\n  print(a*b)\\n else:\\n  print(a/b)\\na=int(input())\\nb=int(input())\\nc=input()\\ncal(a,b,c)\\n\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c==\\\"+\\\":\\n print(a+b)\\nelif c==\\\"-\\\":\\n print(a-b)\\nelif c==\\\"*\\\":\\n print(a*b)\\nelif c==\\\"/\\\":\\n print(a/b)\\n\", \"A=int(input())\\nB=int(input())\\nC=input()\\nif C==\\\"+\\\":\\n print(A+B)\\nelif C==\\\"-\\\":\\n print(A-B)\\nelif C==\\\"*\\\":\\n print(A*B)\\nelif C==\\\"/\\\":\\n print(A/B)\\n \\n\", \"# cook your dish here\\nx = int(input())\\ny = int(input())\\nz = str(input())\\nif z=='+':\\n print(x+y)\\nelif z=='-':\\n print(x-y)\\nelif z=='*':\\n print(x*y)\\nelif z=='/':\\n print(x/y)\", \"a = int(input())\\nb = int(input())\\nc = input()\\nif(c == '+'):\\n print(a+b)\\nelif c == '-':\\n print(a - b)\\nelif c == '*':\\n print(a * b)\\nelse:\\n print(a/b)\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c=='+':\\n print(a+b)\\nelif c=='-':\\n print(a-b)\\nelif c=='*':\\n print(a*b)\\nelif c=='/':\\n print(a/b) \\n\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nc=input()\\nif c==\\\"+\\\":\\n print(a+b)\\nelif c==\\\"-\\\":\\n print(a-b)\\nelif c==\\\"*\\\":\\n print(a*b)\\nelif c==\\\"/\\\":\\n print(a/b)\\n\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif(c=='+'):\\n print(a+b)\\nelif(c=='-'):\\n print(a-b)\\nelif(c=='/'):\\n print(a/b)\\nelif(c=='*'):\\n print(a*b)\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c=='+':\\n print(a+b)\\nelif c=='-':\\n print(a-b)\\nelif c=='*':\\n print(a*b)\\nelif c=='/':\\n print(a/b) \", \"a=int(input())\\nb=int(input())\\nc=str(input())\\nif(c==\\\"+\\\"):\\n print(a+b)\\nelif(c==\\\"-\\\"):\\n print(a-b)\\nelif(c==\\\"*\\\"):\\n print(a*b)\\nelse:\\n print(a/b)\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nc=input()\\n\\nif c=='+':\\n print(a+b)\\nelif c=='-':\\n print(a-b)\\nelif c=='*':\\n print(a*b)\\nelif c=='/':\\n print(a/b)\\n \\n\", \"# cook your dish here\\na = int(input())\\nb = int(input())\\np = input()\\nif p == '+':\\n print(a+b)\\nif p == '-':\\n print(a-b)\\nif p == '*':\\n print(a*b)\\nif p == '/':\\n print(a/b)\", \"n1=int(input())\\nn2=int(input())\\nc=input()\\nif(c==\\\"+\\\"):\\n print(n1+n2)\\nelif(c==\\\"-\\\"):\\n print(n1-n2)\\nelif(c==\\\"*\\\"):\\n print(n1*n2)\\nelse:\\n print(n1/n2)\\n\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nc=input()\\nif c==\\\"+\\\":\\n print(a+b)\\nelif c==\\\"-\\\":\\n print(a-b)\\nelif c==\\\"*\\\":\\n print(a*b)\\nelse:\\n d=a/b\\n print(\\\"%.6f\\\"%d)\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nop=input()\\n\\nif op=='+':\\n res=a+b\\n print(float(res))\\nif op=='-':\\n res=a-b\\n print(float(res))\\nif op=='*':\\n res=a*b \\n print(float(res))\\nif op=='/':\\n res=a/b \\n print(float(res))\\n\"]",
        "difficulty": "interview",
        "input": [
            "8",
            "2",
            "/"
        ],
        "output": [
            "4.0"
        ],
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://www.codechef.com/problems/URCALC"
    },
    {
        "id": 406,
        "task_id": 2681,
        "test_case_id": 2,
        "question": "Write a program to obtain 2 numbers $($ $A$ $and$ $B$ $)$ and an arithmetic operator $(C)$ and then design a $calculator$ depending upon the operator entered by the user.\nSo for example if C=\"+\", you have to sum the two numbers.\nIf C=\"-\", you have to subtract the two numbers.\nIf C=\" * \", you have to print the product.\nIf C=\" / \", you have to divide the two numbers.\n\n-----Input:-----\n- First line will contain the first number $A$.\n- Second line will contain the second number $B$.\n- Third line will contain the operator $C$, that is to be performed on A and B.\n\n-----Output:-----\nOutput a single line containing the answer, obtained by, performing the operator on the numbers. Your output will be considered to be correct if the difference between your output and the actual answer is not more than $10^{-6}$.\n\n-----Constraints-----\n- $-1000 \\leq A \\leq 1000$\n- $-1000 \\leq B \\leq 1000$ $and$ $B \\neq 0$\n- $C$ $can$ $only$ $be$ $one$ $of$ $these$ $4$ $operators$ {\" + \", \" - \", \" * \", \" / \"}\n\n-----Sample Input:-----\n8\n2\n/\n\n-----Sample Output:-----\n4.0\n\n-----Sample Input:-----\n5\n3\n+\n\n-----Sample Output:-----\n8",
        "solutions": "[\"one = int(input())\\ntwo = int(input())\\nelement = input()\\nif element == '/':\\n print(one / two)\\nelif element == '*':\\n print(one * two)\\nelif element == '-':\\n print(one - two)\\nelif element == '+':\\n print(one + two)\", \"a=int(input())\\nb=int(input())\\nch=input()\\nif(ch==\\\"/\\\"):\\n print(a/b)\\nelif(ch==\\\"*\\\"):\\n print(a*b)\\nelif(ch==\\\"-\\\"):\\n print(a-b)\\nelse:\\n print(a+b)\\n\", \"a=int(input())\\nb=int(input())\\nch=input()\\nif(ch==\\\"/\\\"):\\n print(a/b)\\nelif(ch==\\\"*\\\"):\\n print(a*b)\\nelif(ch==\\\"-\\\"):\\n print(a-b)\\nelse:\\n print(a+b)\\n\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c=='+':\\n print(a+b)\\nelif c=='*':\\n print(a*b)\\nelif c=='-':\\n print(a-b)\\nelse:\\n print(a/b)\", \"# cook your dish here\\nx=int(input())\\ny=int(input())\\no=input()\\nif o=='+':\\n print(x+y)\\nelif o=='-':\\n print(x-y)\\nelif o=='/':\\n print(x/y)\\nelif o=='*':\\n print(x*y)\", \"A=int(input())\\nB=int(input())\\nc=input()\\nif c=='+':\\n print(A+B)\\nelif c=='-':\\n print(A-B)\\nelif c=='*':\\n print(A*B)\\nelif c=='/':\\n print(A/B)\\n\\n\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nc=input()\\nif(c=='+'):\\n print(a+b)\\nelif(c=='-'):\\n print(a-b)\\nelif(c=='*'):\\n print(a*b)\\nelse:\\n print(a/b)\", \"# cook your dish here\\nn=int(input())\\nk=int(input())\\ns=input()\\nif s=='+':\\n print(n+k)\\nelif s=='-':\\n print(n-k)\\nelif s=='*':\\n print(n*k)\\nelif s=='/':\\n print(n/k)\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c=='+':\\n print(a+b)\\nelif c=='-':\\n print(a-b)\\nelif c=='*':\\n print(a*b)\\nelif c=='/':\\n print(a/b)\\n\", \"# cook your dish here\\ndef cal (a,b,s):\\n if s=='+':\\n  print(a+b)\\n elif s=='-':\\n  print(a-b)\\n elif s=='*':\\n  print(a*b)\\n else:\\n  print(a/b)\\na=int(input())\\nb=int(input())\\nc=input()\\ncal(a,b,c)\\n\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c==\\\"+\\\":\\n print(a+b)\\nelif c==\\\"-\\\":\\n print(a-b)\\nelif c==\\\"*\\\":\\n print(a*b)\\nelif c==\\\"/\\\":\\n print(a/b)\\n\", \"A=int(input())\\nB=int(input())\\nC=input()\\nif C==\\\"+\\\":\\n print(A+B)\\nelif C==\\\"-\\\":\\n print(A-B)\\nelif C==\\\"*\\\":\\n print(A*B)\\nelif C==\\\"/\\\":\\n print(A/B)\\n \\n\", \"# cook your dish here\\nx = int(input())\\ny = int(input())\\nz = str(input())\\nif z=='+':\\n print(x+y)\\nelif z=='-':\\n print(x-y)\\nelif z=='*':\\n print(x*y)\\nelif z=='/':\\n print(x/y)\", \"a = int(input())\\nb = int(input())\\nc = input()\\nif(c == '+'):\\n print(a+b)\\nelif c == '-':\\n print(a - b)\\nelif c == '*':\\n print(a * b)\\nelse:\\n print(a/b)\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c=='+':\\n print(a+b)\\nelif c=='-':\\n print(a-b)\\nelif c=='*':\\n print(a*b)\\nelif c=='/':\\n print(a/b) \\n\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nc=input()\\nif c==\\\"+\\\":\\n print(a+b)\\nelif c==\\\"-\\\":\\n print(a-b)\\nelif c==\\\"*\\\":\\n print(a*b)\\nelif c==\\\"/\\\":\\n print(a/b)\\n\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif(c=='+'):\\n print(a+b)\\nelif(c=='-'):\\n print(a-b)\\nelif(c=='/'):\\n print(a/b)\\nelif(c=='*'):\\n print(a*b)\", \"a=int(input())\\nb=int(input())\\nc=input()\\nif c=='+':\\n print(a+b)\\nelif c=='-':\\n print(a-b)\\nelif c=='*':\\n print(a*b)\\nelif c=='/':\\n print(a/b) \", \"a=int(input())\\nb=int(input())\\nc=str(input())\\nif(c==\\\"+\\\"):\\n print(a+b)\\nelif(c==\\\"-\\\"):\\n print(a-b)\\nelif(c==\\\"*\\\"):\\n print(a*b)\\nelse:\\n print(a/b)\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nc=input()\\n\\nif c=='+':\\n print(a+b)\\nelif c=='-':\\n print(a-b)\\nelif c=='*':\\n print(a*b)\\nelif c=='/':\\n print(a/b)\\n \\n\", \"# cook your dish here\\na = int(input())\\nb = int(input())\\np = input()\\nif p == '+':\\n print(a+b)\\nif p == '-':\\n print(a-b)\\nif p == '*':\\n print(a*b)\\nif p == '/':\\n print(a/b)\", \"n1=int(input())\\nn2=int(input())\\nc=input()\\nif(c==\\\"+\\\"):\\n print(n1+n2)\\nelif(c==\\\"-\\\"):\\n print(n1-n2)\\nelif(c==\\\"*\\\"):\\n print(n1*n2)\\nelse:\\n print(n1/n2)\\n\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nc=input()\\nif c==\\\"+\\\":\\n print(a+b)\\nelif c==\\\"-\\\":\\n print(a-b)\\nelif c==\\\"*\\\":\\n print(a*b)\\nelse:\\n d=a/b\\n print(\\\"%.6f\\\"%d)\", \"# cook your dish here\\na=int(input())\\nb=int(input())\\nop=input()\\n\\nif op=='+':\\n res=a+b\\n print(float(res))\\nif op=='-':\\n res=a-b\\n print(float(res))\\nif op=='*':\\n res=a*b \\n print(float(res))\\nif op=='/':\\n res=a/b \\n print(float(res))\\n\"]",
        "difficulty": "interview",
        "input": [
            "5",
            "3",
            "+"
        ],
        "output": [
            "8"
        ],
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://www.codechef.com/problems/URCALC"
    },
    {
        "id": 407,
        "task_id": 2803,
        "test_case_id": 1,
        "question": "You are playing a game in which a group of players take turns saying animal names. The animal name you say when it is your turn must start with the same letter as the previously said animal ends with and it must not have been said previously in this round of the game. If there is no valid name or you cannot come up with one you are eliminated. \n\nGiven the last animal name said before your turn and a list of all names not yet used, can you make it through this turn? If so, can you make sure to eliminate the next player?\n\n-----Input-----\nThe first line of input contains a single word, the animal that the previous player just said. The next line contains a single integer $n$ ($0 \\le n \\leq 10^5$), the number of valid unused animal names. Each of the following $n$ lines contains one valid unused animal name.\n\nAll animal names (including the one the previous player said) are unique and consist of at least $1$ and at most $20$ lower case letters ‘a’-‘z’.\n\n-----Output-----\nIf there is any animal name you can play that eliminates the next player, output the first such name from the input list, followed by an exclamation mark. Otherwise, if there is any animal name that you can play, output the first such name. Otherwise, output a question mark (in this case you will just have to make up a fake name in the hope that the others will trust you that this is a real animal).\n\n-----Examples-----\nSample Input 1:\npig\n2\ngoat\ntoad\nSample Output 1:\ngoat\n\nSample Input 2:\ndog\n2\nsnake\nemu\nSample Output 2:\n?",
        "solutions": "",
        "difficulty": "interview",
        "input": "pig\n2\ngoat\ntoad\n",
        "output": "goat\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/alphabetanimals"
    },
    {
        "id": 408,
        "task_id": 2803,
        "test_case_id": 2,
        "question": "You are playing a game in which a group of players take turns saying animal names. The animal name you say when it is your turn must start with the same letter as the previously said animal ends with and it must not have been said previously in this round of the game. If there is no valid name or you cannot come up with one you are eliminated. \n\nGiven the last animal name said before your turn and a list of all names not yet used, can you make it through this turn? If so, can you make sure to eliminate the next player?\n\n-----Input-----\nThe first line of input contains a single word, the animal that the previous player just said. The next line contains a single integer $n$ ($0 \\le n \\leq 10^5$), the number of valid unused animal names. Each of the following $n$ lines contains one valid unused animal name.\n\nAll animal names (including the one the previous player said) are unique and consist of at least $1$ and at most $20$ lower case letters ‘a’-‘z’.\n\n-----Output-----\nIf there is any animal name you can play that eliminates the next player, output the first such name from the input list, followed by an exclamation mark. Otherwise, if there is any animal name that you can play, output the first such name. Otherwise, output a question mark (in this case you will just have to make up a fake name in the hope that the others will trust you that this is a real animal).\n\n-----Examples-----\nSample Input 1:\npig\n2\ngoat\ntoad\nSample Output 1:\ngoat\n\nSample Input 2:\ndog\n2\nsnake\nemu\nSample Output 2:\n?",
        "solutions": "",
        "difficulty": "interview",
        "input": "dog\n2\nsnake\nemu\n",
        "output": "?\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/alphabetanimals"
    },
    {
        "id": 409,
        "task_id": 2803,
        "test_case_id": 3,
        "question": "You are playing a game in which a group of players take turns saying animal names. The animal name you say when it is your turn must start with the same letter as the previously said animal ends with and it must not have been said previously in this round of the game. If there is no valid name or you cannot come up with one you are eliminated. \n\nGiven the last animal name said before your turn and a list of all names not yet used, can you make it through this turn? If so, can you make sure to eliminate the next player?\n\n-----Input-----\nThe first line of input contains a single word, the animal that the previous player just said. The next line contains a single integer $n$ ($0 \\le n \\leq 10^5$), the number of valid unused animal names. Each of the following $n$ lines contains one valid unused animal name.\n\nAll animal names (including the one the previous player said) are unique and consist of at least $1$ and at most $20$ lower case letters ‘a’-‘z’.\n\n-----Output-----\nIf there is any animal name you can play that eliminates the next player, output the first such name from the input list, followed by an exclamation mark. Otherwise, if there is any animal name that you can play, output the first such name. Otherwise, output a question mark (in this case you will just have to make up a fake name in the hope that the others will trust you that this is a real animal).\n\n-----Examples-----\nSample Input 1:\npig\n2\ngoat\ntoad\nSample Output 1:\ngoat\n\nSample Input 2:\ndog\n2\nsnake\nemu\nSample Output 2:\n?",
        "solutions": "",
        "difficulty": "interview",
        "input": "hare\n3\nbee\ncat\neagle\n",
        "output": "eagle!\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/alphabetanimals"
    },
    {
        "id": 410,
        "task_id": 2897,
        "test_case_id": 1,
        "question": "The world is made up of $10$ kinds of people, those who understand binary and those who do not. These different kinds of people do not always get along so well. Bob might ask for a $10000$ ounce coffee (meaning binary) and Alice might make misinterpret his request as being in decimal and give him a $10011100010000$ ounce coffee (binary). After Sue explains that this much coffee costs $100$ dollars (decimal), Bob might assume he only has to pay $4$ dollars (interpreting the price as being in binary). In response to these differences that are difficult to resolve, these two groups have divided the world into two regions, the binary-friendly zones and the decimal-friendly zones. They have even published a map like the following to help people keep up with where the areas are (they have used ones and zeros so nobody would have trouble reading it).1111100000\n\n1111000000\n\n1110000011\n\n0111100111\n\n0011111111\n\nUsers of binary have to stay in the zones marked with a zero. Users of decimal have to stay in the zones marked with a one. You have to figure out if it is possible for either type of person to get between various locations of interest. People can move north, south, east or west, but cannot move diagonally.\n\n-----Input-----\nInput starts with a line containing two positive integers, $1 \\le r \\le 1000$ and $1 \\le c \\le 1000$. The next $r$ input lines give the contents of the map, each line containing exactly $c$ characters (which are all chosen from $0$ or $1$).\n\nThe next line has an integer $0 \\le n \\le 1000$. The following $n$ lines each contain one query, given as four integers: $r_1,c_1$ and $r_2,c_2$. These two pairs indicate two locations on the map, and their limits are $1 \\le r_1, r_2 \\le r$ and $1 \\le c_1, c_2 \\le c$.\n\n-----Output-----\nFor each query, output binary if a binary user can start from location $r_1, c_1$ and move to location $r_2, c_2$. Output decimal if a decimal user can move between the two locations. Otherwise, output neither.\n\n-----Examples-----\nSample Input:\n1 4\n1100\n2\n1 1 1 4\n1 1 1 1\nSample Output:\nneither\ndecimal",
        "solutions": "",
        "difficulty": "interview",
        "input": "1 4\n1100\n2\n1 1 1 4\n1 1 1 1\n",
        "output": "neither\ndecimal\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/10kindsofpeople"
    },
    {
        "id": 411,
        "task_id": 2897,
        "test_case_id": 2,
        "question": "The world is made up of $10$ kinds of people, those who understand binary and those who do not. These different kinds of people do not always get along so well. Bob might ask for a $10000$ ounce coffee (meaning binary) and Alice might make misinterpret his request as being in decimal and give him a $10011100010000$ ounce coffee (binary). After Sue explains that this much coffee costs $100$ dollars (decimal), Bob might assume he only has to pay $4$ dollars (interpreting the price as being in binary). In response to these differences that are difficult to resolve, these two groups have divided the world into two regions, the binary-friendly zones and the decimal-friendly zones. They have even published a map like the following to help people keep up with where the areas are (they have used ones and zeros so nobody would have trouble reading it).1111100000\n\n1111000000\n\n1110000011\n\n0111100111\n\n0011111111\n\nUsers of binary have to stay in the zones marked with a zero. Users of decimal have to stay in the zones marked with a one. You have to figure out if it is possible for either type of person to get between various locations of interest. People can move north, south, east or west, but cannot move diagonally.\n\n-----Input-----\nInput starts with a line containing two positive integers, $1 \\le r \\le 1000$ and $1 \\le c \\le 1000$. The next $r$ input lines give the contents of the map, each line containing exactly $c$ characters (which are all chosen from $0$ or $1$).\n\nThe next line has an integer $0 \\le n \\le 1000$. The following $n$ lines each contain one query, given as four integers: $r_1,c_1$ and $r_2,c_2$. These two pairs indicate two locations on the map, and their limits are $1 \\le r_1, r_2 \\le r$ and $1 \\le c_1, c_2 \\le c$.\n\n-----Output-----\nFor each query, output binary if a binary user can start from location $r_1, c_1$ and move to location $r_2, c_2$. Output decimal if a decimal user can move between the two locations. Otherwise, output neither.\n\n-----Examples-----\nSample Input:\n1 4\n1100\n2\n1 1 1 4\n1 1 1 1\nSample Output:\nneither\ndecimal",
        "solutions": "",
        "difficulty": "interview",
        "input": "10 20\n11111111111111111111\n11000000000000000101\n11111111111111110000\n11111111111111110000\n11000000000000000111\n00011111111111111111\n00111111111111111111\n10000000000000001111\n11111111111111111111\n11111111111111111111\n3\n2 3 8 16\n8 1 7 3\n1 1 10 20\n",
        "output": "binary\ndecimal\nneither\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/10kindsofpeople"
    },
    {
        "id": 412,
        "task_id": 2959,
        "test_case_id": 1,
        "question": "Dee Siduous is a botanist who specializes in trees. A lot of her research has to do with the formation of tree rings, and what they say about the growing conditions over the tree’s lifetime. She has a certain theory and wants to run some simulations to see if it holds up to the evidence gathered in the field.\n\nOne thing that needs to be done is to determine the expected number of rings given the outline of a tree. Dee has decided to model a cross section of a tree on a two dimenional grid, with the interior of the tree represented by a closed polygon of grid squares. Given this set of squares, she assigns rings from the outer parts of the tree to the inner as follows: calling the non-tree grid squares “ring $0$”, each ring $n$ is made up of all those grid squares that have at least one ring $(n-1)$ square as a neighbor (where neighboring squares are those that share an edge).\n\nAn example of this is shown in the figure below.\n\n Figure D.1 \n\nMost of Dee’s models have been drawn on graph paper, and she has come to you to write a program to do this automatically for her. This way she’ll use less paper and save some $\\ldots $ well, you know.\n\n-----Input-----\nThe input will start with a line containing two positive integers $n$ $m$ specifying the number of rows and columns in the tree grid, where $n, m \\leq 100$. After this will be $n$ rows containing $m$ characters each. These characters will be either ‘T’ indicating a tree grid square, or ‘.’.\n\n\n\n-----Output-----\nOutput a grid with the ring numbers. If the number of rings is less than 10, use two characters for each grid square; otherwise use three characters for each grid square. Right justify all ring numbers in the grid squares, and use ‘.’ to fill in the remaining characters.\n\nIf a row or column does not contain a ring number it should still be output, filled entirely with ‘.’s.\n\n-----Examples-----\nSample Input:\n6 6\n.TT...\nTTTT..\nTTTTT.\nTTTTT.\nTTTTTT\n..T...\nSample Output:\n...1.1......\n.1.2.2.1....\n.1.2.3.2.1..\n.1.2.3.2.1..\n.1.1.2.1.1.1\n.....1......",
        "solutions": "",
        "difficulty": "interview",
        "input": "6 6\n.TT...\nTTTT..\nTTTTT.\nTTTTT.\nTTTTTT\n..T...\n",
        "output": "...1.1......\n.1.2.2.1....\n.1.2.3.2.1..\n.1.2.3.2.1..\n.1.1.2.1.1.1\n.....1......\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/rings2"
    },
    {
        "id": 413,
        "task_id": 2959,
        "test_case_id": 2,
        "question": "Dee Siduous is a botanist who specializes in trees. A lot of her research has to do with the formation of tree rings, and what they say about the growing conditions over the tree’s lifetime. She has a certain theory and wants to run some simulations to see if it holds up to the evidence gathered in the field.\n\nOne thing that needs to be done is to determine the expected number of rings given the outline of a tree. Dee has decided to model a cross section of a tree on a two dimenional grid, with the interior of the tree represented by a closed polygon of grid squares. Given this set of squares, she assigns rings from the outer parts of the tree to the inner as follows: calling the non-tree grid squares “ring $0$”, each ring $n$ is made up of all those grid squares that have at least one ring $(n-1)$ square as a neighbor (where neighboring squares are those that share an edge).\n\nAn example of this is shown in the figure below.\n\n Figure D.1 \n\nMost of Dee’s models have been drawn on graph paper, and she has come to you to write a program to do this automatically for her. This way she’ll use less paper and save some $\\ldots $ well, you know.\n\n-----Input-----\nThe input will start with a line containing two positive integers $n$ $m$ specifying the number of rows and columns in the tree grid, where $n, m \\leq 100$. After this will be $n$ rows containing $m$ characters each. These characters will be either ‘T’ indicating a tree grid square, or ‘.’.\n\n\n\n-----Output-----\nOutput a grid with the ring numbers. If the number of rings is less than 10, use two characters for each grid square; otherwise use three characters for each grid square. Right justify all ring numbers in the grid squares, and use ‘.’ to fill in the remaining characters.\n\nIf a row or column does not contain a ring number it should still be output, filled entirely with ‘.’s.\n\n-----Examples-----\nSample Input:\n6 6\n.TT...\nTTTT..\nTTTTT.\nTTTTT.\nTTTTTT\n..T...\nSample Output:\n...1.1......\n.1.2.2.1....\n.1.2.3.2.1..\n.1.2.3.2.1..\n.1.1.2.1.1.1\n.....1......",
        "solutions": "",
        "difficulty": "interview",
        "input": "3 4\nTT..\nTT..\n....\n",
        "output": ".1.1....\n.1.1....\n........\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/rings2"
    },
    {
        "id": 414,
        "task_id": 3465,
        "test_case_id": 1,
        "question": "The people of Absurdistan discovered how to build roads only last year. After the discovery, each city decided to build its own road, connecting the city to some other city. Each newly built road can be used in both directions.\n\nYou bought a tourist guide which has a map of the country with the newly built roads. However, since you are very interested in history, you would like to know which city built which road.\n\nGiven the description of $n$ roads, can you find an assignment of roads to $n$ cities, such that each city built one road? If there are multiple assignments, you are happy with any one. At least one solution is guaranteed to exist.\n\n-----Input-----\nThe first line contains an integer $n$ $(2\\le n\\le 100000)$ – the number of cities and roads. Then follow $n$ lines with $2$ numbers each. A line containing “$a$ $b$” indicates that there is a road between cities $a$ and $b$, $1 \\le a, b\\le n, a \\not= b$. There can be multiple roads between the same pair of cities.\n\n-----Output-----\nPrint $n$ lines with two integers “$a$$b$” denoting that a road between $a$ and $b$ was built by city $a$. Each road from the input must appear exactly once in the output. If there are multiple solutions, you can print any one and you can print the roads in any order.\n\n-----Examples-----\nSample Input:\n4\n1 2\n2 3\n3 1\n4 1\nSample Output:\n4 1\n2 1\n3 2\n1 3",
        "solutions": "",
        "difficulty": "competition",
        "input": "4\n1 2\n2 3\n3 1\n4 1\n",
        "output": "4 1\n2 1\n3 2\n1 3\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/absurdistan3"
    },
    {
        "id": 415,
        "task_id": 3465,
        "test_case_id": 2,
        "question": "The people of Absurdistan discovered how to build roads only last year. After the discovery, each city decided to build its own road, connecting the city to some other city. Each newly built road can be used in both directions.\n\nYou bought a tourist guide which has a map of the country with the newly built roads. However, since you are very interested in history, you would like to know which city built which road.\n\nGiven the description of $n$ roads, can you find an assignment of roads to $n$ cities, such that each city built one road? If there are multiple assignments, you are happy with any one. At least one solution is guaranteed to exist.\n\n-----Input-----\nThe first line contains an integer $n$ $(2\\le n\\le 100000)$ – the number of cities and roads. Then follow $n$ lines with $2$ numbers each. A line containing “$a$ $b$” indicates that there is a road between cities $a$ and $b$, $1 \\le a, b\\le n, a \\not= b$. There can be multiple roads between the same pair of cities.\n\n-----Output-----\nPrint $n$ lines with two integers “$a$$b$” denoting that a road between $a$ and $b$ was built by city $a$. Each road from the input must appear exactly once in the output. If there are multiple solutions, you can print any one and you can print the roads in any order.\n\n-----Examples-----\nSample Input:\n4\n1 2\n2 3\n3 1\n4 1\nSample Output:\n4 1\n2 1\n3 2\n1 3",
        "solutions": "",
        "difficulty": "competition",
        "input": "2\n1 2\n1 2\n",
        "output": "2 1\n1 2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/absurdistan3"
    },
    {
        "id": 416,
        "task_id": 3598,
        "test_case_id": 1,
        "question": "Instead of worrying about the current hyperinflation you decide to go down to the local bar and have a drink.\n\nThe prices at the bar are displayed using magnetic signs with numbers printed on them, with each magnet showing one or more digits. For instance, the price of $1106$ megacredits is displayed like this:\n\n\nWhile the bartender is busy serving the next customer, you have just enough time to rearrange the price of your favourite beverage to make it as cheap as possible. But be quick about it!\n\nInvidual magnets can be moved around in any order and turned upside-down. The numbers are shown in a script that makes it difficult for the bartender to distinguish $0$, $1$, and $8$ from their upside-down counterpart. Moreover, $6$ and $9$ look the same when one is turned upside-down. The example price above could be made almost ten times cheaper by turning the first magnet:\n\n\nYou have to use all the magnets, otherwise the bartender will immediately suspect foul play.\n\n-----Input-----\nOn the first line, the number $n$ of magnets, with $1\\in \\{ 1,\\ldots , 1000\\} $. On each of the following $n$ lines, exactly one sequence $m_ i$ of digits describing the $i$th magnet. Each magnet $m_ i$ for $i\\in \\{ 1,\\ldots , n\\} $ consists of at least one and at most $10$ digits from $0$, $1$, $\\ldots $, $9$. The price currently displayed on the bar is the integer described by the juxtaposition $m_1\\cdots m_ n$ of the magnets in the order they are given, from left to right. Note that a magnet can be all $0$s, even though the current price at the bar, alas!, is certainly not.\n\n-----Output-----\nA single line containing the cheapest price formed by the magnets $m_1,\\ldots ,m_ n$, rearranged in any order, and each of them possibly turned upside-down.\n\n-----Examples-----\nSample Input:\n2\n110\n6\nSample Output:\n0116",
        "solutions": "",
        "difficulty": "competition",
        "input": "2\n110\n6\n",
        "output": "0116\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/cheaperdrink"
    },
    {
        "id": 417,
        "task_id": 3598,
        "test_case_id": 2,
        "question": "Instead of worrying about the current hyperinflation you decide to go down to the local bar and have a drink.\n\nThe prices at the bar are displayed using magnetic signs with numbers printed on them, with each magnet showing one or more digits. For instance, the price of $1106$ megacredits is displayed like this:\n\n\nWhile the bartender is busy serving the next customer, you have just enough time to rearrange the price of your favourite beverage to make it as cheap as possible. But be quick about it!\n\nInvidual magnets can be moved around in any order and turned upside-down. The numbers are shown in a script that makes it difficult for the bartender to distinguish $0$, $1$, and $8$ from their upside-down counterpart. Moreover, $6$ and $9$ look the same when one is turned upside-down. The example price above could be made almost ten times cheaper by turning the first magnet:\n\n\nYou have to use all the magnets, otherwise the bartender will immediately suspect foul play.\n\n-----Input-----\nOn the first line, the number $n$ of magnets, with $1\\in \\{ 1,\\ldots , 1000\\} $. On each of the following $n$ lines, exactly one sequence $m_ i$ of digits describing the $i$th magnet. Each magnet $m_ i$ for $i\\in \\{ 1,\\ldots , n\\} $ consists of at least one and at most $10$ digits from $0$, $1$, $\\ldots $, $9$. The price currently displayed on the bar is the integer described by the juxtaposition $m_1\\cdots m_ n$ of the magnets in the order they are given, from left to right. Note that a magnet can be all $0$s, even though the current price at the bar, alas!, is certainly not.\n\n-----Output-----\nA single line containing the cheapest price formed by the magnets $m_1,\\ldots ,m_ n$, rearranged in any order, and each of them possibly turned upside-down.\n\n-----Examples-----\nSample Input:\n2\n110\n6\nSample Output:\n0116",
        "solutions": "",
        "difficulty": "competition",
        "input": "2\n7\n72\n",
        "output": "727\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/cheaperdrink"
    },
    {
        "id": 418,
        "task_id": 3932,
        "test_case_id": 1,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "4\n1 1 1 4\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 419,
        "task_id": 3932,
        "test_case_id": 2,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "5\n1 1 5 2 1\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 420,
        "task_id": 3932,
        "test_case_id": 3,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "13\n1 1 1 1 1 1 1 1 1 4 4 4 13\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 421,
        "task_id": 3932,
        "test_case_id": 4,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "4\n1 1 1 3\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 422,
        "task_id": 3932,
        "test_case_id": 5,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "24\n1 1 1 1 1 1 1 1 1 1 1 1 24 1 1 1 1 1 1 1 1 1 1 1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 423,
        "task_id": 3932,
        "test_case_id": 6,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "24\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 424,
        "task_id": 3932,
        "test_case_id": 7,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "10\n1 1 1 1 7 1 1 1 4 10\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 425,
        "task_id": 3932,
        "test_case_id": 8,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "24\n1 1 3 1 1 10 2 9 13 1 8 1 4 1 3 24 1 1 1 1 4 1 3 1\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 426,
        "task_id": 3932,
        "test_case_id": 9,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "24\n2 3 20 1 4 9 1 3 1 2 1 3 1 2 1 1 1 2 1 2 4 24 2 1\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 427,
        "task_id": 3932,
        "test_case_id": 10,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "24\n8 5 3 1 1 5 10 1 1 1 1 5 1 2 7 3 4 1 1 24 1 1 2 8\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 428,
        "task_id": 3932,
        "test_case_id": 11,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "24\n1 1 1 3 4 1 24 1 1 3 1 1 1 5 14 2 17 1 2 2 5 1 1 6\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 429,
        "task_id": 3932,
        "test_case_id": 12,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "1\n1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 430,
        "task_id": 3932,
        "test_case_id": 13,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "17\n6 1 1 1 3 1 1 17 6 1 4 1 1 1 3 1 1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 431,
        "task_id": 3932,
        "test_case_id": 14,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "23\n1 1 1 1 3 7 3 1 1 1 3 7 1 3 1 15 1 3 7 3 23 1 1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 432,
        "task_id": 3932,
        "test_case_id": 15,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "24\n1 24 1 1 1 3 8 1 1 3 1 1 6 1 1 1 1 3 5 1 3 7 13 1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 433,
        "task_id": 3932,
        "test_case_id": 16,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "16\n1 1 1 1 1 1 1 1 1 1 1 1 16 1 1 1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 434,
        "task_id": 3932,
        "test_case_id": 17,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "21\n1 1 1 6 1 1 13 21 1 1 3 1 8 1 19 3 3 1 1 1 1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 435,
        "task_id": 3932,
        "test_case_id": 18,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "22\n1 1 1 6 1 1 13 21 1 1 2 1 8 1 19 3 3 1 1 1 1 2\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 436,
        "task_id": 3932,
        "test_case_id": 19,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "19\n9 7 1 8 1 1 1 13 1 1 3 3 19 1 1 1 1 1 1\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 437,
        "task_id": 3932,
        "test_case_id": 20,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "18\n6 1 1 3 1 1 1 1 1 1 4 1 8 1 1 18 1 5\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 438,
        "task_id": 3932,
        "test_case_id": 21,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "14\n4 1 1 1 3 1 1 1 1 14 1 5 1 3\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 439,
        "task_id": 3932,
        "test_case_id": 22,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "2\n1 2\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 440,
        "task_id": 3932,
        "test_case_id": 23,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "24\n3 3 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\n",
        "output": "NO",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 441,
        "task_id": 3932,
        "test_case_id": 24,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "20\n20 9 4 4 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 442,
        "task_id": 3932,
        "test_case_id": 25,
        "question": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. \n\nIahub asks Iahubina: can you build a rooted tree, such that\n\n  each internal node (a node with at least one son) has at least two sons;  node i has c_{i} nodes in its subtree? \n\nIahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.\n\n\n-----Input-----\n\nThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents c_{i} (1 ≤ c_{i} ≤ n).\n\n\n-----Output-----\n\nOutput on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). \n\n\n-----Examples-----\nInput\n4\n1 1 1 4\n\nOutput\nYES\nInput\n5\n1 1 5 2 1\n\nOutput\nNO",
        "solutions": "[\"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            child=Children[i][j]\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Parent[x]=i\\n            Children[i].append(x)\\n            return True\\n    for i in range(x):\\n        if(Seen[i][x]):\\n            continue\\n        Y=[]\\n        for j in range(len(Children[i])):\\n            \\n            child=Children[i][j]\\n            if(Seen[i][child]):\\n                continue\\n            Parent[child]=-1\\n            Rem[i]+=C[child]\\n            Seen[i][child]=True\\n            Seen[child][i]=True\\n            if(DFS(child)):\\n                Seen[i][child]=False\\n                Seen[child][i]=False\\n                continue\\n            Seen[i][child]=False\\n            Seen[child][i]=False\\n            Parent[child]=i\\n            Rem[i]-=C[child]\\n            Y.append(child)\\n        Children[i]=list(Y)\\n        if(Rem[i]>=C[x]):\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n                continue\\n            Rem[i]-=C[x]\\n            Children[i].append(x)\\n            Parent[x]=i\\n            return True\\n    return False\\n                \\n        \\n\\n\\n\\n\\nn=int(input())\\n\\nC=list(map(int,input().split()))\\nRem=[-1]*n\\nParent=[-1]*n\\nChildren=[]\\nSeen=[]\\nfor i in range(n):\\n    Seen.append([False]*n)\\nC.sort(reverse=True)\\n\\nif(C[0]!=n or C.count(2)>0):\\n    print(\\\"NO\\\")\\n\\nelse:\\n    for i in range(n):\\n        Rem[i]=C[i]-1\\n        Children.append([])\\n    Parent[0]=0\\n    Ans=\\\"YES\\\"\\n    for i in range(1,n):\\n        if(DFS(i)==False):\\n            Ans=\\\"NO\\\"\\n            break\\n    for i in range(n):\\n        if(Rem[i]!=0 and C[i]!=1):\\n            Ans=\\\"NO\\\"\\n            break\\n    print(Ans)\\n            \\n\", \"def DFS(x):\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Parent[x]=i\\n\\n            Children[i].append(x)\\n\\n            return True\\n\\n    for i in range(x):\\n\\n        if(Seen[i][x]):\\n\\n            continue\\n\\n        Y=[]\\n\\n        for j in range(len(Children[i])):\\n\\n            \\n\\n            child=Children[i][j]\\n\\n            if(Seen[i][child]):\\n\\n                continue\\n\\n            Parent[child]=-1\\n\\n            Rem[i]+=C[child]\\n\\n            Seen[i][child]=True\\n\\n            Seen[child][i]=True\\n\\n            if(DFS(child)):\\n\\n                Seen[i][child]=False\\n\\n                Seen[child][i]=False\\n\\n                continue\\n\\n            Seen[i][child]=False\\n\\n            Seen[child][i]=False\\n\\n            Parent[child]=i\\n\\n            Rem[i]-=C[child]\\n\\n            Y.append(child)\\n\\n        Children[i]=list(Y)\\n\\n        if(Rem[i]>=C[x]):\\n\\n            if(Rem[i]==C[x] and len(Children[i])==0):\\n\\n                continue\\n\\n            Rem[i]-=C[x]\\n\\n            Children[i].append(x)\\n\\n            Parent[x]=i\\n\\n            return True\\n\\n    return False\\n\\n                \\n\\n        \\n\\n\\n\\n\\n\\n\\n\\n\\n\\nn=int(input())\\n\\n\\n\\nC=list(map(int,input().split()))\\n\\nRem=[-1]*n\\n\\nParent=[-1]*n\\n\\nChildren=[]\\n\\nSeen=[]\\n\\nfor i in range(n):\\n\\n    Seen.append([False]*n)\\n\\nC.sort(reverse=True)\\n\\n\\n\\nif(C[0]!=n or C.count(2)>0):\\n\\n    print(\\\"NO\\\")\\n\\n\\n\\nelse:\\n\\n    for i in range(n):\\n\\n        Rem[i]=C[i]-1\\n\\n        Children.append([])\\n\\n    Parent[0]=0\\n\\n    Ans=\\\"YES\\\"\\n\\n    for i in range(1,n):\\n\\n        if(DFS(i)==False):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    for i in range(n):\\n\\n        if(Rem[i]!=0 and C[i]!=1):\\n\\n            Ans=\\\"NO\\\"\\n\\n            break\\n\\n    print(Ans)\\n\\n            \\n\\n\\n\\n\\n\\n# Made By Mostafa_Khaled\\n\"]",
        "difficulty": "competition",
        "input": "12\n12 7 4 3 3 1 1 1 1 1 1 1\n",
        "output": "YES",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://codeforces.com/problemset/problem/429/C"
    },
    {
        "id": 443,
        "task_id": 4127,
        "test_case_id": 1,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "198 1.10\n",
        "output": "217\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 444,
        "task_id": 4127,
        "test_case_id": 2,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "1 0.01\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 445,
        "task_id": 4127,
        "test_case_id": 3,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "1000000000000000 9.99\n",
        "output": "9990000000000000\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 446,
        "task_id": 4127,
        "test_case_id": 4,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "776013196293085 2.60\n",
        "output": "2017634310362021\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 447,
        "task_id": 4127,
        "test_case_id": 5,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "776013196293085 8.11\n",
        "output": "6293467021936919\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 448,
        "task_id": 4127,
        "test_case_id": 6,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "999990000000001 9.99\n",
        "output": "9989900100000009\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 449,
        "task_id": 4127,
        "test_case_id": 7,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "999990000000010 9.90\n",
        "output": "9899901000000099\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 450,
        "task_id": 4127,
        "test_case_id": 8,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "999990000000100 9.99\n",
        "output": "9989900100000999\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 451,
        "task_id": 4127,
        "test_case_id": 9,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "981260158257699 5.74\n",
        "output": "5632433308399192\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 452,
        "task_id": 4127,
        "test_case_id": 10,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "547116602434646 4.44\n",
        "output": "2429197714809828\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 453,
        "task_id": 4127,
        "test_case_id": 11,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "408917861643436 0.80\n",
        "output": "327134289314748\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 454,
        "task_id": 4127,
        "test_case_id": 12,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "842184971396729 3.24\n",
        "output": "2728679307325401\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 455,
        "task_id": 4127,
        "test_case_id": 13,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "664706138336385 9.79\n",
        "output": "6507473094313209\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 456,
        "task_id": 4127,
        "test_case_id": 14,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "755808190852409 4.65\n",
        "output": "3514508087463701\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 457,
        "task_id": 4127,
        "test_case_id": 15,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "901335694041665 3.32\n",
        "output": "2992434504218327\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 458,
        "task_id": 4127,
        "test_case_id": 16,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "586599810888828 0.09\n",
        "output": "52793982979994\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 459,
        "task_id": 4127,
        "test_case_id": 17,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "719260799964413 3.27\n",
        "output": "2351982815883630\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 460,
        "task_id": 4127,
        "test_case_id": 18,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "609041597884348 1.20\n",
        "output": "730849917461217\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 461,
        "task_id": 4127,
        "test_case_id": 19,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "816458265788623 1.96\n",
        "output": "1600258200945701\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 462,
        "task_id": 4127,
        "test_case_id": 20,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "814793613347395 1.99\n",
        "output": "1621439290561316\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 463,
        "task_id": 4127,
        "test_case_id": 21,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "0 9.98\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 464,
        "task_id": 4127,
        "test_case_id": 22,
        "question": "Compute A \\times B, truncate its fractional part, and print the result as an integer.\n\n-----Constraints-----\n - 0 \\leq A \\leq 10^{15}\n - 0 \\leq B < 10\n - A is an integer.\n - B is a number with two digits after the decimal point.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nA B\n\n-----Output-----\nPrint the answer as an integer.\n\n-----Sample Input-----\n198 1.10\n\n-----Sample Output-----\n217\n\nWe have 198 \\times 1.10 = 217.8. After truncating the fractional part, we have the answer: 217.",
        "solutions": "[\"a, b = input().split()\\na = int(a)\\nb1, b2 = b.split('.')\\nb3 = int(b1)*100 + int(b2)\\n\\nprint((a*b3//100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB = B[0]+B[2:]\\n\\nif A*int(B) >= 100:\\n  print(str(A*int(B))[:-2])\\nelse:\\n  print(0)\", \"from decimal import Decimal\\na, b = list(map(Decimal, input().split()))\\nprint((int(a*b)))\\n\", \"\\ndef ri():\\n    return int(input())\\n\\n\\ndef rii():\\n    return [str(v) for v in input().split()]\\n\\nA, B = rii()\\nA = int(A)\\nB, F = [int(v) for v in B.split(\\\".\\\")]\\nB = 100 * B + F\\n\\nprint((A * B) // 100)\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nA_ = int(A)\\nB_ = (B*100)\\n\\nprint((int(A_*B_/100)))\\n\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(''.join(b.split('.')))\\n\\nprint(((a*b)//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint((a * b // 100))\\n\", \"a,b=input().split()\\nnum=int(b[0])*100+int(b[2])*10+int(b[3])\\nprint(num*int(a)//100)\", \"A, B = input().split()\\nA = int(A)\\ni, d = list(map(int, B.split(\\\".\\\")))\\nB_m = i * 100 + d\\nans = A * B_m // 100\\nprint(ans)\\n\", \"import math\\nl = input().split(\\\" \\\")\\na = int(l[0])\\n\\nb = (l[1].split(\\\".\\\"))\\nc = int(b[0])\\nd = int(b[1])\\n\\ne = a*(c*100 + d)//100\\nprint(e)\", \"A,B = input().split()\\nprint((int(A)*round(100*float(B)))//100)\", \"import decimal\\n\\na, b = input().split()\\na = int(a)\\nb = decimal.Decimal(b)\\nc = b * 100\\nx = a * int(c)\\nprint(x//100)\", \"import decimal as d\\na,b=input().split()\\nprint(int(int(a)*d.Decimal(b)))\", \"a, b = map(float, input().split())\\nib = b * 100\\nans = int(a) * round(ib) // 100\\nprint(ans)\", \"#n = int(input())\\n#a, b = map(int, input().split())\\n#al = list(map(int, input().split()))\\n#al=[list(input()) for i in range(n)]\\n\\na, b = list(map(str, input().split()))\\n\\na = int(a)\\nb = int(b[0]+b[2:])\\nprint((a*b//100))\\n\", \"a,b = list(map(str,input().split()))\\na = int(a)\\nb = 100*int(b[0])+10*int(b[2])+int(b[3])\\nprint((a*b//100))\\n\\n\", \"A, B = list(map(str, input().split()))\\nans = int(A) * int(B[0]) * 100\\nans += (int(A) * int(B[2]) * 10)\\nans += (int(A) * int(B[3]))\\nprint((ans // 100))\\n\", \"A,B = input().split()\\nA = int(A)\\nB1, B2 = B.split('.')\\nB = int(B1)*10**len(B2)+int(B2)\\nprint(((A*B)//10**len(B2)))\\n\", \"inputs = input().split(\\\" \\\")\\nproduct = int(inputs[0])*(round(float(inputs[1])*100))\\nprint(product//100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100*float(B))\\n\\nprint(A*B//100)\", \"a, b = input().split()\\n \\na = int(a)\\nb = int(b.replace('.', ''))\\n \\nans = a * b // 100\\nprint(ans)\", \"x, y = input().split()\\ny = float(y) * 100 + 0.01\\nans = int(x) * int(y)\\nprint(ans//100)\", \"a,b = input().split()\\na = int(a)\\nb = int(b[0]+b[2]+b[3])\\nprint(a * b // 100)\", \"a,b = input().split()\\n\\na = int(a)\\nb = int(b.replace('.',''))\\n\\nprint((a*b//100))\\n\", \"a, B = input().split()\\na = int(a)\\ni = 2\\nans = 0\\nfor b in B:\\n    if b == \\\".\\\":\\n        continue\\n    ans += int(b) * a * 10 ** i\\n    i -= 1\\nprint((ans // 100))\\n\", \"A,B = input().split()\\n\\n\\nA = int(A)\\nB = int(B[:len(B)-3] + B[len(B)-2:])\\n\\nprint(int((A*B)//100))\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(int(a*b//100))\", \"A, B = input().split()\\n\\nprint(int(A) * round(float(B) * 100) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"A,B=input().split()\\nA=int(A)\\nB=round(100*float(B))\\nprint(A*B//100)\", \"# C\\nfrom decimal import Decimal\\nA,B = map(Decimal,input().split())\\nans = A * B\\n\\nprint(int(ans))\", \"import sys\\nimport math\\nfrom collections import defaultdict, deque, Counter\\nfrom copy import deepcopy\\nfrom bisect import bisect, bisect_right, bisect_left\\nfrom heapq import heapify, heappop, heappush\\n    \\ninput = sys.stdin.readline\\ndef RD(): return input().rstrip()\\ndef F(): return float(input().rstrip())\\ndef I(): return int(input().rstrip())\\ndef MI(): return map(int, input().split())\\ndef MF(): return map(float,input().split())\\ndef LI(): return list(map(int, input().split()))\\ndef TI(): return tuple(map(int, input().split()))\\ndef LF(): return list(map(float,input().split()))\\ndef Init(H, W, num): return [[num for i in range(W)] for j in range(H)]\\n    \\n    \\ndef main():\\n    A, B = input().rstrip().split()\\n    A = int(A)\\n    B = int(B.replace('.', ''))\\n    print((A*B)//100)\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"import math\\nA,B = map(float,input().split())\\nB =  B*100\\nans = int(A)*round(B)//100\\nprint(ans)\", \"a=input().split()\\na1=int(a[0])\\na2=a[1]\\na3=a2[0]+a2[2:]\\na3=int(a3)\\nprint(((a1*a3)//100))\\n\", \"from decimal import Decimal\\nimport math\\na,b=map(str,input().split())\\n\\nc=math.floor(Decimal(a)*Decimal(b))\\n\\nprint(c)\", \"a,b = input().split()\\nb = b.replace('.','')\\na = int(a)\\nprint((a*int(b)//100))\\n\", \"A,B = map(str,input().split())\\nA = int(A)\\nC,D = map(int,B.split('.'))\\nB1 = C*100+D\\nprint(int((A*B1)//100))\", \"def main():\\n    from decimal import Decimal\\n    N, M = (Decimal(i) for i in input().split())\\n    print((int(N * M)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"def LS():\\n    return list(input().split())\\n\\n\\nA, B = LS()\\nA = int(A)\\nB = B.replace(\\\".\\\", \\\"\\\", 1)\\nB = int(B)\\nans = A*B\\nans //= 100\\nprint(ans)\\n\", \"a, b = map(str, input().split())\\ni, f = b.split(\\\".\\\")[0], b.split(\\\".\\\")[1][0:2]\\nb = int(i) * 100 + int(f)\\nprint(int(a) * b // 100)\", \"A, B = input().split()\\nA = int(A)\\nB = round(100 * float(B))\\nprint(A*B//100)\", \"a,b=input().split()\\na=int(a)\\nb=int(b[0])*100+int(b[2])*10+int(b[3])\\ns=a*b\\nprint(s//100)\", \"from decimal import Decimal, ROUND_DOWN\\na, b = map(lambda x: Decimal(x), input().split())\\nprint(Decimal(a * b).quantize(Decimal('1.'), rounding=ROUND_DOWN))\", \"A, B = input().split()\\nA = int(A)\\nB = int(''.join([b for b in B if b != '.']))\\n\\nprint(A * B // 100)\", \"a, b = input().split()\\na = int(a)\\nprint((a * int(b[0]) + a * (int(b[2]) * 10 + int(b[3])) // 100))\\n\", \"a,b=input().split();print(int(a)*int(b[0]+b[2:])//100)\", \"A, B=(input().split())\\nA=int(A)\\nC=int(B[0])*100+int(B[2])*10+int(B[3])\\nprint((int(A*C//100)))\\n\\n\", \"import decimal\\na, b = input().split()\\nx=decimal.Decimal(a)\\ny=decimal.Decimal(b)\\nans = int(x * y) \\nprint(ans)\", \"import math\\nimport fractions\\na, b = list(map(str, input().split()))\\na, b = int(a), fractions.Fraction(b)\\nprint((math.floor(a*b)))\\n\", \"from decimal import *\\nimport math\\n\\na, b = list(map(Decimal, input().split()))\\nprint((math.floor(a * b)))\\n\", \"a,b = input().split()\\na = int(a)\\nb = int(b.replace(\\\".\\\",\\\"\\\"))\\nprint((a*b)//100)\", \"A,B=input().split()\\nA=int(A)\\nB=100*int(B[0])+10*int(B[2])+int(B[3])\\nprint(A*B//100)\", \"import math\\nfrom decimal import *\\na,b=map(str,input().split())\\nans=(Decimal(a)*Decimal(b))//1\\nprint(ans)\", \"a, b = input().split()\\nc, d = b.split('.')\\ne = int(c) * 100 + int(d)\\nf = int(a) * e\\nprint((f // 100))\\n\", \"import decimal\\nA,B = map(decimal.Decimal,input().split())\\nnum = A*B\\nprint(int(num)//1)\", \"line = input().split()\\na = int(line[0])\\nb = round(float(line[1])*100)\\n\\nprint(a*b//100)\", \"import math\\n\\n\\ndef main() -> None:\\n    a, b = input().split()\\n\\n    print(((int(a)*int(b.replace('.', ''))) // 100))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"A,B=input().split()\\nA=int(A)\\nB=int(100*float(B)+0.5)\\nprint((A*B//100))\\n\", \"a, b = input().split()\\na = int(a)\\nb = int(b.replace('.', ''))\\nprint(int(a * b) // 100)\", \"a, b = input().split()\\na = int(a)\\nb = round(100*float(b))\\nprint(a*b//100)\", \"from fractions import Decimal, Fraction\\na,b = input().split()\\na = Fraction(a)\\nx = Decimal(b).as_integer_ratio()\\nb = Fraction(x[0], x[1])\\nprint(int(a*b))\", \"import math\\nimport decimal\\n\\nA, B = map(str, input().split())\\nA = int(A)\\nB = decimal.Decimal(B)\\nprint(math.floor(A*B))\", \"def main(A, B):\\n    B = round(100 * B)\\n    ans = A * B\\n    return int(ans // 100)\\n\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    ans = main(A, B)\\n    print(ans)\\n\\n__starting_point()\", \"A,B = input().split()\\nA = int(A)\\nC = \\\"\\\"\\nfor i in range(len(B)):\\n    if(i != 1):\\n        C += B[i]\\nC = int(C)\\nmultiply = str(A * C)\\nif(A * C < 100):\\n    print(0)\\n    return\\nans = \\\"\\\"\\nfor i in range(len(multiply) - 2):\\n    ans += multiply[i]\\nprint(int(ans))\", \"a, b = input().split()\\n\\na = int(a)\\n\\nb = round(float(b) * 100)\\n\\nprint(int(a * b // 100))\", \"import math\\nfrom decimal import *\\na,b=map(str, input().split())\\na_ = Decimal(a)\\nb_ = Decimal(b)\\nprint(math.floor(a_*b_))\", \"x,y = list(input().split())\\nx = int(x)\\ny = int(y[0]+y[2]+y[3])\\nprint(x*y//100)\", \"s=input().split()\\na=int(s[0])\\nb=int(s[1].replace('.',''))\\nprint((a*b//100))\\n\", \"from decimal import *\\nA,B=list(map(Decimal,input().split()))\\n#print(A)\\n#print(B*100)\\nprint((int((A*(B*100))//100)))\\n\", \"#from statistics import median\\n#import collections\\n#aa = collections.Counter(a) # list to list || .most_common(2)\\u3067\\u6700\\u5927\\u306e2\\u500b\\u3068\\u308a\\u3060\\u305b\\u308b\\u304a a[0][0]\\nfrom fractions import gcd\\nfrom itertools import combinations,permutations,accumulate, product # (string,3) 3\\u56de\\n#from collections import deque\\nfrom collections import deque,defaultdict,Counter\\nimport decimal\\nimport re\\nimport math\\nimport bisect\\nimport heapq\\n#\\n#\\n#\\n# python\\u3067\\u7121\\u7406\\u306a\\u3068\\u304d\\u306f\\u3001pypy\\u3067\\u3084\\u308b\\u3068\\u6b63\\u89e3\\u3059\\u308b\\u304b\\u3082\\uff01\\uff01\\n#\\n#\\n# my_round_int = lambda x:np.round((x*2 + 1)//2)\\n# \\u56db\\u6368\\u4e94\\u5165g\\n#\\n# \\u30a4\\u30f3\\u30c7\\u30c3\\u30af\\u30b9\\u7cfb\\n# int min_y = max(0, i - 2), max_y = min(h - 1, i + 2);\\n# int min_x = max(0, j - 2), max_x = min(w - 1, j + 2);\\n#\\n#\\nimport sys\\nsys.setrecursionlimit(10000000)\\nmod = 10**9 + 7\\n#mod = 9982443453\\n#mod = 998244353\\nfrom sys import stdin\\nreadline = stdin.readline\\ndef readInts():\\n  return list(map(int,readline().split()))\\ndef readTuples():\\n    return tuple(map(int,readline().split()))\\ndef I():\\n    return int(readline())\\na,b = list(map(decimal.Decimal,input().split()))\\nprint((int(a*b)))\\n\", \"a,b=input().split()\\na = int(a)\\nb = int(b.replace('.',\\\"\\\"))\\n\\nprint((int(a*b)//100))\\n\", \"from decimal import *\\nA, B = list(map(Decimal, input().split()))\\nprint((int(A*B)))\\n\", \"# coding=utf-8\\n\\ndef __starting_point():\\n    A, B = input().split()\\n    A = int(A)\\n    B = float(B)\\n    B = int(B*100+0.5)\\n\\n    print((A*B//100))\\n\\n__starting_point()\", \"#submit 16999743\\na, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\\n\", \"from math import floor\\nfrom fractions import Fraction\\na,b = input().split()\\na = int(a)\\nb = Fraction(b)\\n\\nprint(floor(a*b))\", \"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time, copy,bisect\\n#from operator import itemgetter\\n#from heapq import heappush, heappop\\n#import numpy as np\\n#from scipy.sparse.csgraph import breadth_first_order, depth_first_order, shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson\\n#from scipy.sparse import csr_matrix\\n#from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN\\nimport sys\\n\\nsys.setrecursionlimit(10**7)\\ninf = 10**20\\nmod = 10**9 + 7\\n\\nstdin = sys.stdin\\n\\nni = lambda: int(ns())\\nnf = lambda: float(ns())\\nna = lambda: list(map(int, stdin.readline().split()))\\nnb = lambda: list(map(float, stdin.readline().split()))\\nns = lambda: stdin.readline().rstrip()  # ignore trailing spaces\\n\\nfrom decimal import Decimal\\na, b = map(Decimal, input().split())\\nprint(int(a*b))\", \"from decimal import Decimal\\nfrom decimal import ROUND_FLOOR\\n\\nA, B = [Decimal(i) for i in input().split()]\\n\\nprint(((A*B).quantize(Decimal(0), rounding=ROUND_FLOOR)))\\n\", \"from decimal import *\\n\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(int(a*b))\", \"a,b = map(str,input().split())\\na = int(a)\\nb = list(b)\\nc = int(b[0])*100 + int(b[2])*10 + int(b[3])\\nnum = a*c\\nprint(num//100)\", \"a,b = map(str, input().split())\\na = int(a)\\nli_b = []\\nfor i in range(4):\\n    B = b[i]\\n    if B!=\\\".\\\":\\n        li_b.append(int(B))\\nb = 100*li_b[0] + 10*li_b[1] + li_b[2]\\n\\nans = a*b // 100\\nprint(ans)\", \"from decimal import Decimal\\nA, B = input().split()\\na=Decimal(A)\\nb=Decimal(B)\\nprint(int(a*b))\", \"import re\\na,b,c=map(int, re.split(\\\"[ .]\\\",input()))\\nprint(a*(b*100+c)//100)\", \"A,B=map(float,input().split())\\nA =int(A)\\nB=round(100*B)\\nprint(A*B//100)\", \"from decimal import Decimal\\nfrom math import floor\\n\\n\\ndef main():\\n    a, b = list(map(Decimal, input().split()))\\n    print((floor(a * b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"from decimal import Decimal\\n\\nA, B = list(map(Decimal, input().split()))\\n\\nans = A * B\\n\\nprint((int(ans)))\\n\\n\", \"from decimal import Decimal\\nfrom math import floor\\na, b = map(Decimal, input().split())\\nprint(floor(a*b))\", \"from decimal import Decimal\\na, b = map(Decimal,input().split())\\nscore=a*b\\nscore = int(score)\\nprint(score)\", \"a, b = input().split()\\n\\na = int(a)\\nb1, b2 = b.split('.')\\n\\nans = a * (int(b1) * 100 + int(b2)) // 100\\nprint(ans)\", \"from decimal import Decimal\\n\\na, b = input().split()\\n\\na = Decimal(a)\\nb = Decimal(b)\\n\\nprint(int(a*b))\", \"# -*- coding: utf-8 -*-\\nfrom decimal import Decimal  \\nimport math\\n\\na, b = input().split()\\n\\na = int(a)\\nb = Decimal(b)\\n\\nx = a * b\\n\\nprint((math.floor(int(a) * Decimal(b))))\\n\\n\", \"a,b=map(int,input().replace('.','').split())\\nprint(a*b//100)\", \"#!/usr/bin/env python3\\n\\nimport decimal\\n#import\\n#import math\\n#import numpy as np\\n#= int(input())\\n#= input()\\nA, B = list(map(decimal.Decimal, input().split()))\\n\\nprint((int(A * B)))\\n\", \"a, b = map(str, input().split())\\na, b = int(a), int(b.split(\\\".\\\")[0])*100 + int(b.split(\\\".\\\")[1])\\nprint(a*b//100)\", \"from math import floor\\nfrom decimal import Decimal\\na, b = input().split()\\na = int(a)\\nb = Decimal(b)\\nprint(floor(a * b))\", \"import math\\nimport decimal\\ndef i_input(): return int(input())\\n\\n\\ndef i_map(): return map(int, input().split())\\n\\n\\ndef i_list(): return list(map(int, input().split()))\\n\\n\\ndef i_row(N): return [int(input()) for _ in range(N)]\\n\\n\\ndef i_row_list(N): return [list(map(int, input().split())) for _ in range(N)]\\n\\na,b=map(decimal.Decimal, input().split())\\nprint(int(a*b))\", \"import sys\\nfrom collections import deque, defaultdict, Counter\\nfrom itertools import accumulate, product, permutations, combinations\\nfrom operator import itemgetter\\nfrom bisect import bisect_left, bisect_right\\nfrom heapq import heappop, heappush\\nfrom math import ceil, floor, sqrt, gcd, inf\\nfrom copy import deepcopy\\nimport numpy as np\\nimport scipy as sp\\n\\nINF = inf\\nMOD = 1000000007\\n\\na, b = input().split()\\n\\ntmp = 0\\nres = 0\\n\\na = int(a)\\nb = int(b.replace(\\\".\\\", \\\"\\\"))\\nres = a * b // 100\\n\\nprint(res)\\n\", \"import math\\n\\na, b = list(map(float, input().split()))\\n\\na = int(a)\\nb = int(round(b * 100))\\n\\nans = a * b\\n\\nans = ans // 100\\n\\nprint(ans)\\n\", \"import sys\\ninput = sys.stdin.readline\\n\\ndef main():\\n    a, b = input().split()\\n    c, d = b.split(\\\".\\\")\\n    if len(d) == 1:\\n        d = d + '0'\\n    \\n    p, q = int(a), int(c) * 100 + int(d)\\n    ans = p * q // 100\\n\\n    print(ans)\\n    \\n    \\n    \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\nimport decimal\\nA,B = input().split(' ')\\nanswer = math.floor(int(A)*decimal.Decimal(B))\\nprint(answer)\\n\\n\", \"\\nM, N = input().split()   # 2\\u3064\\u6574\\u6570\\u306e\\u8aad\\u307f\\u53d6\\u308a\\nA=int(M)\\nB=N.replace(\\\".\\\",\\\"\\\")\\nB=int(B)\\n\\nC=A*B//100\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "999999999999999 0.00\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc169/tasks/abc169_c"
    },
    {
        "id": 465,
        "task_id": 4297,
        "test_case_id": 1,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "3\n",
        "output": "6\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 466,
        "task_id": 4297,
        "test_case_id": 2,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "10\n",
        "output": "10\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 467,
        "task_id": 4297,
        "test_case_id": 3,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "999999999\n",
        "output": "1999999998\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 468,
        "task_id": 4297,
        "test_case_id": 4,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "1\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 469,
        "task_id": 4297,
        "test_case_id": 5,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "2\n",
        "output": "2\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 470,
        "task_id": 4297,
        "test_case_id": 6,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "36426\n",
        "output": "36426\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 471,
        "task_id": 4297,
        "test_case_id": 7,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "79445\n",
        "output": "158890\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 472,
        "task_id": 4297,
        "test_case_id": 8,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "90081\n",
        "output": "180162\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 473,
        "task_id": 4297,
        "test_case_id": 9,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "433933447\n",
        "output": "867866894\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 474,
        "task_id": 4297,
        "test_case_id": 10,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "476190629\n",
        "output": "952381258\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 475,
        "task_id": 4297,
        "test_case_id": 11,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "262703497\n",
        "output": "525406994\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 476,
        "task_id": 4297,
        "test_case_id": 12,
        "question": "You are given a positive integer N.\nFind the minimum positive integer divisible by both 2 and N.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - All values in input are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the minimum positive integer divisible by both 2 and N.\n\n-----Sample Input-----\n3\n\n-----Sample Output-----\n6\n\n6 is divisible by both 2 and 3.\nAlso, there is no positive integer less than 6 that is divisible by both 2 and 3.\nThus, the answer is 6.",
        "solutions": "[\"n = int(input())\\nprint((n if n%2==0 else n*2))\\n\", \"N =int(input())\\nif N%2==0:\\n    print(N)\\nelse:\\n    print((2*N))\\n\", \"N = int(input())\\n\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print((n*2))\\n\", \"N = int(input())\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n  \\tprint(n * 2)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"from math import gcd\\nprint((n:=int(input()))*2//gcd(2,n))\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"\\nN = int(input())\\n\\nif(N % 2 == 0):\\n    print(N)\\nelse:\\n    print((2 * N))\\n\", \"n = int(input())\\nprint(n if n%2 == 0 else 2*n)\", \"import sys\\nimport math\\n\\nN = int(input())\\n\\nprint(int((N*2)/math.gcd(N, 2)))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"a=int(input())\\nb=2\\nimport math\\nprint(int(a*b/math.gcd(a, b)))\", \"N = int(input())\\nif N % 2 == 0:\\n  ans = N\\nelse:\\n  ans = 2 * N\\n  \\nprint(ans)\", \"n=int(input())\\nprint(n if n%2==0 else n*2)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n=int(input())\\nans=n if n%2==0 else 2*n\\nprint(ans)\", \"N = int(input())\\nprint(N if N % 2 == 0 else 2 * N)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n * 2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"n=input()\\nif int(n)%2==0:\\n  print(n)\\nelse:\\n  print((int(n)*2))\\n\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"n=int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print((2*n))\\n\", \"N=int(input())\\nif N%2==0:\\n    ans=N\\nelse:\\n    ans=N*2\\nprint(ans)\", \"\\nn=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int (input ())\\nif n%2 == 0:\\n  print (n)\\nelse:\\n  print (n*2)\", \"num = int(input())\\nif(num %2 != 0):\\n  print(num*2)\\nelse:\\n  print(num)\", \"n = int(input())\\nif n%2:\\n  print(2*n)\\nelse:\\n  print(int(2*(n/2)))\", \"#\\n# abc102 a\\n#\\n\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"3\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"6\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"999999999\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"1999999998\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((N*2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\nif n%2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"\\nn = int(input())\\n\\nif n % 2 == 0: print(n)\\nelse: print(2*n)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"import math\\ndef lcm(x, y):\\n    return (x * y) // math.gcd(x, y)\\n\\n\\nn = int(input())\\nprint(lcm(2, n))\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2 * n)\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\", \"import math\\nN = int(input())\\ndef lcm(a,b):\\n    return int(a*b//math.gcd(a,b))\\nprint(lcm(2,N))\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"n = int(input())\\nprint([n, 2*n][n%2])\", \"from numpy import lcm\\nn = int(input())\\nprint(lcm(2, n))\", \"N = int(input().rstrip())\\nif N&1==1:\\n    print(N*2)\\nelse:\\n    print(N)\", \"\\ndef main():\\n    n = int(input())\\n    if n % 2 == 0:\\n        print(n)\\n    else:\\n        print((2 * n))\\n        \\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\nif N % 2 == 0:\\n  print(N)\\nelse:\\n  print(N*2)\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nif (n%2==0):\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"import math\\n\\nn = int(input())\\n\\nprint(2 * n // math.gcd(2, n))\", \"n = int(input())\\n\\nprint((n if n % 2 == 0 else 2 * n))\\n\", \"n = int(input())\\nprint(2*n if n%2 else n)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"a = int(input())\\n\\nif a%2 == 0:\\n    print(a)\\nelse:\\n    print((a*2))\\n\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelif n % 2 != 0:\\n    print(2 * n)\", \"N=int(input())\\nif N%2==0:\\n  print(N)\\nelse:\\n  print(2*N)\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N * 2)\", \"import math\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = 2 * n // gcd\\nprint(lcm)\\n\", \"N=int(input())\\nif N%2==0 :\\n  print(N)\\nelse :\\n  print(N*2)\", \"a=int(input())\\nprint(a*((a%2)+1))\", \"import math\\nN = int(input())\\nprint((2*N)//math.gcd(2,N))\", \"num = int(input())\\n\\nif num % 2 == 0:\\n    print(num)\\nelse:\\n    print((num * 2))\\n\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"def main():\\n    n = int(input())\\n    print(n if n%2==0 else 2*n)\\n\\n\\nmain()\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"# -*- coding: utf-8 -*-\\n\\ndef get_input() -> int:\\n    \\\"\\\"\\\"\\n    \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\u3059\\u308b.\\n\\n    Returns:\\\\n\\n        int: \\u6a19\\u6e96\\u5165\\u529b\\n    \\\"\\\"\\\"\\n    N = int(input())\\n\\n    return N\\n\\n\\ndef main(N: int) -> None:\\n    \\\"\\\"\\\"\\n    \\u30e1\\u30a4\\u30f3\\u51e6\\u7406.\\n\\n    Args:\\\\n\\n        N (int): \\u6b63\\u6574\\u6570(1 <= N <= 10^9)\\n    \\\"\\\"\\\"\\n    # \\u6c42\\u89e3\\u51e6\\u7406\\n    ans = N\\n    if ans % 2 != 0:\\n        ans *= 2\\n\\n    # \\u7d50\\u679c\\u51fa\\u529b\\n    print(ans)\\n\\n\\ndef __starting_point():\\n    # \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\n    N = get_input()\\n\\n    # \\u30e1\\u30a4\\u30f3\\u51e6\\u7406\\n    main(N)\\n\\n__starting_point()\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(2*n)\", \"a=int(input())\\nif a%2==0:\\n  print(a)\\nelse:\\n  print(a*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n * 2)\", \"import math\\n\\nn = int(input())\\ngcd = math.gcd(2, n)\\nlcm = int(2*n/gcd)\\nans = lcm\\n\\nprint(ans)\", \"n = int(input())\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(2*n)\", \"N = int(input())\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"n = int(input())\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n * 2)\", \"import math\\n\\nN=int(input())\\nprint((2*N//math.gcd(2,N)))\\n\", \"import sys\\n\\nread = sys.stdin.read\\nreadline = sys.stdin.readline\\nreadlines = sys.stdin.readlines\\nsys.setrecursionlimit(10 ** 9)\\nINF = 1 << 60\\nMOD = 1000000007\\n\\n\\ndef main():\\n    N = int(readline())\\n\\n    if N % 2 == 0:\\n        print(N)\\n    else:\\n        print((2 * N))\\n\\n    return\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"N = int(input())\\n\\nif N % 2 == 0:\\n    print(N)\\nelse:\\n    print((N * 2))\\n\", \"# -*- coding: utf-8 -*-\\n# \\u6a19\\u6e96\\u5165\\u529b\\u3092\\u53d6\\u5f97\\nN = int(input())\\n\\n# \\u6c42\\u89e3\\u51e6\\u7406\\nans = N\\nif ans % 2 != 0:\\n    ans *= 2\\n\\n# \\u7d50\\u679c\\u51fa\\u529b\\nprint(ans)\\n\", \"n=int(input())\\nprint(n*(1+n%2))\", \"import sys\\nimport math\\n\\n#https://atcoder.jp/contests/agc008/submissions/15248942\\nsys.setrecursionlimit(10 ** 8)\\nini = lambda: int(sys.stdin.readline())\\ninm = lambda: map(int, sys.stdin.readline().split())\\ninl = lambda: list(inm())\\nins = lambda: sys.stdin.readline().rstrip()\\ndebug = lambda *a, **kw: print(\\\"\\\\033[33m\\\", *a, \\\"\\\\033[0m\\\", **dict(file=sys.stderr, **kw))\\n\\nN = ini()\\n\\nif N%2 == 0:\\n    print(N)\\nelse:\\n    print(N*2)\", \"import math\\nn = int(input())\\na = math.gcd(n, 2)  # \\u6700\\u5927\\u516c\\u7d04\\u6570\\nprint(n * 2 // a)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"N = int(input())\\n\\nif N % 2 == 0 :\\n    print(N)\\nelse :\\n    print(2*N)\", \"import math\\na = int(input())\\nprint(a*2//math.gcd(a, 2))\", \"N = int(input())\\n\\nif N % 2 == 0:\\n   print(N)\\nelse:\\n   print(2 * N)\", \"N = int(input())\\nprint(N if N%2 == 0 else N*2)\", \"n=int(input())\\nprint(n if n%2==0 else 2*n)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"#\\nimport sys\\nimport math\\nimport numpy as np\\nimport itertools\\n\\n\\nn = int(input())\\n\\nif n % 2 == 0:\\n    print(n)\\nelse:\\n    print((n*2))\\n\\n\\n\", \"n=int(input())\\nif n%2==0:\\n    print(n)\\nelse:\\n    print(n*2)\", \"n = int(input())\\n\\nif n % 2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"import math\\nN=int(input())\\nprint(2*N//math.gcd(2,N))\", \"N = int(input())\\nprint((N if N%2==0 else N*2))\\n\", \"n = int(input())\\nprint(n if n % 2 == 0 else n * 2)\", \"a = int(input())\\nif a % 2 == 0:\\n  print(a)\\nelse:\\n  print(a * 2)\", \"n=int(input())\\nif n%2:print(2*n)\\nelse:print(n)\", \"N = int(input())\\n\\nfor i in range(2, 10**6):\\n    if N % 2 == 0:\\n        break\\n    N *= i\\n\\nprint(N)\", \"n = int(input())\\nif n%2 == 0:\\n  print(n)\\nelse:\\n  print(n*2)\", \"n = int(input())\\nif n%2==0:\\n  print(n)\\nelse:\\n  print(2*n)\"]",
        "difficulty": "introductory",
        "input": "1000000000\n",
        "output": "1000000000\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc102/tasks/abc102_a"
    },
    {
        "id": 477,
        "task_id": 4311,
        "test_case_id": 1,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "8\n",
        "output": "5\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 478,
        "task_id": 4311,
        "test_case_id": 2,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "7\n",
        "output": "18\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 479,
        "task_id": 4311,
        "test_case_id": 3,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "54\n",
        "output": "114\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 480,
        "task_id": 4311,
        "test_case_id": 4,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "1\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 481,
        "task_id": 4311,
        "test_case_id": 5,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "2\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 482,
        "task_id": 4311,
        "test_case_id": 6,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "3\n",
        "output": "9\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 483,
        "task_id": 4311,
        "test_case_id": 7,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "4\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 484,
        "task_id": 4311,
        "test_case_id": 8,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "100\n",
        "output": "27\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 485,
        "task_id": 4311,
        "test_case_id": 9,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "99\n",
        "output": "27\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 486,
        "task_id": 4311,
        "test_case_id": 10,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "97\n",
        "output": "120\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 487,
        "task_id": 4311,
        "test_case_id": 11,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "95\n",
        "output": "107\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 488,
        "task_id": 4311,
        "test_case_id": 12,
        "question": "A sequence a=\\{a_1,a_2,a_3,......\\} is determined as follows:\n - The first term s is given as input.\n - Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.\n - a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.\nFind the minimum integer m that satisfies the following condition:\n - There exists an integer n such that a_m = a_n (m > n).\n\n-----Constraints-----\n - 1 \\leq s \\leq 100\n - All values in input are integers.\n - It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.\n\n-----Input-----\nInput is given from Standard Input in the following format:\ns\n\n-----Output-----\nPrint the minimum integer m that satisfies the condition.\n\n-----Sample Input-----\n8\n\n-----Sample Output-----\n5\n\na=\\{8,4,2,1,4,2,1,4,2,1,......\\}. As a_5=a_2, the answer is 5.",
        "solutions": "[\"from collections import defaultdict\\n\\nd = defaultdict(bool)\\n\\nn = int(input())\\nfor i in range(1000000):\\n\\n    if d[n]:\\n        print((i + 1))\\n        return\\n    d[n] = True\\n    if n & 1:\\n        n = n * 3 + 1\\n    else:\\n        n >>= 1\\n\", \"a=int(input())\\nb=[]\\nb.append(a)\\nwhile True:\\n    if a%2==0:\\n        a=a/2\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\\n    elif a%2!=0:\\n        a=3*a+1\\n        if a in b:\\n            print(len(b)+1)\\n            break\\n        else:\\n            b.append(a)\", \"s = int(input())\\na = s\\nc = 0\\nif a == 1 or a == 2:\\n  ans = 4\\nelse:\\n  while a != 1:\\n    if a%2 == 0:\\n      a = int(a/2)\\n      c += 1\\n    else:\\n      a = int(3*a+1)\\n      c += 1\\n  ans = c+2\\nprint(ans)\", \"s = int(input())\\nans = [0]*1000001\\ncnt = 1\\n\\nwhile True:\\n    if ans[s] == 0:\\n        ans[s] += 1\\n\\n        if s%2 == 0:\\n            s = s//2\\n        else:\\n            s = 3*s+1\\n        cnt += 1\\n\\n    if ans[s] != 0:\\n        print(cnt)\\n        return\\n\\n\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n\\nprint(i)\", \"n=int(input())\\nli = []\\nwhile not n in li:\\n  li.append(n)\\n  if n % 2 == 0:\\n    n //= 2\\n  else:\\n    n = n * 3 + 1\\n  \\nprint(len(li)+1)\", \"s = int(input())\\n\\nlst = [s]\\nprev = s\\nfor m in range(2, 1000001):\\n    if prev % 2 == 0:\\n        i = int(prev / 2)\\n    else:\\n        i = 3 * prev + 1\\n    if i in lst:\\n        print(m)\\n        break\\n    lst.append(i)\\n    prev = i\", \"s = int(input())\\na = [s]\\nwhile True:\\n  if a.count(a[-1]) == 2:\\n    print(len(a))\\n    return\\n  if a[-1]%2 == 0:\\n    a.append(a[-1]/2)\\n  else:\\n    a.append(3*a[-1]+1)\", \"n = int(input())\\nc = 0\\nx = []\\nwhile True:\\n    c+=1\\n    if n in x:\\n        print(c)\\n        break\\n    x.append(n)\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\", \"n=int(input())\\na=[n]\\ncnt=1\\nwhile len(set(a))==len(a):\\n    if n%2==0: \\n        n//=2\\n    else:\\n        n=3*n+1\\n    a.append(n)\\n    cnt+=1\\nprint(cnt)\\n\", \"s=int(input())\\na=[0]*10**6\\na[0]=s\\n\\ndef f(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x+1\\nt=0 \\nwhile f(a[t])>0:\\n  p=f(a[t])\\n  if p in a:\\n    print((t+2))\\n    return\\n  a[t+1]=p\\n  t+=1\\n\", \"def func(n: int) -> int:\\n    return n // 2 if n % 2 == 0 else n * 3 + 1\\n\\n\\ndef answer(s: int) -> int:\\n    sequence_a = [s]\\n    while True:\\n        num = func(sequence_a[-1])\\n        if num in sequence_a:\\n            return len(sequence_a) + 1\\n        sequence_a.append(num)\\n\\n\\ndef main():\\n    s = int(input())\\n    print((answer(s)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return list(map(int,input().split()))\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\nnum = []\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\ndef f(n):\\n    if n % 2 == 0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\ns = k()\\nnum.append(s)\\nwhile True:\\n    cnt += 1\\n    s = f(s)\\n    if s in num:\\n        print((cnt+1))\\n        return\\n    else:\\n        num.append(s)\\n        \\n\\n\\n\", \"s = int(input())\\nTMP = [s]\\n\\nif s==1 or s==2:\\n    print(4)\\nelse:\\n    while TMP[-1]!=1:\\n        if TMP[-1] % 2 == 0:\\n            TMP.append(TMP[-1]//2)\\n        elif TMP[-1] % 2 != 0:\\n            TMP.append(3 * TMP[-1] + 1)\\n    print(len(TMP)+1)\", \"s = int(input())\\nl = []\\ndef myfunc(x):\\n  if x%2 == 0:\\n    x = x//2\\n  else:\\n    x = 3*x + 1\\n  return x\\nfor i in range(10**6):\\n  l.append(s)\\n  s = myfunc(s)\\n  if s in l:\\n    print(i+2)\\n    break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    # \\u524d\\u56de\\u306e\\u5024\\u306b\\u3088\\u3063\\u3066\\u8a08\\u7b97\\u3092\\u5909\\u3048\\u308b\\u3002\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    # \\u6570\\u5217\\u306b\\u540c\\u3058\\u5024\\u304c\\u542b\\u307e\\u308c\\u3066\\u3044\\u308b\\u304b\\u3069\\u3046\\u304b\\uff1f\\n    if n in a:\\n\\t  \\t# \\u914d\\u5217\\u304c0\\u304b\\u3089\\u59cb\\u307e\\u308b\\u305f\\u3081\\u3001\\u30ab\\u30a6\\u30f3\\u30c8\\u30a2\\u30c3\\u30d7\\u3002\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s=int(input())\\ncol=[]\\na=s\\ncount=1\\nwhile True:\\n  col.append(a) \\n  if a%2==0:\\n    a=a/2\\n  else:\\n    a=a*3+1\\n  if a in col:\\n    print(count+1)\\n    break\\n  count+=1\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = []\\nans.append(s)\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"def main():\\n    def f(n):\\n        return 3 * n + 1 if n % 2 else n // 2\\n    s = int(input())\\n    a = [s]\\n    for i in range(1, 11**6):\\n        x = f(a[i-1])\\n        if x in a:\\n            return len(a) + 1; return\\n        a.append(x)\\n\\n\\nprint(main())\", \"s=int(input())\\na=[]\\nans=1\\nwhile True:\\n  a.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  ans+=1\\n  if s in a:\\n    print(ans)\\n    break\", \"s = int(input())\\nli = []\\nli.append(s)\\n\\nfor i in range(1,1000000000):\\n    if li[i-1] % 2 == 0:\\n        li.append(li[i-1]//2)\\n    else:\\n        li.append(li[i-1]*3+1)\\n\\n    for j in range(len(li)-1):\\n        if li[j] ==li[i]:\\n            print((i+1))\\n            return\\n\", \"s = int(input())\\na = [s]\\nb = 1\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = 3 * s + 1\\n    if s in a:\\n        print(len(a) + 1)\\n        return\\n    a.append(s)\", \"s = int(input())\\nL = []\\nfor c in range(2 , 10 ** 6 + 1):\\n  L.append(s)\\n  if s % 2 == 0:\\n    s = s // 2\\n  elif s % 2 == 1:\\n    s = s * 3 + 1\\n  if s in L:\\n    break\\nprint(c)\", \"s = int(input())\\n\\nif s == 1 or s == 2:\\n    print(4)\\n    return\\n\\ndef function(n):\\n    if n % 2 == 0:\\n        return int(n/2)\\n    else:\\n        return int(n*3+1)\\ni = 0\\ncount = 0\\na = []\\na.append(s)\\nwhile count < 2:\\n    a.append(function(a[i]))\\n    if a[i] == 4:\\n        count += 1\\n    i += 1\\nprint(i)\", \"n=int(input())\\nl=[n]\\nwhile True:\\n    if n%2==0:\\n        n//=2\\n    else:\\n        n=n*3+1\\n    if n in l:\\n        break\\n    else:\\n        l.append(n)\\nprint((len(l)+1))\\n\", \"s = int(input())\\nlist_a = [None]\\nlist_a.append(s)\\nans = 0\\nfor i in range(1, 10 ** 6 + 1):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] // 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n    if list_a[i] in list_a[:i]:\\n        ans = i\\n        break\\nprint(ans)\", \"s = int(input())\\nS = [str(s)]\\ni = 1\\nwhile True:\\n    if s % 2 == 0:\\n        i += 1\\n        s = s//2\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\n    else:\\n        i += 1\\n        s = int(3 * s + 1)\\n        S.append(str(s))\\n        if S.count(str(s)) == 2:\\n            print(i)\\n            return\\npass\\n\", \"import sys\\nimport copy\\ns = int(input())\\n\\ndef f(n):\\n    if n%2==0:\\n        return int(n/2)\\n    else:\\n        return 3*n+1\\n\\nfor i in range(1000000):\\n    if i == 0:\\n        a=[s]\\n    else:\\n        a.append(f(a[i-1]))\\n    \\n    if a.count(a[i]) == 2:\\n        print((i+1))\\n        return\\n\", \"# import math\\n# import statistics\\na=int(input())\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\n# e1,e2 = map(int,input().split())\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\n\\nda=True\\nap=[a]\\ncount=1\\nwhile da:\\n    if a%2==0:\\n        a=a//2\\n        ap.append(a)\\n    elif a%2==1:\\n        a=3*a+1\\n        ap.append(a)\\n    count+=1\\n    if len(set(ap))<len(ap):\\n        print(count)\\n        da=False\\n\", \"a = int(input())\\n \\ndic = {}\\ndic[a] = 1\\n\\ni = 1\\nwhile True:\\n  i += 1\\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n    \\n  if a in dic: break\\n  dic[a] = 1\\n  \\nprint(i)\", \"s = int(input())\\n\\nif s < 3:\\n  print(4)\\n  return\\n\\ncnt = 1\\nval = s\\nwhile True:\\n  if cnt > 1 and val == 1:\\n    break\\n  \\n  if val % 2 == 0:\\n    val = val//2\\n  else:\\n    val = val*3+1\\n    \\n  cnt += 1\\n             \\nprint(cnt+1)\", \"s=int(input())\\ndef calc(n):\\n  if n % 2 == 0:\\n    return n / 2\\n  else:\\n    return 3*n +1\\nans = [s]\\nfor i in range(1000001):\\n  if calc(ans[i]) in ans:\\n    print(len(ans) +1)\\n    return\\n  else:\\n    ans.append(int(calc(ans[i])))\", \"n = int(input())\\na = [n]\\nindex = 0\\n\\nfor i in range(1, 1000000):\\n    if a[i - 1] % 2 == 0:\\n        m = a[i - 1] / 2\\n    else:\\n        m = 3 * a[i - 1] + 1\\n    if m in a:\\n        index = i + 1\\n        break\\n    a.append(m)\\nprint(index)\", \"s = int(input())\\n\\nmax_ = 1000000\\nchk = [0]*max_\\na = s\\ni = 1\\nwhile i <= max_:\\n    if chk[a] == 0:\\n        chk[a] += 1\\n    else:\\n        print(i)\\n        return\\n    if a%2 == 0:\\n        a = int(a/2)\\n    else:\\n        a = 3*a + 1\\n    i += 1\\n\", \"s = int(input())\\n\\nA = [s]\\nidx = 1\\nwhile True:\\n    n = A[idx-1]\\n    if n % 2:\\n        f = 3*n + 1\\n    else:\\n        f = n / 2\\n    idx += 1\\n    A.append(f)\\n    if len(A) != len(set(A)):\\n        break\\nprint(idx)\", \"s = int(input())\\n\\ncount = 1\\nn = s\\ncheck = 0\\nlist = [s]\\n\\n\\nfor i in range(30000):\\n        if n % 2 == 0:\\n            n = n / 2\\n            list.append(n)\\n        else:\\n            n = n*3 + 1\\n            list.append(n)\\n        \\n        count = count + 1\\n        list.sort()\\n        for j in range(len(list) - 1):\\n            if list[j] ==list[j+1]:\\n                check = 1\\n                break\\n            \\n        if check == 1:\\n            break\\n        \\n\\n\\nprint(count)\\n\\n\", \"S = int(input())\\ns, c = S, 1\\nresult = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    elif s % 2 == 1:\\n        s = s * 3 + 1\\n\\n    result.append(s)\\n    c += 1\\n    if len(set(result)) < len(result):\\n        break\\n\\nprint(c)\", \"#-*-coding:utf-8-*-\\nimport sys\\ninput=sys.stdin.readline\\n\\ndef func(n):\\n    ans =0\\n    if n%2==0:\\n        ans=n//2\\n    else:\\n        ans=3*n+1\\n    return ans\\n\\ndef main():\\n    s = int(input())\\n    dp=[s]\\n    counter=0\\n\\n    if s==1 or s==2:\\n        print(4)\\n        return\\n\\n    while counter < 1000001:\\n        n=dp.pop()\\n        tmp = func(n)\\n        dp.append(n)\\n        dp.append(tmp)\\n        counter+=1\\n        if tmp==4:\\n            print(dp.index(tmp)+4)\\n            break\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\nS = int(input())\\n\\na = [S]\\ncnt = 1\\nwhile True:\\n    if S%2 == 0:\\n        S /= 2\\n    else:\\n        S = 3*S + 1\\n    cnt += 1\\n    if S in a:\\n        break\\n    else:\\n        a.append(S)\\n\\nprint(cnt)\", \"s = int(input())\\n\\nnum_lists = [s]\\ncnt = 1\\nwhile True:\\n    if (num_lists[-1])%2 == 0:\\n        tmp = num_lists[-1]/2\\n    else:\\n        tmp =(num_lists[-1]*3)+1\\n    cnt += 1\\n    if tmp in num_lists:\\n        ans = cnt\\n        break\\n    else:\\n        num_lists.append(tmp)\\n\\nprint(ans)\", \"import sys\\ns=int(input())\\n\\ncnt=0\\n\\nif s==1 or s==2:\\n  print('4')\\n  return\\n\\nwhile s!=4:\\n  if s%2!=0:\\n    s=3*s+1\\n    cnt+=1\\n  elif s%2==0:\\n    s=s//2\\n    cnt+=1\\n\\nif s==4:\\n  print(cnt+4)\", \"s=int(input())\\na=[]\\nna=[]\\na.append(s)\\nfor i in range(1,10**6):\\n    if a[i-1]%2==0:\\n        a.append(a[i-1]/2)\\n    else:\\n        a.append(a[i-1]*3+1)\\n    na=set(a)\\n    if len(na)!=i+1:\\n        print(i+1)\\n        return\", \"s = int(input())\\n\\na = []\\na.append(s)\\nfor i in range(1000000):\\n  if a[i]%2 == 0:\\n    a.append(a[i] // 2)\\n  else:\\n    a.append(3*a[i] + 1)\\n  for j in range(i-1):\\n    if a[i+1] == a[j]:\\n      print(len(a))\\n      return\", \"s = int(input())\\ndef p(n):\\n    if n%2 ==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\nl = [s]\\ncnt = 1\\nwhile True:\\n    cnt +=1\\n    s = p(s)\\n    if s in l:\\n        print(cnt)\\n        return\\n    else:\\n        l.append(s)\", \"s = int (input ())\\nl = []\\na = 0\\nl.append (s)\\nfor i in range (1000000):\\n  a += 1\\n  if s%2 == 0:\\n    s = round(s/2)\\n  else:\\n    s = s*3+1\\n  if l.count (s) != 0:\\n    print (a+1)\\n    break\\n  else:\\n    l.append (s)\", \"s = int(input())\\n\\n\\nclass Solution:\\n    def __init__(self,s):\\n        self.s = s\\n    \\n    def function_a(self):\\n        if self.s % 2 == 0:\\n            return self.s / 2\\n        else:\\n            return 3 * self.s + 1\\n    \\n    def answer(self):\\n        list_a = [self.s]\\n        self.s = self.function_a()\\n        ans = 2\\n        while self.s not in list_a:\\n            list_a.append(self.s)\\n            self.s = self.function_a()\\n            ans += 1\\n        print(ans)\\n\\n\\nconditon = Solution(s)\\nconditon.answer()\", \"S = int(input())\\nl = []\\n\\nwhile S not in l:\\n    l.append(S)\\n    if S%2 == 0:\\n        S //=2\\n    else:\\n        S = 3*S + 1\\nprint((len(l)+1))\\n\", \"s = int(input())\\nS = {s}\\ni = 1\\nwhile True:\\n  i += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    break\\n  S.add(s)\\nprint(i)\", \"s = int(input())\\n\\nbox = set()\\nbox.add(s)\\n\\nfor i in range(2, 1000000):\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = s * 3 + 1\\n  if s in box:\\n    print(i)\\n    return\\n  else:\\n    box.add(s)\\n\", \"s = int(input())\\n\\ndef collatz(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\ncoll = s\\ni = 1\\nwhile 1:\\n    if coll == 1 or coll == 2 or coll == 4:\\n        print(i  + 3)\\n        break\\n    coll = collatz(coll)\\n    i += 1\", \"a = int(input())\\n \\nx = set()\\nx.add(a)\\n\\ni = 1\\nwhile True:\\n  i += 1\\n    \\n  if a % 2 == 0: a //= 2\\n  else: a = 3*a + 1\\n  \\n  if a in x: break\\n  x.add(a)\\n  \\nprint(i)\", \"S=int(input())\\n\\na=[S]\\ntemp=S\\n\\ni=0\\n\\nwhile i<200:\\n\\ti+=1\\n\\tif temp%2==0:\\n\\t\\ta.append(temp//2)\\n\\telse:\\n\\t\\ta.append(temp*3+1)\\n\\ttemp=a[-1]\\n\\nfor n in range(200):\\n\\tfor m in range(n+1,200):\\n\\t\\tif a[n]==a[m]:\\n\\t\\t\\tprint(m+1)\\n\\t\\t\\treturn\", \"s=int(input())\\n\\na_list=[s]\\n\\n\\na=s\\nwhile True:\\n    \\n    if a%2==0:\\n        a=a//2\\n    else:\\n        a=3*a+1\\n    \\n    if a in a_list:\\n        break\\n    else:\\n        a_list.append(a)\\n\\nans=len(a_list)+1\\n\\nprint(ans)\", \"s = int(input())\\na = [s]\\n\\ndef func(n):\\n  if n % 2 == 0:\\n    a.append(n//2)\\n  elif n % 2 == 1:\\n    a.append(3*n + 1)\\n  \\ni = 1\\nwhile True:\\n  func(a[-1])\\n  i += 1\\n  if a.count(a[-1]) == 2:\\n    break\\n  else:\\n    pass\\n\\n\\nprint(i)\", \"def f(n):\\n    if n % 2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\n\\ns = int(input())\\ncnt = 0\\na = [s]\\nwhile True:\\n\\n    temp = f(a[cnt])\\n\\n    if temp in a:\\n        print((len(a)+1))\\n        return\\n    a.append(temp)\\n    cnt += 1\\n\", \"s = int(input())\\n\\ndef f(x):\\n    if x%2 == 0:\\n        return int(x/2)\\n    else:\\n        return 3*x + 1\\ni = 1\\nm_max = 1000000\\nb_s = s\\nb = set([s])\\nwhile i <= m_max:\\n    i += 1\\n    a = f(b_s)\\n    if a in b:\\n        break\\n    b.add(a)\\n    b_s = a\\nprint(i)\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"s = int(input())\\na = [s]\\nans = 0\\nfor i in range(1000000):\\n    if a[i] % 2 == 0:\\n        if a[i]/2 in a:\\n            ans = i + 2\\n            break\\n        a.append(a[i]/2)\\n    else:\\n        if 3*a[i] + 1 in a:\\n            ans = i + 2\\n            break\\n        a.append(3*a[i] + 1)\\nprint(ans)\", \"n = int(input())\\nc = 1\\nx = []\\nx.append(n)\\nwhile True:\\n    if n%2 == 0:\\n        n = n//2\\n    else:\\n        n = 3*n+1\\n    c+=1\\n    if n in x:\\n        break\\n    x.append(n)\\nprint(c)\", \"import sys\\ninput = sys.stdin.readline\\n\\n\\ndef main():\\n    S = int(input())\\n\\n    x = set()\\n    x.add(S)\\n\\n    i = 1\\n    prev = S\\n    while True:\\n        i += 1\\n        if prev % 2 == 0:\\n            prev = prev // 2\\n        else:\\n            prev = prev * 3 + 1\\n\\n        if prev in x:\\n            print(i)\\n            return\\n\\n        x.add(prev)\\n\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n\\n__starting_point()\", \"s = int(input())\\narr = []\\nans = 0\\ndef calc(n, cnt):\\n    arr.append(n)\\n\\n    if cnt >= 1000000:\\n        return n\\n\\n    if n % 2 == 0:\\n        n = int(n / 2)\\n    else:\\n        n = int(3 * n + 1)\\n\\n    if n in arr:\\n        return cnt\\n\\n    cnt += 1\\n    calc(n, cnt)\\ncalc(s, 0)\\nprint((len(arr) + 1))\\n\", \"def func(x):\\n  if x%2==0:\\n    return x//2\\n  else:\\n    return 3*x + 1\\nA = [True for i in range(1000001)]\\nN = int(input())\\ncount = 1\\nwhile A[N]:\\n  A[N] = False\\n  N = func(N)\\n  count += 1\\nprint(count)\", \"a = [int(input())]\\n\\ni = 0\\nwhile True:\\n    if a[i]%2 == 0:\\n        a.append(int(a[i]/2))\\n    else:\\n        a.append(int((3*a[i])+1))\\n    if a.count(a[i]) == 2:\\n        break\\n    i += 1\\n\\nprint(i+1)\", \"s = int(input())\\nlist_a = [s]\\n\\nif s % 2 == 0:\\n    s = s / 2\\nelse:\\n    s = 3 * s + 1\\n    \\ncurrent = 2\\nwhile s not in list_a:\\n    list_a.append(s)\\n    if s % 2 == 0:\\n        s = s / 2\\n    else:\\n        s = 3 * s + 1\\n    current += 1\\n\\nprint(current)\\n\", \"s = int(input())\\n\\na = [0,s]\\nfor n in range(2,10**6+1):\\n  if a[n-1] % 2 == 0:\\n    an = a[n-1] // 2\\n  else:\\n    an = a[n-1] * 3 + 1\\n  \\n  if an in a:\\n    m = n\\n    break\\n  \\n  a.append(an)\\n  \\nprint(m)\", \"s=int(input())\\n\\nans=1\\ns_st=set()\\nwhile s not in s_st:\\n  s_st.add(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=3*s+1\\n  ans+=1\\n\\nprint(ans)\", \"import sys\\ns = int(input())\\nf = [0 for _ in range(1000005)]\\nf[s] = 1\\nn = s\\nfor i in range(1000005):\\n  if(n%2==0):\\n    n = int(n/2)\\n  else:\\n    n = int(3*n + 1)\\n  if(f[n] == 1):\\n    print(i+2)\\n    return\\n  else:\\n    f[n] = 1\", \"s = int(input())\\n\\nsec = [s]\\ncount = 1\\nwhile(s):\\n  if sec[-1]%2 == 0:\\n    sec.append(sec[-1]/2)\\n  else:\\n    sec.append(3*sec[-1]+1)\\n  count+=1\\n    \\n  if sec[-1] in sec[:-1]:\\n    print(count)\\n    break\", \"s = int(input())\\nline = [0 for i in range(1000001)]\\nans = 1\\nline[s] += 1\\nwhile True:\\n  ans += 1\\n  if s % 2 == 0:\\n    s = int(s/2)\\n  else:\\n    s = 3*s + 1\\n  line[s] += 1\\n  if line[s] > 1:\\n    break\\nprint(ans)\", \"a = int(input())\\nl = [a]\\nfor i in range(1000000):\\n  if a % 2 == 0:\\n    a = a//2\\n  else:\\n    a = a*3 + 1\\n  if l.count(a)==2:\\n    print((1+max([i for i, x in enumerate(l) if x == a])))\\n    break\\n  else:\\n    l.append(a)\\n\", \"s = int(input())\\na = [s]\\nwhile True:\\n    if s % 2 == 0:\\n        s = s // 2\\n    else:\\n        s = s * 3 + 1\\n    a.append(s)\\n    if a.count(s) == 2:\\n        print(len(a))\\n        break\", \"s = int(input())\\na = [s]\\ni = 0\\nwhile True:\\n    i = i+1\\n    if a[i-1] % 2 == 0:\\n        n = a[i-1]//2\\n    else:\\n        n = 3*a[i-1]+1\\n    if n in a:\\n        print((i+1))\\n        break\\n    a.append(n)\\n\", \"s = int(input())\\na = [s]\\ni = 1\\nwhile True:\\n  if s % 2 == 0:\\n    s = s // 2\\n  else:\\n    s = 3 * s + 1\\n  if s in a:\\n    print(len(a) + 1)\\n    break\\n  a.append(s)\", \"s=int(input())\\ncnt = 1\\nS = [s]\\nwhile(1):\\n  cnt += 1\\n  if s % 2 == 0:\\n    s //= 2\\n  else:\\n    s = 3*s + 1\\n  if s in S:\\n    print(cnt)\\n    break\\n  S.append(s)\\n\", \"def readinput():\\n    s=int(input())\\n    return s\\n\\ndef main(s):\\n    hist=[0]*1000001\\n    i=1\\n    n=s\\n    hist[n]+=1\\n    while hist[n]<=1:\\n        if n%2==0:\\n            n=n//2\\n        else:\\n            n=3*n+1\\n        i+=1\\n        hist[n]+=1\\n    return i\\n\\ndef __starting_point():\\n    s=readinput()\\n    ans=main(s)\\n    print(ans)\\n\\n__starting_point()\", \"s = int(input())\\n\\nmp = [False]*(10**6+1)\\ndef even_f(n):\\n    return n//2\\n\\ndef odd_f(n):\\n    return 3*n+1\\n\\nmp[s]=True\\nnow = s\\nfor i in range(1,10**6+1):\\n    if(now%2==0):\\n        now = even_f(now)\\n    else:\\n        now = odd_f(now)\\n\\n    if(mp[now]):\\n        savei=i\\n        break\\n    mp[now]=True\\n\\nprint((savei+1))\\n        \\n\", \"s = int(input())\\nans = [s]\\ni = 1\\nif s == 1 or s == 2:\\n    ans = 4\\nelse:\\n    while ans[i-1] != 4:\\n        if ans[i-1] % 2 ==0:\\n            ans.append(ans[i-1]//2)\\n        else:\\n            ans.append(ans[i-1]*3 + 1 )\\n        i += 1\\n    ans = i + 3\\nprint(ans)\", \"import sys\\n\\n\\ndef input(): return sys.stdin.readline().strip()\\ndef I(): return int(input())\\ndef LI(): return list(map(int, input().split()))\\ndef IR(n): return [I() for i in range(n)]\\ndef LIR(n): return [LI() for i in range(n)]\\ndef SR(n): return [S() for i in range(n)]\\ndef S(): return input()\\ndef LS(): return input().split()\\n\\n\\nINF = float('inf')\\n\\ns = I()\\nvs = set()\\nvs.add(s)\\nnow = 0 + s\\ni = 1\\nwhile True:\\n    i += 1\\n    now = now / 2 if now % 2 == 0 else 3*now + 1\\n    if now in vs:\\n        break\\n    else:\\n        vs.add(now)\\n\\nprint(i)\\n\", \"s = int(input())\\nlist_a = [s]\\n\\nfor i in range(1000000):\\n    if list_a[i] % 2 == 0:\\n        list_a.append(list_a[i] / 2)\\n    else:\\n        list_a.append(3 * list_a[i] + 1)\\n        \\nfor index, ai in enumerate(list_a, 1):\\n    if ai in list_a[:index - 1]:\\n        print(index)\\n        break\\n\", \"\\nurl = \\\"https://atcoder.jp//contests/abc116/tasks/abc116_b\\\"\\n\\ndef calc(n):\\n    if n % 2 == 0:\\n        return n // 2\\n    else:\\n        return 3 * n + 1\\n\\n\\ndef main():\\n    s = int(input())\\n    ans = [s]\\n    while True:\\n        tmp = calc(ans[-1])\\n        ans.append(tmp)\\n        if ans.index(tmp) != len(ans)-1:\\n            print((len(ans)))\\n            break\\n\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"s=int(input())\\nL=[]\\nn=1\\nwhile not s in L:\\n  L.append(s)\\n  if s%2==0:\\n    s//=2\\n  else:\\n    s=s*3+1\\n  n+=1\\nprint(n)\", \"n = int(input())\\ndata =[0]* 1000000\\ndata[0] = n\\ni = 2\\nif n % 2 == 0:\\n    data[1] = n //2\\nelse:\\n    data[1] = 3 * n + 1\\nwhile data[i - 1] not in data[0: i -2]:\\n    if data[i-1] % 2 == 0:\\n            data[i] = data[i - 1]//2\\n    else:\\n            data[i] = 3 * data[i - 1] + 1\\n    i += 1\\nprint(i)\", \"s=int(input())\\nG =[]\\nwhile (s not in G):\\n  G.append(s)\\n  if s % 2==0:\\n    s = int(s//2)\\n  else:\\n    s = int(3*s+1)\\nprint(len(G)+1)\", \"s = int(input())\\nl = [s]\\na = set(l)\\nfor i in range(10**6):\\n  if l[-1] % 2 == 0:\\n    n = l[-1] // 2\\n  else:\\n    n = 3*l[-1] + 1\\n  if n not in a:\\n    a.add(n)\\n    l.append(n)\\n  else:\\n    print(len(l)+1)\\n    break\", \"a=int(input())\\ns=set()\\ni=1\\nwhile True:\\n    if a in s:\\n        print(i)\\n        break\\n    s|={a}\\n    if a%2==0:\\n        a>>=1\\n    else:\\n        a=3*a+1\\n    i+=1\\n\", \"s = int(input())\\n\\ndef f(n):\\n    if n%2 == 0:\\n        return n/2\\n    else:\\n        return 3*n+1\\n\\nx = set()\\nans = 0\\nwhile True:\\n    ans += 1\\n    if s in x:\\n        print(ans)\\n        break\\n    x.add(s)\\n    s = f(s)\", \"a=int(input())\\ni=1\\nli=[a]\\nimport copy\\nwhile True:\\n    if li[i-1]%2==0:\\n        b=li[i-1]//2\\n    else:\\n        b=3*li[i-1]+1\\n    if b in li:\\n        print((i+1))\\n        return\\n    li.append(b)\\n    i+=1\\n        \\n\", \"s=int(input())\\ndef f(n):\\n    if n%2==0:\\n        return n//2\\n    else:\\n        return 3*n+1\\n\\na=[0]*(10**8)\\na[s]=1\\ncnt=1\\nfor _ in range(10**7):\\n    s=f(s)\\n    cnt+=1\\n    if a[s]:\\n        print(cnt)\\n        break\\n    a[s]=1\\n\", \"s = int(input())\\na = s\\nans = 0\\n\\nif (a == 1)or(a == 2)or(a == 4):\\n    ans = 4\\n\\nelse:\\n\\n    for i in range(10**6 + 1):\\n        if a%2 == 0:\\n            a = int(a/2)\\n        else:\\n            a = 3*a + 1\\n\\n        if a == 4:\\n            ans = i + 5\\n            break\\n\\nprint(ans)\\n\", \"n = int(input())\\n\\ndp = [True]*(n*1000000)\\ndp[n] = False\\nres =1\\nwhile n <1000001:\\n    res +=1\\n    if n % 2 ==1:\\n        n = n*3+1\\n    else:\\n        n = n//2\\n    \\n    if dp[n]:\\n        dp[n] = False\\n    else:\\n        print(res)\\n        return\", \"s = int(input())\\n\\na = [0]*(10**6+1)\\nc = [0]*(10**6+1)\\na[1] = s\\nc[s] = 1\\nfor i in range(2, 10**6+1):\\n    v = a[i-1]//2 if a[i-1] % 2 == 0 else 3*a[i-1]+1\\n    a[i] = v\\n    if c[v] == 1:\\n        print(i)\\n        return\\n    c[v] = 1\", \"S = int(input())\\narray = []\\narray.append(S)\\n\\nwhile True:\\n  count = 0\\n  if S % 2 == 0:\\n    S = S / 2\\n    array.append(S)\\n  else:\\n    S = 3 * S + 1\\n    array.append(S)\\n  for i in range(len(array)):\\n    if S == array[i]:\\n      count += 1\\n      if count == 2:\\n        print((i + 1))\\n        return\\n\", \"a=int(input())\\nb=0\\nif a==2:\\n  print(4)\\nelif a==1:\\n  print(4)\\nelse:\\n  while a!=4:\\n    if a%2==0:\\n      a=a//2\\n      b=b+1\\n    else:\\n      a=3*a+1\\n      b=b+1\\n  print(b+4)\", \"s = int(input())\\n\\nans_list = [s]\\ncurr_value = s\\nindex = 1\\nwhile(True):\\n    if curr_value%2==0:\\n        curr_value = int(curr_value/2)\\n    else:\\n        curr_value = 3*curr_value + 1\\n    index += 1\\n    if curr_value in ans_list:\\n        break\\n    else:\\n        ans_list.append(curr_value)\\nprint(index)\", \"a = int(input())\\ns = set([a])\\n\\nfor i in range(10**6):\\n\\tif a % 2 == 0:\\n\\t\\t# print(\\\"Process for even.\\\")\\n\\t\\ta = a//2\\n\\telse:\\n\\t\\t# print(\\\"Process for odd.\\\")\\n\\t\\ta = 3*a + 1\\n\\tif a not in s:\\n\\t\\ts.add(a)\\n\\telse:\\n\\t\\tprint((i+2))\\n\\t\\tbreak\\n\", \"def f(n):\\n\\tif n % 2 == 0:\\n\\t\\treturn n / 2\\n\\telse:\\n\\t\\treturn 3 * n + 1\\n\\t\\t\\ns = int(input())\\n\\na = []\\nfor i in range(1000000):\\n\\tif i == 0:\\n\\t\\ta.append(s)\\n\\telse:\\n\\t\\tif f(a[-1]) in a:\\n\\t\\t\\tprint(i+1)\\n\\t\\t\\tbreak\\n\\t\\telse:\\n\\t\\t\\ta.append(f(a[-1]))\", \"s = int(input())\\nvisited = [False]*(10**6+1)\\n\\nvisited[s] = True\\ncnt = 1\\n\\nwhile True:\\n    if s & 1:\\n        s = s * 3 + 1\\n    else:\\n        s //= 2\\n    \\n    cnt += 1\\n\\n    if visited[s]:\\n        print(cnt)\\n        break\\n\\n    visited[s] = True\", \"s = int(input())\\na = [s]\\nfor i in range(1, 1000001):\\n    if a[i-1]%2 == 0:\\n        x = a[i-1]//2\\n        if x in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(x)\\n    else:\\n        y = a[i-1]*3 + 1\\n        if y in a:\\n            print(i+1)\\n            break\\n        else:\\n            a.append(y)\", \"from sys import stdin\\n\\ns = int(stdin.readline().strip())\\nmem = []\\na = s\\n\\nfor i in range(1000000):\\n  if a in mem:\\n    print(i+1)\\n    return\\n  mem.append(a)\\n  if a % 2 == 0: a = a // 2\\n  else: a = 3 * a + 1\"]",
        "difficulty": "introductory",
        "input": "27\n",
        "output": "113\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc116/tasks/abc116_b"
    },
    {
        "id": 489,
        "task_id": 4367,
        "test_case_id": 1,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "2 2919\n",
        "output": "3719\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 490,
        "task_id": 4367,
        "test_case_id": 2,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "22 3051\n",
        "output": "3051\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 491,
        "task_id": 4367,
        "test_case_id": 3,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "1 4111\n",
        "output": "5011\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 492,
        "task_id": 4367,
        "test_case_id": 4,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "100 4111\n",
        "output": "4111\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 493,
        "task_id": 4367,
        "test_case_id": 5,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "9 3141\n",
        "output": "3241\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 494,
        "task_id": 4367,
        "test_case_id": 6,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "10 3141\n",
        "output": "3141\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 495,
        "task_id": 4367,
        "test_case_id": 7,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "11 3141\n",
        "output": "3141\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 496,
        "task_id": 4367,
        "test_case_id": 8,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "10 0\n",
        "output": "0\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 497,
        "task_id": 4367,
        "test_case_id": 9,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "3 1741\n",
        "output": "2441\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 498,
        "task_id": 4367,
        "test_case_id": 10,
        "question": "Takahashi is a member of a programming competition site, ButCoder.\nEach member of ButCoder is assigned two values: Inner Rating and Displayed Rating.\nThe Displayed Rating of a member is equal to their Inner Rating if the member has participated in 10 or more contests. Otherwise, the Displayed Rating will be their Inner Rating minus 100 \\times (10 - K) when the member has participated in K contests.\nTakahashi has participated in N contests, and his Displayed Rating is R. Find his Inner Rating.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 100\n - 0 \\leq R \\leq 4111\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN R\n\n-----Output-----\nPrint his Inner Rating.\n\n-----Sample Input-----\n2 2919\n\n-----Sample Output-----\n3719\n\nTakahashi has participated in 2 contests, which is less than 10, so his Displayed Rating is his Inner Rating minus 100 \\times (10 - 2) = 800.\nThus, Takahashi's Inner Rating is 2919 + 800 = 3719.",
        "solutions": "[\"n, r = map(int, input().split())\\n\\nprint(r+100*(10-min(10, n)))\", \"n,x = list(map(int,input().split()))\\nif n >= 10:\\n  print(x)\\nelse:\\n  y = x + (10-n) * 100\\n  print(y)\\n\\n\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"n, r = map(int, input().split())\\nif n < 10:\\n  print((r + 100*(10-n)))\\nelse:\\n  print(r)\", \"n, r = list(map(int, input().split()))\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100 * (10 - n)))\\n\", \"N,R = map(int,input().split())\\nprint(R) if N>=10 else print(R+(100*(10-N)))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\nelse:\\n  print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    ans = r + (100 * (10 - n))\\n    print(ans)\\nelse: \\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n,r = map(int,input().split())\\n\\nif n < 10:\\n  print(100 * (10 - n) + r)\\nelse :\\n  print(r)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  ans=R\\nelse:\\n  ans=R+100*(10-N)\\nprint(ans)\", \"n,r=map(int,input().split())\\n \\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"N, R = map(int, input().split())\\nif N >= 10:\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = list(map(int, input().split()))\\nprint((R+100*(10-N) if N <10 else R))\\n\", \"n, r =map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+1000-100*n)\", \"import os, sys, re, math\\n\\n(N, R) = [int(n) for n in input().split()]\\n\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"N,R = map(int,input().split())\\nprint(R+100*max(0,10-N))\", \"n,r=map(int,input().split())\\nif n<10:\\n  ans=r+(100*(10-n))\\nelse:\\n  ans=r\\nprint(ans)\", \"N,R=map(int,input().split())\\nans=0;\\nif N>=10:\\n  ans+=R\\nelse:\\n  ans+=R+100*(10-N)\\nprint(ans)\", \"N, R = map(int, input().split())\\nans = R + 100*max(0, (10-N))\\nprint(ans)\", \"N , R = [int(x) for x in input().split()]\\nif N >= 10 :\\n  print(R)\\nelse:\\n  print(100*(10-N) + R)\", \"n,r = map(int,input().split())\\nprint(r+100*(10-n) if n<10 else r)\", \"N,R=map(int,input().split())\\nif N>9:\\n  print(R)\\nelse:\\n  print(R+(10-N)*100)\", \"m = input(\\\"\\\")\\nlist = m.split(\\\" \\\")\\nif eval(list[0])<10:\\n    print(eval(list[1])+100*(10-eval(list[0])))\\nif eval(list[0])>=10:\\n    print(eval(list[1]))\", \"n,r=list(map(int,input().split()))\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\\n\\n\", \"n,r = list(map(int,input().split()))\\nprint((r if n>=10 else r+(10-n)*100))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    print(R+100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n  print(r)\\nelse:\\n  print(r + (100 * (10 - n)))\", \"n,r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"n, r = list(map(int, input().split()))\\nif n <= 10:\\n    print((r + (100 * (10 - n))))\\nelse:\\n    print(r)\\n\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+100*(10-N))\", \"n,r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r + 100*(10-n)))\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n  ans = r\\nelse:\\n  ans = r + 100*(10-n)\\nprint(ans)\", \"n,r = list(map(int,input().split()))\\nif(n <=10):\\n  print((r-100*(n-10)))\\nelse:\\n  print(r)\\n\", \"n,k = map(int,input().split())\\nif n >= 10:\\n  print(k)\\nelse:\\n  print(k + (10 - n)* 100 )\", \"N, R = list(map(int, input().split()))\\nif N >= 10:\\n    print(R)\\nelse:\\n    print((R + 100 * (10 - N)))\\n\", \"n,r=map(int,input().split())\\nprint([r+100*(10-n),r][n>=10])\", \"n,r = map(int,input().split())\\nif n >= 10 :\\n    print(r)\\nelse :\\n    k = n\\n    x = r+100*(10-k)\\n    print(x)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n    print(R)\\n    return\\nelse:\\n    print(R + 100 * (10 - N))\\n    return\", \"n,p = map(int,input().split())\\nif n < 10:\\n  rate = p + 100*(10-n)\\nelse:\\n  rate = p\\nprint(rate)\", \"n, r = map(int, input().split())\\nif n < 10:\\n    print(r + 100 * (10 - n))\\nelse:\\n    print(r)\", \"N,R = list(map(int,input().split()))\\n\\nif N<10:\\n  print((100*(10-N)+R))\\nelse:\\n  print (R)\\n\", \"n,r = map(int,input().split())\\n\\nif n >= 10:\\n    print(r)\\n\\nelse:\\n    a = 100 * (10 - n)\\n    b = a + r\\n    print(b)\", \"N, R = map(int, input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  print(R + 100*(10-N))\", \"n,r= map(int, input().split())\\n\\nif n>=10:\\n  print(r)\\nelse:\\n  print(r+100*(10-n))\", \"n,r=map(int,input().split())\\n\\nprint(r) if n>=10 else print(r+100*(10-n))\\n\", \"N, R = list(map(int,input().split()))\\nif N >= 10:\\n  print(R)\\nelse:\\n  print((R + 100*(10-N)))\\n\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n  print(R)\\nelse:\\n  R = R+100*(10-N)\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N = list(map(int,input().split()))\\nif(N[0] < 10):\\n  print(N[1]+(100*(10-N[0])))\\nelse:\\n  print(N[1])\", \"n,r = map(int,input().split())\\nprint(r if n>=10 else r+100*(10-n))\", \"n, r = map(int, input().split())\\nprint(r+100*(10-n) if n < 10 else r)\", \"n,r=map(int,input().split())\\nprint(r-100*min(0,n-10))\", \"N,R=map(int, input().split())\\n\\nif N>=10:\\n    print(str(R))\\nelse:\\n    x=R+(100*(10-N))\\n    print(str(x))\", \"n, r = map(int, input().split(\\\" \\\"))\\nif  n < 10:\\n  print(r + 100 * (10 - n))\\nelse:\\n  print(r)\", \"n, r = map(int,input().split())\\nprint(r if n >= 10 else r + 100*(10-n))\", \"\\ndef main():\\n\\tn, r = list(map(int, input().split()))\\n\\tif n>= 10:\\n\\t\\treturn r\\n\\telse:\\n\\t\\treturn r + (100 * (10 -n))\\n\\t\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"n,r=map(int, input().split())\\nprint(r+100*(10-n)*(n<10))\", \"N, R = map(int,input().split())\\n\\nif N <= 9:\\n    ans = R + (1000-100*N)\\nelse:\\n    ans = R\\nprint(ans)\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+ 100 * (10 - n)))\\n\", \"n, r = map(int,input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"def resolve():\\n\\tn,r = map(int,input().split())\\n\\tprint(r if n>=10 else r+100*(10-n))\\nresolve()\", \"N,R = map(int,input().split())\\nif N <= 10:\\n  print(100 * (10 - N) + R)\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n    print(R)\\nelse:\\n    print(R+100*(10-N))\", \"N, R = map(int, input().split())\\nprint(R+max(1000-100*N, 0))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    r = r + 100*(10-n)\\n    print(r)\", \"N, R = map(int, input().split())\\n\\nif N < 10:\\n    print((100 * (10 - N)) + R)\\nelse:\\n    print(R)\", \"n,r=list(map(int,input().split()))\\nif n<10:\\n  r+=(10-n)*100\\nprint(r)\\n\", \"# coding: utf-8\\n# Your code here!\\n\\n[n,r] = input().split()\\nn = int(n)\\nr = int(r)\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    ans = r + 100*(10-n)\\n    print(ans)\", \"n, r = map(int, input().split())\\n\\nif n < 10:\\n    r += 100*(10-n)\\n\\nprint(r)\", \"N,R=map(int,input().split())\\nprint(R+max(0,(100*(10-N))))\", \"N,R = map(int, input().split())\\nif N < 10:\\n  print(R+(100*(10-N)))\\nelse:\\n  print(R)\", \"N,R=map(int,input().split())\\nif N<10:\\n    print(R+100*(10-N))\\nelse:\\n    print(R)\", \"#!/usr/bin/env python3\\nn,r=list(map(int,input().split()))\\nans=r\\nif n>=10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"N,R = map(int,input().split())\\nprint((R,R +100*(10-N))[N<=10])\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n  print(r)\\n  \\nelse:\\n  print((r + 100*(10 - n)))\\n\\n\", \"n,r=map(int,input().split())\\nif n>=10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R = map(int,input().split())\\n\\nif N >= 10:\\n    print(R)\\n\\nelse:\\n    r = 100*(10-N)\\n    print(r+R)\", \"def main():\\n    N, R = map(int, input().split())\\n\\n    if N >= 10:\\n        print(R)\\n    else:\\n        print(R+(100*(10-N)))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"a, b = map(int, input().split())\\nif a >= 10:\\n    print(b)\\nelse:\\n    print(b+100*(10-a))\", \"N,R=list(map(int,input().split()))\\nif N>=10:\\n    print(R)\\nelse:\\n    K=10-N\\n    I=100*K\\n    print((R+I))\\n\", \"N, R = map(int, input().split())\\n\\nif N >= 10 :\\n    print(R)\\nelse :\\n    print(R + 100 * (10 - N))\", \"n, r = list(map(int, input().split()))\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print((r+100*(10-n)))\\n\", \"n, r = map(int, input().split())\\n\\nif n >=10:\\n  print(r)\\nelse:\\n  print(r + 100 * (10 - n))\", \"N,R = map(int,input().split())\\nif(N >= 10):\\n    print(R)\\nelse:\\n    print(R + 100*(10-N))\", \"N,R = map(int,input().split())\\n\\nif N<10:\\n  print(100*(10-N)+R)\\nelse:\\n  print (R)\", \"N,R=map(int,input().split())\\nif N>=10:\\n  print(R)\\nelse:\\n  print(R+(100*(10-N)))\", \"N, R = list(map(int, input().split()))\\nprint(R if N >= 10 else R + 100*(10-N))\", \"n, r = map(int, input().split())\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r + 100*(10-n))\", \"N,R=map(int,input().split())\\nif N<10:\\n  print(R+100*(10-N))\\nelse:\\n  print(R)\", \"n, r = list(map(int, input().split()))\\nif n < 10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\", \"n, r = map(int, input().split())\\n\\nif n >= 10:\\n    print(r)\\nelse:\\n    print(r+100*(10-n))\", \"N,R=map(int,input().split())\\nif N >= 10:\\n    print (R)\\nelse:\\n    print (100*(10-N)+R)\", \"n, r = list(map(int, input().split()))\\nprint((r if n >= 10 else r + 1000 - (100 * n)))\\n\", \"[N, R] = [int(i) for i in input().split()]\\nprint(R + 100*max(10-N, 0))\", \"n,r=map(int,input().split())\\nif n<10:\\n    print(r+(100*(10-n)))\\nelse:\\n    print(r)\"]",
        "difficulty": "introductory",
        "input": "7 3909\n",
        "output": "4209\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_a"
    },
    {
        "id": 499,
        "task_id": 4368,
        "test_case_id": 1,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "11 2\n",
        "output": "4\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 500,
        "task_id": 4368,
        "test_case_id": 2,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "1010101 10\n",
        "output": "7\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 501,
        "task_id": 4368,
        "test_case_id": 3,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "314159265 3\n",
        "output": "18\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 502,
        "task_id": 4368,
        "test_case_id": 4,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "1000000000 2\n",
        "output": "30\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 503,
        "task_id": 4368,
        "test_case_id": 5,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "1 2\n",
        "output": "1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 504,
        "task_id": 4368,
        "test_case_id": 6,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "282475249 7\n",
        "output": "11\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 505,
        "task_id": 4368,
        "test_case_id": 7,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "282475248 7\n",
        "output": "10\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 506,
        "task_id": 4368,
        "test_case_id": 8,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "282475250 7\n",
        "output": "11\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 507,
        "task_id": 4368,
        "test_case_id": 9,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "25863031 5\n",
        "output": "11\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 508,
        "task_id": 4368,
        "test_case_id": 10,
        "question": "Given is an integer N. Find the number of digits that N has in base K.\n\n-----Notes-----\nFor information on base-K representation, see Positional notation - Wikipedia.\n\n-----Constraints-----\n - All values in input are integers.\n - 1 \\leq N \\leq 10^9\n - 2 \\leq K \\leq 10\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN K\n\n-----Output-----\nPrint the number of digits that N has in base K.\n\n-----Sample Input-----\n11 2\n\n-----Sample Output-----\n4\n\nIn binary, 11 is represented as 1011.",
        "solutions": "[\"n, k = list(map(int, input().split()))\\nans = 0\\n\\nwhile int(n) > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"N, K = map(int, input().split())\\nn = N\\ni = 1\\n\\nwhile 1 > 0:\\n  n = n // K\\n  if n == 0:\\n    print(i)\\n    break\\n  i += 1\", \"n,k = map(int,input().split())\\nl = []\\nwhile n != 0 :\\n    r = divmod(n,k)\\n    n = r[0]\\n    l.append(r[1])\\nprint(len(l))\", \"\\nn,k = list(map(int, input().split()))\\ni=0\\na=[]\\n\\nwhile n!=0:\\n    a.append(n%k)\\n\\n    n=n//k\\n    i=i+1\\n\\nprint((len(a)))\\n\\n\\n\\n\\n\", \"N, K=map(int, input().split())\\ncount=0\\nwhile True:\\n    if N >= pow(K, count):\\n        count+=1\\n    else:break\\nprint(count)\", \"def Base_10_to_n(X, n):\\n    if (int(X/n)):\\n        return Base_10_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn, k = map(int, input().split())\\nprint(len(list(Base_10_to_n(n, k))))\", \"N,K = map(int,input().split())\\nans = 0\\nwhile(K**ans <= N):\\n    ans += 1\\nprint(ans)\", \"nk = list(map(int, input().split()))\\nn, k = nk[0], nk[1]\\ndigit = 0\\n\\nwhile n > k ** digit - 1:\\n    digit += 1\\n\\nprint(digit)\\n\", \"n, k = map(int, input().split())\\n\\nans = 1\\nwhile(True):\\n    n = n//k\\n    if(n == 0):\\n        break\\n    ans += 1\\n\\nprint(ans)\", \"import math  \\ndef findNumberOfDigits(n, b): \\n    dig = (math.floor(math.log(n) /math.log(b)) + 1) \\n    return dig\\nn, k = map(int, input().strip().split())\\nprint(findNumberOfDigits(n, k))\", \"N,K=map(int,input().split())\\ni=0\\nwhile N>=1:\\n  N//=K\\n  i+=1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\nfor a in range(10**9):\\n    if k**a > n:\\n        print(a)\\n        break\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    #print(q)\\n    #print(mod)\\n    if q <=0 :\\n        break\\nif mod_list[-1] == 0:\\n    result = len(mod_list) - 1\\nelse:\\n    result =len(mod_list)\\nprint(result)\", \"N, K = map(int, input().split())\\n\\npower = 1\\n\\nwhile True:\\n    if N < K ** power:\\n        break\\n    else:\\n        power += 1\\n\\nprint(power)\", \"from math import log\\nN, K = map(int, input().split())\\nprint(int(log(N, K))+1)\", \"\\nn, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"n, k = list(map(int, input().split()))\\n\\nfor i in range(10 ** 9):\\n    if n < k ** i:\\n        print(i)\\n        break\\n\", \"#https://atcoder.jp/contests/abc156/tasks/abc156_b\\nN,K = map(int,input().split())\\nq, mod = divmod(N,K)\\nmod_list = [mod]\\nwhile True:\\n    q , mod =divmod(q,K)\\n    mod_list.append(mod)\\n    if q <=0 :\\n        break\\n\\nn_ary = int(\\\"\\\".join(map(str,mod_list[::-1])))\\nprint(len(str(n_ary)))\", \"N,K=map(int,input().split())\\nans=1\\nwhile N>1:\\n    N=N//K\\n    ans+=1\\nif N%K==0:\\n    ans-=1\\nprint(ans)\", \"n, k = map(int, input().split())\\nlists = []\\n\\nwhile True:\\n    if n < k:\\n        lists.append(n)\\n        break\\n    n, b = divmod(n, k)\\n    lists.append(b)\\n\\nans_list = reversed(lists)\\nprint(len(''.join(map(str, ans_list))))\", \"N, K = map(int, input().split())\\ncnt = 0\\nwhile N//K != 0:\\n  N = N//K\\n  cnt += 1\\nprint(cnt+1)\", \"N, K = list(map(int, input().split()))\\n\\ni = 1\\nwhile N // K >= 1:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\\n\", \"N,K = map(int,input().split())\\nketa = 0\\nwhile N>0:\\n  N = N//K\\n  keta = keta + 1\\n\\nprint(keta)\", \"def readinput():\\n    n,k=list(map(int,input().split()))\\n    return n,k\\n\\ndef main(n,k):\\n    keta = 0\\n    while n > 0:\\n        keta += 1\\n        r = n % k\\n        n = n // k\\n    return keta\\n\\ndef __starting_point():\\n    n,k=readinput()\\n    ans=main(n,k)\\n    print(ans)\\n\\n__starting_point()\", \"import os, sys, re, math\\n\\n(N, K) = [int(n) for n in input().split()]\\n\\nd = 0\\na = K ** 0\\nwhile a <= N:\\n    d += 1\\n    a *= K\\n\\nprint(d)\\n\", \"N,K=map(int,input().split())\\nresult=1\\nwhile N>=K:\\n  N=int(N/K)\\n  result+=1\\nprint(result)\", \"n, k = map(int, input().split())\\nans = 1\\nwhile n>=k:\\n    n = n//k\\n    ans += 1\\nprint(ans)\", \"def L():\\n  return list(map(int, input().split()))\\nimport math\\n[n,k]=L()\\n\\nprint(math.floor(math.log(n,k))+1)\", \"n, k = list(map(int, input().split()))\\nlists = []\\nans = 0\\n\\nwhile int(n) > 0:\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 1\\nwhile n // k >  0:\\n    n = n // k\\n    i += 1\\nprint(i)\", \"import math\\nn, k = map(int, input().split())\\n\\nans = 0;\\nwhile(n):\\n    n = int(n / k)\\n    ans += 1\\n\\nprint(ans)\", \"n,k=map(int,input().split())\\ntotal=[]\\n\\nwhile True:\\n    if n>=k:\\n        total.append((n%k))\\n        n=n//k\\n    if n<k:\\n        total.append((n))\\n        break\\nprint(len(total))\", \"N, K = map(int, input().split())\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n, k = map(int, input().split())\\na = 1\\nb = n\\nwhile b >= k:\\n    b = b / k\\n    a += 1\\nprint(a)\", \"def answer(n: int, k: int) -> int:\\n    digits = 0\\n    while 0 < n:\\n        n //= k\\n        digits += 1\\n\\n    return digits\\n\\n\\ndef main():\\n    n, k = map(int, input().split())\\n    print(answer(n, k))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"N, K = map(int, input().split())\\ni = 0\\nwhile N != 0:\\n    N //= K\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ni = 1\\ncnt = 0\\nwhile i <= n:\\n    i *= k\\n    cnt += 1\\nprint(cnt)\", \"def Base_10_to_n(X, n):\\n    if int(X/n):\\n        return Base_10_to_n(int(X/n), n) + str(X%n)\\n    return str(X%n)\\n\\nN, K = list(map(int, input().split()))\\nprint((len(Base_10_to_n(N,K))))\\n\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(1000):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"n,k = map(int,input().split())\\nketa = 1\\nwhile k ** keta <= n:\\n    keta += 1\\nprint(keta)\", \"N,K = list(map(int,input().split()))\\n\\nans = 0\\nwhile True:\\n    if not N - K**ans >= 0:\\n        print(ans)\\n        break\\n    else:\\n        ans += 1\\n\", \"N,K = map(int,input().split())\\nketa = 1\\n\\nwhile N >= K:\\n    keta += 1\\n    N = N / K\\nprint(keta)\", \"import math\\nn, k = map(int, input().split())\\nx = int(math.log(n)//math.log(k)) + 1\\nprint(x)\", \"n, k = map(int, input().split())\\ncount = 0\\nwhile n != 0:\\n  n = n//k\\n  count += 1\\nprint(count)\", \"def main():\\n\\tt, n = list(map(int, input().split()))\\n\\tbinary = 0\\n\\tctr = 0\\n\\ttemp = t  \\n#calculating binary\\n\\twhile(temp > 0):\\n\\t\\tbinary = ((temp%n)*(10**ctr)) + binary\\n\\t\\ttemp = int(temp/n)\\n\\t\\tctr += 1\\n\\treturn len(str(binary))\\n\\ndef __starting_point():\\n    print((main()))\\n\\n__starting_point()\", \"N, K = map(int, input().split())\\n\\nn = 1\\n\\nwhile N >= K**n:\\n    n += 1\\n\\nprint(n)\", \"N,K = map(int,input().split())\\nans = 0\\n\\nwhile(N>0):\\n    N= N//K\\n    ans += 1\\n\\nprint(ans)\", \"# \\u6574\\u6570N\\u3092K\\u9032\\u6570\\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nN,K = map(int,input().split())\\n\\ni = 0\\nwhile N > 0:\\n    N = N // K\\n    i += 1\\n\\nprint(i)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\n\\nwhile N >= K:\\n    N = N // K\\n    ans += 1\\n\\nprint((ans + 1))\\n\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n != 0:\\n    n //= k\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans \\n    count += 1\\n\\nprint(count)\", \"N, K = map(int, input().split())\\n# N\\u304c\\u5341\\u9032\\u6570\\u306e\\u3068\\u304d\\u3001N\\u3088\\u308aK\\u306ei\\u4e57\\u304c\\u8d85\\u3048\\u305f\\u6570\\u306e\\u3068\\u304d\\u3001\\n# i\\u304cK\\u9032\\u6570\\u306e\\u6841\\u6570\\nfor i in range(10 ** 9):\\n    if N < K ** i:\\n        print(i)\\n        break\", \"#abc156b\\nn,k = map(int,input().split())\\nfor i in range(100):\\n    if k**i <= n and n <= k**(i+1)-1:\\n        print(i+1)\\n        break\", \"N,K=map(int,input().split())\\n\\ndef ans156(N:int, K:int):\\n    length=1#0\\u6841\\u306f\\u306a\\u3044\\u305f\\u3081\\u30011\\u304b\\u3089\\u30b9\\u30bf\\u30fc\\u30c8\\n    while True:\\n        if N<K:\\n            break\\n        N=int(N/K)#\\u5272\\u308a\\u5207\\u308c\\u308b\\u3054\\u3068\\u306b1\\u6841\\u305a\\u3064\\u5897\\u3048\\u3066\\u3044\\u304f\\u3002\\n        length+=1\\n    return length\\n\\nprint(ans156(N,K))\", \"n, k = map(int, input().split())\\nlists = []\\nans = 0\\n\\nwhile True:\\n    if n < k:\\n        ans += 1\\n        break\\n    n, b = divmod(n, k)\\n    ans += 1\\n\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\n# \\u6574\\u6570N \\u3092 K\\u9032\\u6570 \\u3067\\u8868\\u3057\\u305f\\u3068\\u304d\\u3001\\u4f55\\u6841\\u306b\\u306a\\u308b\\u304b\\u3092\\u51fa\\u529b\\n# \\u4f4d\\u53d6\\u308a\\u8a18\\u6570\\u6cd5\\uff1ahttps://xtech.nikkei.com/atcl/learning/lecture/19/00049/00001/\\n\\ndigit = 0\\n\\nwhile N > 0:\\n    N = N // K\\n    digit += 1\\n\\nprint(digit)\", \"n,k = map(int,input().split())\\ncnt = 0\\nwhile n//k != 0:\\n    n = n//k\\n    cnt += 1\\n\\nprint(cnt+1)\", \"def resolve():\\n\\tn,k = map(int,input().split())\\n\\tans  = 0\\n\\twhile n!=0:\\n\\t\\tn = n//k\\n\\t\\tans += 1\\n\\tprint(ans)\\nresolve()\", \"N,K=map(int,input().split())\\nrank=1\\nS=K\\n\\nwhile N>=S:\\n  rank+=1\\n  S*=K\\n#  print(S)\\n  \\nprint(rank)\", \"n, k = map(int, input().split())\\nans = 0\\n\\nwhile n > 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\", \"N,K=map(int,input().split())\\nans=0\\nwhile N>0:\\n  N//=K\\n  ans+=1\\nprint(ans)\", \"N, K = map(int, input().split())\\ni = 0\\nwhile K ** i <= N:\\n    i += 1\\nprint(i)\", \"n,k = map(int,input().split())\\ncounter = 0\\nwhile(n >= k):\\n  n = n//k\\n  counter = counter + 1\\nprint(counter+1)\", \"N, K = map(int, input().split())\\n\\n# \\u4f59\\u308a\\u3092\\u4ed8\\u3051\\u52a0\\u3048\\u3066\\u3044\\u304f\\u6587\\u5b57\\u5217\\u3092\\u5b9a\\u7fa9\\nans_str = ''\\n\\n# \\u5272\\u308a\\u7b97\\u306e\\u5546\\u3092\\u8868\\u3059\\u5909\\u6570\\u3092\\u5b9a\\u7fa9\\nn = N\\n\\nwhile (n>=K):\\n    n = n//K\\n    ans_str += str(n%K)\\n    # print(f'n\\uff1a{n}')\\nans_str += str(n)\\n# print(ans_str[::-1])\\nprint(len(ans_str))\", \"N , K = map(int,input().split())\\n\\nD = []\\nwhile (N > 0):\\n    D.append(N % K)\\n    N = N // K\\n\\nprint(len(D))\", \"n,k=list(map(int, input().split()))\\ni=0\\nwhile True:\\n  if k**i>n:\\n    print(i)\\n    break\\n  i+=1\\n\", \"import queue\\nN,K = map(int,input().split())\\nans = queue.Queue()\\nwhile N >= K:\\n    N,amari = divmod(N,K)\\n    ans.put(amari)\\nans.put(N)\\nanswer = \\\"\\\"\\nwhile not ans.empty():\\n    answer += str(ans.get())\\nprint(len(answer))\", \"n,k = map(int, input().split())\\ncnt = 0\\nwhile n>0:\\n  cnt += 1\\n  n //= k\\nprint(cnt)\", \"N,K = map(int, input().split())\\ncount = 0\\nwhile N > 0:\\n    N //= K\\n    count += 1\\n\\nprint(count)\", \"N,K=list(map(int,input().split()))\\nanswer=1\\n\\nif K==10:\\n  Str=str(N)\\n  answer=len(Str)\\n  print(answer)\\n  return\\n\\nwhile N//K>0:\\n  N=N//K\\n  answer+=1\\n\\nprint(answer)\\n\", \"N,K = map(int,input().split())\\n\\ni = 0\\nanslist = []\\nwhile True:\\n  if N>=K:\\n    i+=1\\n    anslist.append(N%K)\\n    N = N//K\\n    #print (N)\\n  if N<K:\\n    anslist.append(N)\\n    i+=1\\n    break\\n    \\nanslist.reverse()\\n#print (anslist)\\n#print (''.join(map(str, anslist)))\\nprint (i)\", \"N, K = map(int,input().split())\\ncount = 0\\n\\nwhile N >= 1:\\n    ans = N // K\\n    N = ans\\n    count += 1\\n\\nprint(count)\", \"n,k=map(int,input().split())\\nnum=k\\nans=1\\nwhile num-1<n:\\n    ans+=1\\n    num*=k\\nprint(ans)\", \"N, K = map(int, input().split())\\n\\nn = 1\\nwhile True:\\n    if K ** (n - 1) <= N < K ** n:\\n        break\\n    n += 1\\n\\nprint(n)\\nreturn\", \"import math\\nn,k=list(map(int,input().split()))\\na=int(math.log(n,k))+1\\nprint(a)\\n\", \"n, k = list(map(int, input().split()))\\n\\nanswer = n // k\\ncount = 1\\nwhile 0 < answer:\\n    answer = answer // k\\n    count += 1\\n\\nprint(count)\\n\", \"n, k = map(int, input().split())\\nans = 1\\nn1 = n\\nwhile n1 // k >= 1:\\n    n1 = n1 // k\\n    ans += 1\\nprint(ans)\", \"N, K = map(int, input().split())\\nprint(sum(N >= K ** i for i in range(99)))\", \"def Ten_to_n(X, n):\\n    if (int(X/n)):\\n        return Ten_to_n(int(X/n), n)+str(X%n)\\n    return str(X%n)\\n\\nn,k=list(map(int, input().split()))\\nprint((len(Ten_to_n(n,k))))\\n\", \"integer, base = map(int, input().split())\\nconverted_number = ''\\nwhile integer > 0:\\n    converted_number += str(integer % base)\\n    integer //= base\\nprint(len(converted_number[::-1]))\", \"n, k = map(int, input().split())\\na = 1\\nb = k\\nwhile n >= b:\\n    b = b * k\\n    a += 1\\nprint(a)\", \"def calc_digits(n: int, k: int) -> str:\\n    if int(n / k):\\n        return calc_digits(int(n / k), k) + str(n % k)\\n\\n    return str(n % k)\\n\\n\\nn, k = list(map(int, input().split()))\\n\\nprint((len(calc_digits(n, k))))\\n\", \"N,K=map(int,input().split())\\ni = 0\\nwhile N >= K ** i :\\n    i += 1\\nelse :\\n    print(i)\", \"n, k = map(int, input().split())\\n\\nm = 0\\nwhile True:\\n    m += 1\\n    if k**m > n:\\n        print(m)\\n        break\", \"n, k = map(int, input().split())\\n\\nans = []\\nwhile n > 0:\\n  ans.append(n % k)\\n  n /= k\\n  n = int(n)\\nprint(len(ans))\", \"N, K = list(map(int, input().split()))\\ncnt = 0\\nwhile N > 0:\\n    cnt += 1\\n    N //= K\\nprint(cnt)\", \"n, k = list(map(int, input().split()))\\na = 1\\nwhile n >= k ** a:\\n    a += 1\\nprint(a)\\n\\n\", \"n,k=map(int,input().split());p=[]\\nwhile n:\\n  p.append(n%k)\\n  n//=k\\nprint(len(p))\", \"def main():\\n  N, K = map(int, input().split())\\n  \\n  if N < K:\\n    print(1)\\n    return\\n\\n  cnt = 0\\n  while N > 0:\\n    N = N // K\\n    cnt += 1\\n\\n  print(cnt)\\n\\n\\nmain()\", \"n, k = list(map(int, input().split()))\\nl = []\\n\\nwhile (n > 0):\\n    l.append(n%k)\\n    n //= k\\nprint((len(l)))\\n\", \"N, K = map(int,input().split())\\ncount = 1\\nwhile N >= K:\\n    N = N // K\\n    count += 1\\nprint(count)\", \"N, K = map(int,input().split())\\nans = 1\\nwhile(N >= K):\\n    N = N//K\\n    ans += 1\\nprint(ans)\", \"def base10toK_base(num, K):\\n    if num // K:\\n        return base10toK_base(num//K, K) + str(num % K)\\n    return str(num % K)\\n\\nN, K = map(int, input().split())\\nans = len(base10toK_base(N, K))\\nprint(ans) \", \"n, k = list(map(int, input().split()))\\n\\nans = 0\\nwhile n != 0:\\n    n = n // k\\n    ans += 1\\n\\nprint(ans)\\n\", \"n, k = map(int, input().split())\\nans=1\\nwhile k**ans <= n:\\n  ans += 1\\nprint(ans)\", \"n = input()\\nn = n.split()\\nk = int(n[1])\\nn = int(n[0])\\na = 1\\nb = 0\\nwhile a == 1:\\n    b = b + 1\\n    if k**b>n:\\n        a = 0\\nprint(b)\", \"N, K = list(map(int,input().split()))\\n\\nans = 0\\nx = 1\\n\\nwhile x <= N:\\n  x *= K\\n  ans +=1\\n  \\nprint(ans)\\n\", \"n,k = map(int,input().split())\\ni = 0\\nwhile k**i <= n:\\n  i += 1\\nprint(i)\", \"n, k = map(int, input().split())\\n\\n# k\\u306e\\u3079\\u304d\\u4e57\\u3067n\\u3092\\u8d85\\u3048\\u308b\\u6700\\u5927\\u306e\\u51aa\\u6570\\u3092\\u6c42\\u3081\\u308b\\n# \\u6700\\u5927\\u306e\\u51aa\\u6570\\u304b\\u3089\\u9806\\u306b\\u3068\\u308a\\u5c3d\\u304f\\u3057\\u3066\\u3044\\u304f\\n# \\u518d\\u5e30\\u3067\\u66f8\\u3051\\u308b\\uff1f\\n\\ndef max_beki(number, k):\\n    beki = 0\\n    while k**beki <= number:\\n        beki += 1\\n    return beki\\n\\nres = []\\nwaru_kazu = k**(max_beki(n, k) - 1)\\nwhile waru_kazu >= 1:\\n    shou = n//waru_kazu\\n    res.append(str(shou))\\n    n -= shou*waru_kazu\\n    waru_kazu /= k\\n\\nprint(len(res))\"]",
        "difficulty": "introductory",
        "input": "801037529 8\n",
        "output": "10\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc156/tasks/abc156_b"
    },
    {
        "id": 509,
        "task_id": 4543,
        "test_case_id": 1,
        "question": "AtCoDeer the deer has found two positive integers, a and b.\nDetermine whether the concatenation of a and b in this order is a square number.\n\n-----Constraints-----\n - 1 ≤ a,b ≤ 100\n - a and b are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\na b\n\n-----Output-----\nIf the concatenation of a and b in this order is a square number, print Yes; otherwise, print No.\n\n-----Sample Input-----\n1 21\n\n-----Sample Output-----\nYes\n\nAs 121 = 11 × 11, it is a square number.",
        "solutions": "[\"\\n#ABC086B\\na,b = input().split()\\na += b\\na = int(a)\\nprint(\\\"Yes\\\" if int((a**.5))**2 == a else \\\"No\\\")\", \"a, b = input().split()\\nab = int(a+b)\\n\\nfor j in range(ab):\\n    if j ** 2 <= ab:\\n        if j ** 2 == ab:\\n            print(\\\"Yes\\\")\\n            return\\n    else:\\n        print(\\\"No\\\")\\n        return\", \"#-*-coding:utf-8-*-\\nimport sys\\nimport math\\ninput=sys.stdin.readline\\n\\ndef main():\\n    a,b = input().split()\\n    number=0\\n\\n    number=int(a+b)\\n    for i in range(100101):\\n        if i * i ==number:\\n            print(\\\"Yes\\\")\\n            return\\n        else:\\n            continue\\n    print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"a, b = (i for i in input().split())\\nc = int(a + b)\\nans = c ** 0.5\\nif float.is_integer(ans): print('Yes')\\nelse: print('No')\", \"a,b=map(str,input().split())\\nx = a+b\\nx = int(x)\\ny = x**0.5\\nif y.is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b=input().split()\\nx=int(a)*10**len(b)+int(b)\\n\\nfor i in range(0,1000):\\n    if i*i==x:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b=map(int,input().split())\\n\\ndef ans086(a:int, b:int):\\n    ab=int(str(a)+str(b))\\n    import math\\n    if int(math.sqrt(ab))**2==ab:\\n        return(\\\"Yes\\\")\\n    else:\\n        return(\\\"No\\\")\\n\\nprint(ans086(a,b))\", \"a,b=map(str,input().split())\\nans = a+b\\nif (int(ans) ** 0.5).is_integer():\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b = input().split()\\n\\na_b = a + b\\na_b = int(a_b)\\n\\nfor i in range(a_b):\\n    if i * i == a_b:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\", \"num = int(''.join(input().split()))\\nroot = num ** .5\\n\\nprint(('Yes' if root.is_integer() else 'No'))\\n\", \"import math\\nx = int(input().replace(' ',''))\\ny = int(math.sqrt(x))\\nif y * y == x:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"import math\\na,b = map(int, input().split())\\nab = str(a) + str(b)\\n\\nif math.sqrt(int(ab))%1 == 0:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na, b = map(str, input().split())\\nans = int(a+b)\\nfor i in range(ans):\\n    route = pow(i, 2)\\n    if ans == route:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\", \"a, b = map(int, input().split())\\nm = b + a * 10 ** len(str(b))\\nfind = False;\\nfor i in range(m):\\n  if m == i ** 2:\\n    find = True;\\nif find:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=int(a+b)\\nfor i in range(1,1001):\\n    if i**2==c:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\\nreturn\\n\", \"a, b = input().split()\\nx = int(a+b)\\nno = 0\\nfor i in range(1000):\\n    if x == i**2:\\n        print(\\\"Yes\\\")\\n    else:\\n        no += 1\\n        if no == 1000:\\n            print(\\\"No\\\")\", \"import math\\n\\ndef main():\\n    a, b = input().split(\\\" \\\")\\n    x = math.sqrt(int(a + b))\\n    \\n    print((\\\"Yes\\\" if x.is_integer() else \\\"No\\\"))\\n\\n\\nmain()\\n\", \"import math\\n\\na, b = input().split()\\ns = a + b\\ni = int(s)\\nr = math.sqrt(i)\\nif r.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a, b = map(int,input().split())\\n\\nfor i in range(2, 400):\\n    if (10**(len(str(b))) * a + b) == i**2:\\n        ans = 'Yes'\\n        break\\n    else:\\n        ans = 'No'\\nprint(ans)\", \"N = int(input().replace(' ', ''))\\nprint('Yes' if N == int(N**(1/2))**2 else 'No')\", \"import math \\n\\nlist=input().split()\\n\\nnum=int(list[0]+list[1])\\n\\nnum_squrt=math.sqrt(num)\\n\\nif num_squrt.is_integer()==True:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na,b = input().split()\\nn = int(a+b)\\nif math.sqrt(n) % 1 == 0:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b=map(str, input().split())\\nq=0\\nfor i in range(1000):\\n  if int(a+b)==i**2:\\n    print('Yes')\\n    q=1\\n    break\\nif q==0:\\n    print('No')\", \"import math\\na, b = map(str, input().split())\\n\\ns = a + b\\ns = int(s)\\nr = math.sqrt(s)\\nfr = r - int(r)\\nif fr == 0:\\n  print('Yes')\\nelse:\\n  print('No')\", \"import math\\n\\na, b = list(map(str, input().split()))\\nx = int(a + b)\\n\\nif math.sqrt(x).is_integer():\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a,b = input().split()\\nc = int(a + b)\\nif (c**0.5).is_integer() == True:\\n    print('Yes')\\nelse:\\n    print('No')\", \"def resolve():\\n    from math import sqrt\\n    \\n    n = int(\\\"\\\".join(input().split()))\\n    print(\\\"Yes\\\" if n == int(sqrt(n)) ** 2 else \\\"No\\\")\\n\\n\\ndef __starting_point():\\n    resolve()\\n__starting_point()\", \"a, b = input().split()\\ns = int(a+b)\\nresult = 'No'\\nfor i in range(1,round(s)):\\n  if s/i == i:\\n    result = 'Yes'\\n    \\nprint(result)\", \"N = int(input().replace(\\\" \\\",\\\"\\\"))\\n\\nflag = False\\nfor i in range(1,10000):\\n  if N == i**2:\\n    flag = True\\n    break\\n  if N < i**2:\\n    break\\nif flag:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"p = input().split()\\na = int(f\\\"{p[0]}{p[1]}\\\")\\nprint( \\\"Yes\\\" if a == int((a ** 0.5)) **2 else \\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=int(a+b)\\nx=c**(1/2)\\nif x.is_integer():\\n    print('Yes')\\nelse :\\n    print('No')\\n\", \"a,b=input().split()\\n\\nd=int(a+b)\\n\\nfor i in range(1000):\\n    if d==i**2:\\n        print(\\\"Yes\\\")\\n        break\\n\\nlis=[j**2!=d for j in range(1000)]\\nif all(lis)==True:\\n    print(\\\"No\\\")\\n\", \"import math\\n\\na, b = input().split()\\nnum = int(a+b)\\n\\nif math.sqrt(num).is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b =list(map(str,input().split()))\\nx = int(a+b)**0.5\\n\\nif x - int(x) == 0:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b = list(input().split())\\nnum = int(a+b)\\nans = round(num**0.5)\\nif ans**2 == num:\\n\\tprint(\\\"Yes\\\")\\nelse:\\n\\tprint(\\\"No\\\")\", \"import math\\na,b = list(map(int,input().split()))\\nnumber = int(str(a)+str(b))\\nroot = math.sqrt(number)\\nif int(root + 0.5) ** 2 == number:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na = input(\\\"\\\").split(\\\" \\\")\\na = [int(aa) for aa in a]\\nn = int(str(a[0])+str(a[1]))\\nr = math.sqrt(n)\\nif r**2 == int(r)**2:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=a+b\\nc=int(c)\\nfor i in range(1001):\\n  if i**2==c:\\n    print(\\\"Yes\\\")\\n    return\\nprint(\\\"No\\\")\\n\", \"a, b = map(int, input().split())\\n\\nc = int(str(a)+str(b))\\n\\nl = []\\n\\nfor i in range(10, 100100):\\n    if (i ** .5).is_integer():\\n        l.append(i)\\n\\nfor i in l:\\n    if c == i:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"import math\\na, b = input().split()\\n\\nif math.sqrt(int(a + b)) == int(math.sqrt(int(a + b))):\\n  print('Yes')\\nelse:\\n  print('No')\", \"import math\\na,b = input().split()\\nq = int(a+b)\\nif math.sqrt(q)//1 == math.sqrt(q):\\n  print(\\\"Yes\\\")\\nelse:\\n  print('No')\", \"from math import sqrt\\na, b = input().split()\\nn = int(a+b)\\nprint(('Yes' if sqrt(n) == int(sqrt(n)) else 'No'))\\n\", \"import math\\ns = input()\\ns = int(s.replace(\\\" \\\", ''))\\nif math.sqrt(s) == int(math.sqrt(s)):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    ab = int(input().replace(\\\" \\\", \\\"\\\"))\\n    print((\\\"Yes\\\" if int(ab**.5)**2 == ab else \\\"No\\\"))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\n\\n\\ndef answer(a: int, b: int) -> str:\\n    joined_value = int(str(a) + str(b))\\n    return 'Yes' if math.sqrt(joined_value) % 1 == 0 else 'No'\\n\\n\\ndef main():\\n    a, b = list(map(int, input().split()))\\n    print((answer(a, b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\na, b = input().split()\\n\\njudge = int(a+b)\\n\\nif any(i**2 == judge for i in range(judge//2)):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import sys\\na,b=map(str,input().split())\\n\\nc=a+b\\nc=int(c)\\n\\nfor i in range(c//2):\\n    if c==i**2:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"#!/usr/bin/env python3\\nimport sys\\nsys.setrecursionlimit(10**6)\\n\\n\\na, b = list(map(str, input().split()))\\n\\n\\nnum = int(a+b)\\n\\nif num == int(num**0.5)**2:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"n=int(input().replace(\\\" \\\",\\\"\\\"))\\nprint(\\\"Yes\\\" if (n**0.5).is_integer() else \\\"No\\\")\", \"import math\\n\\na, b = input().split()\\nn = int(a + b)\\nprint('Yes') if math.sqrt(n) % 1 == 0 else print('No')\", \"a=int(input().replace(\\\" \\\",\\\"\\\"))\\nprint(\\\"Yes\\\" if int(a**0.5)==a**0.5 else 'No')\", \"a, b = map(str, input().split())\\nans = \\\"No\\\"\\nkey = int(a+b)\\nfor i in range(1000):\\n    if i**2 == key:\\n        ans =\\\"Yes\\\"\\n        break\\nprint(ans)\", \"import numpy as np\\n\\na, b = input().split(' ')\\n\\nc = int(a + b)\\n\\nsqrt_c = np.sqrt(c)//1\\n\\nif(sqrt_c**2 == c) :\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"x = int(''.join(input().split()))\\na = 1\\nwhile True:\\n    aa = a * a\\n    if aa == x:\\n        print(\\\"Yes\\\")\\n        return\\n    elif aa > x:\\n        print(\\\"No\\\")\\n        return\\n    a += 1\", \"from math import ceil, sqrt\\na, b = input().split()\\n\\nsq = sqrt(int(a+b))\\nf = sq - int(sq)\\nprint(('Yes' if ceil(f) == 0 else 'No'))\\n\", \"a, b = [i for i in input().split()]\\nt = int(a + b)\\nans = 'No'\\nn = 1\\nwhile n*n <= t:\\n    if n*n == t:\\n        ans = 'Yes'\\n    n += 1\\nprint(ans)\\n\", \"import math\\nab=list(input().split())\\ns=int(''.join(ab))\\n\\nroot=int(math.sqrt(s))\\nif root*root==s: print('Yes')\\nelse: print('No')\", \"import math\\na, b = list(map(str, input().split()))\\n\\ntarget = math.sqrt(int(a+b))\\n\\nif target.is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\\n\\n\", \"import math\\n\\na, b = input().split()\\nn = int(a + b)\\n\\nif n == round(math.sqrt(n))**2:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na,b = input().split()\\nc = int(a + b)\\n\\nd = math.sqrt(c)\\nprint(\\\"Yes\\\" if d == int(d) else \\\"No\\\")\", \"a,b = map(str,input().split())\\nc = int(a + b)\\n\\nfor i in range(int(c ** 0.5), int(c ** 0.5) + 1 ):\\n    if i ** 2 == c:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"#!/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\nimport math\\n\\nIS = lambda: int(input())\\nIA = lambda: [int(x) for x in input().split()]\\n\\na, b = IA()\\n\\nab = int(str(a) + str(b))\\nrt = math.sqrt(ab)\\nprint((\\\"Yes\\\" if int(rt) ** 2 == ab else \\\"No\\\"))\\n\", \"#!/usr/bin/env python3\\nimport sys\\n\\nYES = \\\"Yes\\\"  # type: str\\nNO = \\\"No\\\"  # type: str\\n\\n\\ndef solve(a: int, b: int):\\n    c = int(str(a) + str(b))\\n    for i in range(400):\\n        if c == i*i:\\n            print(YES)\\n            break\\n    else:\\n        print(NO)\\n    return\\n\\n\\n# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    a = int(next(tokens))  # type: int\\n    b = int(next(tokens))  # type: int\\n    solve(a, b)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"a=input().split()\\nb=int(\\\"\\\".join(a))\\n\\nnum=int(100100**1/2)\\n\\nans=\\\"No\\\"\\nfor i in range(num):\\n    if i**2==b:\\n        ans=\\\"Yes\\\"\\n        break\\n    \\nprint(ans)\", \"a,b = input().split()\\nab = int(a+b)\\nprint(\\\"Yes\\\" if (ab**0.5).is_integer() else \\\"No\\\")\", \"import math\\na, b = list(map(int, input().split()))\\nc = 0\\n\\nif b < 10:\\n    c = a*10 + b\\nelif 10 <= b <= 99:\\n    c = a*100 + b\\nelif b == 100:\\n    c = a*1000 + b\\n\\nd = math.sqrt(c)\\n\\nif d.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b = map(str,input().split())\\nc = int(a + b)\\nif c ** 0.5 ==int(c ** 0.5):\\n  print('Yes')\\nelse:\\n  print('No')\", \"print(('Yes' if int(''.join(input().split())) ** 0.5 % 1 == 0 else 'No'))\\n\\n\", \"a, b = input().split()\\nt = int(a + b)\\nans = 'No'\\nn = 1\\nwhile n*n <= t:\\n    if n*n == t:\\n        ans = 'Yes'\\n    n += 1\\nprint(ans)\", \"import math\\na,b = list(map(str,input().split()))\\nc = int(a+b)\\nif int(math.sqrt(c))**2 == c:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a, b = input().split()\\nt = int(a + b)\\nfor i in range(1,10 ** 3):\\n    if t == (i * i):\\n        print('Yes')\\n        return\\nprint('No')\\n\", \"import sys\\nc = [i for i in input().split()]\\nab = int(c[0]+c[1])\\nfor i in range(int(100100**0.5)+1):\\n    if i**2 == ab:\\n        print(\\\"Yes\\\")\\n        return\\n\\nprint(\\\"No\\\")\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return map(int,input().split())\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\na = L()\\nb = \\\"\\\".join(a)\\nb = int(b)\\nfor i in range(1000):\\n    if b == i**2:\\n        print(\\\"Yes\\\")\\n        return\\n \\nprint(\\\"No\\\")\", \"# import math\\n# import statistics\\n#a=input()\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\ne1,e2 = list(map(str,input().split()))\\n#K = input()\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\ncount=0\\na=e1+e2\\nfor i in range(1,int(a)):\\n\\tif int(a)/int(i)==int(i):\\n\\t\\tcount+=1\\nif count>0:\\n\\tprint('Yes')\\nelse:\\n\\tprint('No')\\n\", \"n = int(input().replace(' ', ''))\\nx = int(n ** 0.5)\\nprint('Yes' if x * x == n else 'No')\", \"ab = int(input().replace(\\\" \\\", \\\"\\\"))\\nans = False\\nfor i in range(320):\\n    if i * i == ab:\\n        ans = True\\n        break\\nprint(\\\"Yes\\\") if ans else print(\\\"No\\\")\", \"ab = int(\\\"\\\".join(input().split()))**0.5\\n\\nif ab.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na, b = map(str, input().split( ))\\nA = int(a+b)\\n\\nif math.sqrt(A).is_integer() == True:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b=map(str,input().split())\\nab=int(a+b)\\n\\nans=\\\"No\\\"\\nfor i in range(1010):\\n    x=i**2\\n    if x==ab:\\n        ans=\\\"Yes\\\"\\n        break\\n\\nprint(ans)\", \"#!/usr/local/bin/python3\\n# https://atcoder.jp/contests/abc086/tasks/abc086_b\\nimport math\\n\\na, b = input().split()\\n\\nif math.sqrt(int(a+b)).is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b = map(int,input().split())\\nc = int(str(a) + str(b))\\nfor i in range(c):\\n    if i ** 2 == c:\\n        print('Yes')\\n        break\\n    elif i ** 2 > c:\\n        print('No')\\n        break\", \"n = int(\\\"\\\".join(input().split()))\\nx = n**0.5\\nif x == int(x):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b = input().split()\\na = int(a + b)\\n\\nfor i in range(1000):\\n    if i ** 2 == a:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\\n\", \"import math\\na,b=input().split()\\nc=int(a+b)\\nd=math.sqrt(c)\\ne=math.floor(d)\\nif e**2==c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na, b = list(map(int, input().split()))\\nc = 0\\n\\nif b < 10:\\n    c = a*10 + b\\nelif 10 <= b <= 99:\\n    c = a*100 + b\\nelif b == 100:\\n    c = a*1000 + b\\n\\nd = math.sqrt(c)\\n\\nif d.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#\\n# abc086 b\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"1 21\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"100 100\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"12 10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B = input().split()\\n\\n    C = int(A+B)\\n    for i in range(1, 100100):\\n        if i**2 == C:\\n            print(\\\"Yes\\\")\\n            break\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"a,b = map(str,input().split())\\nfrom math import sqrt\\nprint(\\\"Yes\\\" if sqrt(int(a+b)) == int(sqrt(int(a+b))) else \\\"No\\\")\", \"a,b=map(str,input().split())\\nc=a+b\\nfor i in range(1,350):\\n    if int(c)==i**2:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\", \"a,b = map(str,input().split())\\nc = int(a + b)\\nd = int(c ** 0.5)\\n\\n\\nif d ** 2 == c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na,b = map(str, input().split())\\nab = int(a+b)\\nsq = math.sqrt(ab)\\nif sq % 1 < 0.01:\\n  sq2 = sq**2\\n  if sq2 == ab:\\n    ans = 'Yes'\\n  else:\\n    ans = 'No'\\nelse:\\n  ans = 'No'\\nprint(ans)\", \"a, b = input().split()\\nab = int(a+b)\\nimport math\\nif math.sqrt(ab).is_integer():\\n  print('Yes')\\nelse:\\n  print('No')\", \"a,b=input().split()\\ns=0\\ns += int(b)\\ns += int(a)*(10**len(b))\\nfor i in range(320):\\n    if s==i*i:\\n        print('Yes')\\n        return\\nprint('No')\\n\", \"import math\\n\\na, b = map(int, input().split())\\nx = int(str(a) + str(b))\\nif math.sqrt(x) == math.ceil(math.sqrt(x)):\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"a, b = list(map(str, input().split(\\\" \\\")))\\n\\nans = False\\nfor i in range(1000):\\n    if int(a + b) == i ** 2:\\n        ans = True\\n\\nprint((\\\"Yes\\\" if ans else \\\"No\\\"))\\n\", \"from math import sqrt\\na,b=input().split()\\nc=int(a+b)\\nd=int(sqrt(c))\\nprint(\\\"Yes\\\" if d**2==c else \\\"No\\\")\", \"a, b = input().split()\\nab = int(a+b)\\ni = 0\\nwhile i**2 <= ab:\\n    flag = (i**2 == ab)\\n    i = i+1\\nif flag:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\n\\na, b = map(str, input().split())\\n\\nX = int(a) * (10 ** len(b)) + int(b)\\n\\nif math.sqrt(X) % 1 == 0:\\n  print('Yes')\\nelse:\\n  print('No')\", \"from math import sqrt\\na, b = input().split()\\nc = a + b\\nif sqrt(int(c)) == int(sqrt(int(c))):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"from math import *\\nlst = input().split()\\n\\nif (sqrt(int(lst[0] + lst[1])) % 1) == 0:\\n   print('Yes')\\nelse:\\n   print('No')\", \"import math\\n\\na, b = input().split()\\nc = int(a + b)\\n\\nfor i in range(int(math.sqrt(c))+1):\\n  if c == i*i:\\n    print(\\\"Yes\\\")\\n    break\\nelse:\\n  print(\\\"No\\\")\\n  \\n\"]",
        "difficulty": "introductory",
        "input": "1 21\n",
        "output": "Yes\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc086/tasks/abc086_b"
    },
    {
        "id": 510,
        "task_id": 4543,
        "test_case_id": 2,
        "question": "AtCoDeer the deer has found two positive integers, a and b.\nDetermine whether the concatenation of a and b in this order is a square number.\n\n-----Constraints-----\n - 1 ≤ a,b ≤ 100\n - a and b are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\na b\n\n-----Output-----\nIf the concatenation of a and b in this order is a square number, print Yes; otherwise, print No.\n\n-----Sample Input-----\n1 21\n\n-----Sample Output-----\nYes\n\nAs 121 = 11 × 11, it is a square number.",
        "solutions": "[\"\\n#ABC086B\\na,b = input().split()\\na += b\\na = int(a)\\nprint(\\\"Yes\\\" if int((a**.5))**2 == a else \\\"No\\\")\", \"a, b = input().split()\\nab = int(a+b)\\n\\nfor j in range(ab):\\n    if j ** 2 <= ab:\\n        if j ** 2 == ab:\\n            print(\\\"Yes\\\")\\n            return\\n    else:\\n        print(\\\"No\\\")\\n        return\", \"#-*-coding:utf-8-*-\\nimport sys\\nimport math\\ninput=sys.stdin.readline\\n\\ndef main():\\n    a,b = input().split()\\n    number=0\\n\\n    number=int(a+b)\\n    for i in range(100101):\\n        if i * i ==number:\\n            print(\\\"Yes\\\")\\n            return\\n        else:\\n            continue\\n    print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"a, b = (i for i in input().split())\\nc = int(a + b)\\nans = c ** 0.5\\nif float.is_integer(ans): print('Yes')\\nelse: print('No')\", \"a,b=map(str,input().split())\\nx = a+b\\nx = int(x)\\ny = x**0.5\\nif y.is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b=input().split()\\nx=int(a)*10**len(b)+int(b)\\n\\nfor i in range(0,1000):\\n    if i*i==x:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b=map(int,input().split())\\n\\ndef ans086(a:int, b:int):\\n    ab=int(str(a)+str(b))\\n    import math\\n    if int(math.sqrt(ab))**2==ab:\\n        return(\\\"Yes\\\")\\n    else:\\n        return(\\\"No\\\")\\n\\nprint(ans086(a,b))\", \"a,b=map(str,input().split())\\nans = a+b\\nif (int(ans) ** 0.5).is_integer():\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b = input().split()\\n\\na_b = a + b\\na_b = int(a_b)\\n\\nfor i in range(a_b):\\n    if i * i == a_b:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\", \"num = int(''.join(input().split()))\\nroot = num ** .5\\n\\nprint(('Yes' if root.is_integer() else 'No'))\\n\", \"import math\\nx = int(input().replace(' ',''))\\ny = int(math.sqrt(x))\\nif y * y == x:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"import math\\na,b = map(int, input().split())\\nab = str(a) + str(b)\\n\\nif math.sqrt(int(ab))%1 == 0:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na, b = map(str, input().split())\\nans = int(a+b)\\nfor i in range(ans):\\n    route = pow(i, 2)\\n    if ans == route:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\", \"a, b = map(int, input().split())\\nm = b + a * 10 ** len(str(b))\\nfind = False;\\nfor i in range(m):\\n  if m == i ** 2:\\n    find = True;\\nif find:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=int(a+b)\\nfor i in range(1,1001):\\n    if i**2==c:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\\nreturn\\n\", \"a, b = input().split()\\nx = int(a+b)\\nno = 0\\nfor i in range(1000):\\n    if x == i**2:\\n        print(\\\"Yes\\\")\\n    else:\\n        no += 1\\n        if no == 1000:\\n            print(\\\"No\\\")\", \"import math\\n\\ndef main():\\n    a, b = input().split(\\\" \\\")\\n    x = math.sqrt(int(a + b))\\n    \\n    print((\\\"Yes\\\" if x.is_integer() else \\\"No\\\"))\\n\\n\\nmain()\\n\", \"import math\\n\\na, b = input().split()\\ns = a + b\\ni = int(s)\\nr = math.sqrt(i)\\nif r.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a, b = map(int,input().split())\\n\\nfor i in range(2, 400):\\n    if (10**(len(str(b))) * a + b) == i**2:\\n        ans = 'Yes'\\n        break\\n    else:\\n        ans = 'No'\\nprint(ans)\", \"N = int(input().replace(' ', ''))\\nprint('Yes' if N == int(N**(1/2))**2 else 'No')\", \"import math \\n\\nlist=input().split()\\n\\nnum=int(list[0]+list[1])\\n\\nnum_squrt=math.sqrt(num)\\n\\nif num_squrt.is_integer()==True:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na,b = input().split()\\nn = int(a+b)\\nif math.sqrt(n) % 1 == 0:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b=map(str, input().split())\\nq=0\\nfor i in range(1000):\\n  if int(a+b)==i**2:\\n    print('Yes')\\n    q=1\\n    break\\nif q==0:\\n    print('No')\", \"import math\\na, b = map(str, input().split())\\n\\ns = a + b\\ns = int(s)\\nr = math.sqrt(s)\\nfr = r - int(r)\\nif fr == 0:\\n  print('Yes')\\nelse:\\n  print('No')\", \"import math\\n\\na, b = list(map(str, input().split()))\\nx = int(a + b)\\n\\nif math.sqrt(x).is_integer():\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a,b = input().split()\\nc = int(a + b)\\nif (c**0.5).is_integer() == True:\\n    print('Yes')\\nelse:\\n    print('No')\", \"def resolve():\\n    from math import sqrt\\n    \\n    n = int(\\\"\\\".join(input().split()))\\n    print(\\\"Yes\\\" if n == int(sqrt(n)) ** 2 else \\\"No\\\")\\n\\n\\ndef __starting_point():\\n    resolve()\\n__starting_point()\", \"a, b = input().split()\\ns = int(a+b)\\nresult = 'No'\\nfor i in range(1,round(s)):\\n  if s/i == i:\\n    result = 'Yes'\\n    \\nprint(result)\", \"N = int(input().replace(\\\" \\\",\\\"\\\"))\\n\\nflag = False\\nfor i in range(1,10000):\\n  if N == i**2:\\n    flag = True\\n    break\\n  if N < i**2:\\n    break\\nif flag:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"p = input().split()\\na = int(f\\\"{p[0]}{p[1]}\\\")\\nprint( \\\"Yes\\\" if a == int((a ** 0.5)) **2 else \\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=int(a+b)\\nx=c**(1/2)\\nif x.is_integer():\\n    print('Yes')\\nelse :\\n    print('No')\\n\", \"a,b=input().split()\\n\\nd=int(a+b)\\n\\nfor i in range(1000):\\n    if d==i**2:\\n        print(\\\"Yes\\\")\\n        break\\n\\nlis=[j**2!=d for j in range(1000)]\\nif all(lis)==True:\\n    print(\\\"No\\\")\\n\", \"import math\\n\\na, b = input().split()\\nnum = int(a+b)\\n\\nif math.sqrt(num).is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b =list(map(str,input().split()))\\nx = int(a+b)**0.5\\n\\nif x - int(x) == 0:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b = list(input().split())\\nnum = int(a+b)\\nans = round(num**0.5)\\nif ans**2 == num:\\n\\tprint(\\\"Yes\\\")\\nelse:\\n\\tprint(\\\"No\\\")\", \"import math\\na,b = list(map(int,input().split()))\\nnumber = int(str(a)+str(b))\\nroot = math.sqrt(number)\\nif int(root + 0.5) ** 2 == number:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na = input(\\\"\\\").split(\\\" \\\")\\na = [int(aa) for aa in a]\\nn = int(str(a[0])+str(a[1]))\\nr = math.sqrt(n)\\nif r**2 == int(r)**2:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=a+b\\nc=int(c)\\nfor i in range(1001):\\n  if i**2==c:\\n    print(\\\"Yes\\\")\\n    return\\nprint(\\\"No\\\")\\n\", \"a, b = map(int, input().split())\\n\\nc = int(str(a)+str(b))\\n\\nl = []\\n\\nfor i in range(10, 100100):\\n    if (i ** .5).is_integer():\\n        l.append(i)\\n\\nfor i in l:\\n    if c == i:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"import math\\na, b = input().split()\\n\\nif math.sqrt(int(a + b)) == int(math.sqrt(int(a + b))):\\n  print('Yes')\\nelse:\\n  print('No')\", \"import math\\na,b = input().split()\\nq = int(a+b)\\nif math.sqrt(q)//1 == math.sqrt(q):\\n  print(\\\"Yes\\\")\\nelse:\\n  print('No')\", \"from math import sqrt\\na, b = input().split()\\nn = int(a+b)\\nprint(('Yes' if sqrt(n) == int(sqrt(n)) else 'No'))\\n\", \"import math\\ns = input()\\ns = int(s.replace(\\\" \\\", ''))\\nif math.sqrt(s) == int(math.sqrt(s)):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    ab = int(input().replace(\\\" \\\", \\\"\\\"))\\n    print((\\\"Yes\\\" if int(ab**.5)**2 == ab else \\\"No\\\"))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\n\\n\\ndef answer(a: int, b: int) -> str:\\n    joined_value = int(str(a) + str(b))\\n    return 'Yes' if math.sqrt(joined_value) % 1 == 0 else 'No'\\n\\n\\ndef main():\\n    a, b = list(map(int, input().split()))\\n    print((answer(a, b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\na, b = input().split()\\n\\njudge = int(a+b)\\n\\nif any(i**2 == judge for i in range(judge//2)):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import sys\\na,b=map(str,input().split())\\n\\nc=a+b\\nc=int(c)\\n\\nfor i in range(c//2):\\n    if c==i**2:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"#!/usr/bin/env python3\\nimport sys\\nsys.setrecursionlimit(10**6)\\n\\n\\na, b = list(map(str, input().split()))\\n\\n\\nnum = int(a+b)\\n\\nif num == int(num**0.5)**2:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"n=int(input().replace(\\\" \\\",\\\"\\\"))\\nprint(\\\"Yes\\\" if (n**0.5).is_integer() else \\\"No\\\")\", \"import math\\n\\na, b = input().split()\\nn = int(a + b)\\nprint('Yes') if math.sqrt(n) % 1 == 0 else print('No')\", \"a=int(input().replace(\\\" \\\",\\\"\\\"))\\nprint(\\\"Yes\\\" if int(a**0.5)==a**0.5 else 'No')\", \"a, b = map(str, input().split())\\nans = \\\"No\\\"\\nkey = int(a+b)\\nfor i in range(1000):\\n    if i**2 == key:\\n        ans =\\\"Yes\\\"\\n        break\\nprint(ans)\", \"import numpy as np\\n\\na, b = input().split(' ')\\n\\nc = int(a + b)\\n\\nsqrt_c = np.sqrt(c)//1\\n\\nif(sqrt_c**2 == c) :\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"x = int(''.join(input().split()))\\na = 1\\nwhile True:\\n    aa = a * a\\n    if aa == x:\\n        print(\\\"Yes\\\")\\n        return\\n    elif aa > x:\\n        print(\\\"No\\\")\\n        return\\n    a += 1\", \"from math import ceil, sqrt\\na, b = input().split()\\n\\nsq = sqrt(int(a+b))\\nf = sq - int(sq)\\nprint(('Yes' if ceil(f) == 0 else 'No'))\\n\", \"a, b = [i for i in input().split()]\\nt = int(a + b)\\nans = 'No'\\nn = 1\\nwhile n*n <= t:\\n    if n*n == t:\\n        ans = 'Yes'\\n    n += 1\\nprint(ans)\\n\", \"import math\\nab=list(input().split())\\ns=int(''.join(ab))\\n\\nroot=int(math.sqrt(s))\\nif root*root==s: print('Yes')\\nelse: print('No')\", \"import math\\na, b = list(map(str, input().split()))\\n\\ntarget = math.sqrt(int(a+b))\\n\\nif target.is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\\n\\n\", \"import math\\n\\na, b = input().split()\\nn = int(a + b)\\n\\nif n == round(math.sqrt(n))**2:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na,b = input().split()\\nc = int(a + b)\\n\\nd = math.sqrt(c)\\nprint(\\\"Yes\\\" if d == int(d) else \\\"No\\\")\", \"a,b = map(str,input().split())\\nc = int(a + b)\\n\\nfor i in range(int(c ** 0.5), int(c ** 0.5) + 1 ):\\n    if i ** 2 == c:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"#!/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\nimport math\\n\\nIS = lambda: int(input())\\nIA = lambda: [int(x) for x in input().split()]\\n\\na, b = IA()\\n\\nab = int(str(a) + str(b))\\nrt = math.sqrt(ab)\\nprint((\\\"Yes\\\" if int(rt) ** 2 == ab else \\\"No\\\"))\\n\", \"#!/usr/bin/env python3\\nimport sys\\n\\nYES = \\\"Yes\\\"  # type: str\\nNO = \\\"No\\\"  # type: str\\n\\n\\ndef solve(a: int, b: int):\\n    c = int(str(a) + str(b))\\n    for i in range(400):\\n        if c == i*i:\\n            print(YES)\\n            break\\n    else:\\n        print(NO)\\n    return\\n\\n\\n# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    a = int(next(tokens))  # type: int\\n    b = int(next(tokens))  # type: int\\n    solve(a, b)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"a=input().split()\\nb=int(\\\"\\\".join(a))\\n\\nnum=int(100100**1/2)\\n\\nans=\\\"No\\\"\\nfor i in range(num):\\n    if i**2==b:\\n        ans=\\\"Yes\\\"\\n        break\\n    \\nprint(ans)\", \"a,b = input().split()\\nab = int(a+b)\\nprint(\\\"Yes\\\" if (ab**0.5).is_integer() else \\\"No\\\")\", \"import math\\na, b = list(map(int, input().split()))\\nc = 0\\n\\nif b < 10:\\n    c = a*10 + b\\nelif 10 <= b <= 99:\\n    c = a*100 + b\\nelif b == 100:\\n    c = a*1000 + b\\n\\nd = math.sqrt(c)\\n\\nif d.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b = map(str,input().split())\\nc = int(a + b)\\nif c ** 0.5 ==int(c ** 0.5):\\n  print('Yes')\\nelse:\\n  print('No')\", \"print(('Yes' if int(''.join(input().split())) ** 0.5 % 1 == 0 else 'No'))\\n\\n\", \"a, b = input().split()\\nt = int(a + b)\\nans = 'No'\\nn = 1\\nwhile n*n <= t:\\n    if n*n == t:\\n        ans = 'Yes'\\n    n += 1\\nprint(ans)\", \"import math\\na,b = list(map(str,input().split()))\\nc = int(a+b)\\nif int(math.sqrt(c))**2 == c:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a, b = input().split()\\nt = int(a + b)\\nfor i in range(1,10 ** 3):\\n    if t == (i * i):\\n        print('Yes')\\n        return\\nprint('No')\\n\", \"import sys\\nc = [i for i in input().split()]\\nab = int(c[0]+c[1])\\nfor i in range(int(100100**0.5)+1):\\n    if i**2 == ab:\\n        print(\\\"Yes\\\")\\n        return\\n\\nprint(\\\"No\\\")\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return map(int,input().split())\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\na = L()\\nb = \\\"\\\".join(a)\\nb = int(b)\\nfor i in range(1000):\\n    if b == i**2:\\n        print(\\\"Yes\\\")\\n        return\\n \\nprint(\\\"No\\\")\", \"# import math\\n# import statistics\\n#a=input()\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\ne1,e2 = list(map(str,input().split()))\\n#K = input()\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\ncount=0\\na=e1+e2\\nfor i in range(1,int(a)):\\n\\tif int(a)/int(i)==int(i):\\n\\t\\tcount+=1\\nif count>0:\\n\\tprint('Yes')\\nelse:\\n\\tprint('No')\\n\", \"n = int(input().replace(' ', ''))\\nx = int(n ** 0.5)\\nprint('Yes' if x * x == n else 'No')\", \"ab = int(input().replace(\\\" \\\", \\\"\\\"))\\nans = False\\nfor i in range(320):\\n    if i * i == ab:\\n        ans = True\\n        break\\nprint(\\\"Yes\\\") if ans else print(\\\"No\\\")\", \"ab = int(\\\"\\\".join(input().split()))**0.5\\n\\nif ab.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na, b = map(str, input().split( ))\\nA = int(a+b)\\n\\nif math.sqrt(A).is_integer() == True:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b=map(str,input().split())\\nab=int(a+b)\\n\\nans=\\\"No\\\"\\nfor i in range(1010):\\n    x=i**2\\n    if x==ab:\\n        ans=\\\"Yes\\\"\\n        break\\n\\nprint(ans)\", \"#!/usr/local/bin/python3\\n# https://atcoder.jp/contests/abc086/tasks/abc086_b\\nimport math\\n\\na, b = input().split()\\n\\nif math.sqrt(int(a+b)).is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b = map(int,input().split())\\nc = int(str(a) + str(b))\\nfor i in range(c):\\n    if i ** 2 == c:\\n        print('Yes')\\n        break\\n    elif i ** 2 > c:\\n        print('No')\\n        break\", \"n = int(\\\"\\\".join(input().split()))\\nx = n**0.5\\nif x == int(x):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b = input().split()\\na = int(a + b)\\n\\nfor i in range(1000):\\n    if i ** 2 == a:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\\n\", \"import math\\na,b=input().split()\\nc=int(a+b)\\nd=math.sqrt(c)\\ne=math.floor(d)\\nif e**2==c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na, b = list(map(int, input().split()))\\nc = 0\\n\\nif b < 10:\\n    c = a*10 + b\\nelif 10 <= b <= 99:\\n    c = a*100 + b\\nelif b == 100:\\n    c = a*1000 + b\\n\\nd = math.sqrt(c)\\n\\nif d.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#\\n# abc086 b\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"1 21\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"100 100\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"12 10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B = input().split()\\n\\n    C = int(A+B)\\n    for i in range(1, 100100):\\n        if i**2 == C:\\n            print(\\\"Yes\\\")\\n            break\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"a,b = map(str,input().split())\\nfrom math import sqrt\\nprint(\\\"Yes\\\" if sqrt(int(a+b)) == int(sqrt(int(a+b))) else \\\"No\\\")\", \"a,b=map(str,input().split())\\nc=a+b\\nfor i in range(1,350):\\n    if int(c)==i**2:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\", \"a,b = map(str,input().split())\\nc = int(a + b)\\nd = int(c ** 0.5)\\n\\n\\nif d ** 2 == c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na,b = map(str, input().split())\\nab = int(a+b)\\nsq = math.sqrt(ab)\\nif sq % 1 < 0.01:\\n  sq2 = sq**2\\n  if sq2 == ab:\\n    ans = 'Yes'\\n  else:\\n    ans = 'No'\\nelse:\\n  ans = 'No'\\nprint(ans)\", \"a, b = input().split()\\nab = int(a+b)\\nimport math\\nif math.sqrt(ab).is_integer():\\n  print('Yes')\\nelse:\\n  print('No')\", \"a,b=input().split()\\ns=0\\ns += int(b)\\ns += int(a)*(10**len(b))\\nfor i in range(320):\\n    if s==i*i:\\n        print('Yes')\\n        return\\nprint('No')\\n\", \"import math\\n\\na, b = map(int, input().split())\\nx = int(str(a) + str(b))\\nif math.sqrt(x) == math.ceil(math.sqrt(x)):\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"a, b = list(map(str, input().split(\\\" \\\")))\\n\\nans = False\\nfor i in range(1000):\\n    if int(a + b) == i ** 2:\\n        ans = True\\n\\nprint((\\\"Yes\\\" if ans else \\\"No\\\"))\\n\", \"from math import sqrt\\na,b=input().split()\\nc=int(a+b)\\nd=int(sqrt(c))\\nprint(\\\"Yes\\\" if d**2==c else \\\"No\\\")\", \"a, b = input().split()\\nab = int(a+b)\\ni = 0\\nwhile i**2 <= ab:\\n    flag = (i**2 == ab)\\n    i = i+1\\nif flag:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\n\\na, b = map(str, input().split())\\n\\nX = int(a) * (10 ** len(b)) + int(b)\\n\\nif math.sqrt(X) % 1 == 0:\\n  print('Yes')\\nelse:\\n  print('No')\", \"from math import sqrt\\na, b = input().split()\\nc = a + b\\nif sqrt(int(c)) == int(sqrt(int(c))):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"from math import *\\nlst = input().split()\\n\\nif (sqrt(int(lst[0] + lst[1])) % 1) == 0:\\n   print('Yes')\\nelse:\\n   print('No')\", \"import math\\n\\na, b = input().split()\\nc = int(a + b)\\n\\nfor i in range(int(math.sqrt(c))+1):\\n  if c == i*i:\\n    print(\\\"Yes\\\")\\n    break\\nelse:\\n  print(\\\"No\\\")\\n  \\n\"]",
        "difficulty": "introductory",
        "input": "100 100\n",
        "output": "No\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc086/tasks/abc086_b"
    },
    {
        "id": 511,
        "task_id": 4543,
        "test_case_id": 3,
        "question": "AtCoDeer the deer has found two positive integers, a and b.\nDetermine whether the concatenation of a and b in this order is a square number.\n\n-----Constraints-----\n - 1 ≤ a,b ≤ 100\n - a and b are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\na b\n\n-----Output-----\nIf the concatenation of a and b in this order is a square number, print Yes; otherwise, print No.\n\n-----Sample Input-----\n1 21\n\n-----Sample Output-----\nYes\n\nAs 121 = 11 × 11, it is a square number.",
        "solutions": "[\"\\n#ABC086B\\na,b = input().split()\\na += b\\na = int(a)\\nprint(\\\"Yes\\\" if int((a**.5))**2 == a else \\\"No\\\")\", \"a, b = input().split()\\nab = int(a+b)\\n\\nfor j in range(ab):\\n    if j ** 2 <= ab:\\n        if j ** 2 == ab:\\n            print(\\\"Yes\\\")\\n            return\\n    else:\\n        print(\\\"No\\\")\\n        return\", \"#-*-coding:utf-8-*-\\nimport sys\\nimport math\\ninput=sys.stdin.readline\\n\\ndef main():\\n    a,b = input().split()\\n    number=0\\n\\n    number=int(a+b)\\n    for i in range(100101):\\n        if i * i ==number:\\n            print(\\\"Yes\\\")\\n            return\\n        else:\\n            continue\\n    print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"a, b = (i for i in input().split())\\nc = int(a + b)\\nans = c ** 0.5\\nif float.is_integer(ans): print('Yes')\\nelse: print('No')\", \"a,b=map(str,input().split())\\nx = a+b\\nx = int(x)\\ny = x**0.5\\nif y.is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b=input().split()\\nx=int(a)*10**len(b)+int(b)\\n\\nfor i in range(0,1000):\\n    if i*i==x:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b=map(int,input().split())\\n\\ndef ans086(a:int, b:int):\\n    ab=int(str(a)+str(b))\\n    import math\\n    if int(math.sqrt(ab))**2==ab:\\n        return(\\\"Yes\\\")\\n    else:\\n        return(\\\"No\\\")\\n\\nprint(ans086(a,b))\", \"a,b=map(str,input().split())\\nans = a+b\\nif (int(ans) ** 0.5).is_integer():\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b = input().split()\\n\\na_b = a + b\\na_b = int(a_b)\\n\\nfor i in range(a_b):\\n    if i * i == a_b:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\", \"num = int(''.join(input().split()))\\nroot = num ** .5\\n\\nprint(('Yes' if root.is_integer() else 'No'))\\n\", \"import math\\nx = int(input().replace(' ',''))\\ny = int(math.sqrt(x))\\nif y * y == x:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"import math\\na,b = map(int, input().split())\\nab = str(a) + str(b)\\n\\nif math.sqrt(int(ab))%1 == 0:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na, b = map(str, input().split())\\nans = int(a+b)\\nfor i in range(ans):\\n    route = pow(i, 2)\\n    if ans == route:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\", \"a, b = map(int, input().split())\\nm = b + a * 10 ** len(str(b))\\nfind = False;\\nfor i in range(m):\\n  if m == i ** 2:\\n    find = True;\\nif find:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=int(a+b)\\nfor i in range(1,1001):\\n    if i**2==c:\\n        print(\\\"Yes\\\")\\n        return\\nprint(\\\"No\\\")\\nreturn\\n\", \"a, b = input().split()\\nx = int(a+b)\\nno = 0\\nfor i in range(1000):\\n    if x == i**2:\\n        print(\\\"Yes\\\")\\n    else:\\n        no += 1\\n        if no == 1000:\\n            print(\\\"No\\\")\", \"import math\\n\\ndef main():\\n    a, b = input().split(\\\" \\\")\\n    x = math.sqrt(int(a + b))\\n    \\n    print((\\\"Yes\\\" if x.is_integer() else \\\"No\\\"))\\n\\n\\nmain()\\n\", \"import math\\n\\na, b = input().split()\\ns = a + b\\ni = int(s)\\nr = math.sqrt(i)\\nif r.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a, b = map(int,input().split())\\n\\nfor i in range(2, 400):\\n    if (10**(len(str(b))) * a + b) == i**2:\\n        ans = 'Yes'\\n        break\\n    else:\\n        ans = 'No'\\nprint(ans)\", \"N = int(input().replace(' ', ''))\\nprint('Yes' if N == int(N**(1/2))**2 else 'No')\", \"import math \\n\\nlist=input().split()\\n\\nnum=int(list[0]+list[1])\\n\\nnum_squrt=math.sqrt(num)\\n\\nif num_squrt.is_integer()==True:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na,b = input().split()\\nn = int(a+b)\\nif math.sqrt(n) % 1 == 0:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b=map(str, input().split())\\nq=0\\nfor i in range(1000):\\n  if int(a+b)==i**2:\\n    print('Yes')\\n    q=1\\n    break\\nif q==0:\\n    print('No')\", \"import math\\na, b = map(str, input().split())\\n\\ns = a + b\\ns = int(s)\\nr = math.sqrt(s)\\nfr = r - int(r)\\nif fr == 0:\\n  print('Yes')\\nelse:\\n  print('No')\", \"import math\\n\\na, b = list(map(str, input().split()))\\nx = int(a + b)\\n\\nif math.sqrt(x).is_integer():\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a,b = input().split()\\nc = int(a + b)\\nif (c**0.5).is_integer() == True:\\n    print('Yes')\\nelse:\\n    print('No')\", \"def resolve():\\n    from math import sqrt\\n    \\n    n = int(\\\"\\\".join(input().split()))\\n    print(\\\"Yes\\\" if n == int(sqrt(n)) ** 2 else \\\"No\\\")\\n\\n\\ndef __starting_point():\\n    resolve()\\n__starting_point()\", \"a, b = input().split()\\ns = int(a+b)\\nresult = 'No'\\nfor i in range(1,round(s)):\\n  if s/i == i:\\n    result = 'Yes'\\n    \\nprint(result)\", \"N = int(input().replace(\\\" \\\",\\\"\\\"))\\n\\nflag = False\\nfor i in range(1,10000):\\n  if N == i**2:\\n    flag = True\\n    break\\n  if N < i**2:\\n    break\\nif flag:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"p = input().split()\\na = int(f\\\"{p[0]}{p[1]}\\\")\\nprint( \\\"Yes\\\" if a == int((a ** 0.5)) **2 else \\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=int(a+b)\\nx=c**(1/2)\\nif x.is_integer():\\n    print('Yes')\\nelse :\\n    print('No')\\n\", \"a,b=input().split()\\n\\nd=int(a+b)\\n\\nfor i in range(1000):\\n    if d==i**2:\\n        print(\\\"Yes\\\")\\n        break\\n\\nlis=[j**2!=d for j in range(1000)]\\nif all(lis)==True:\\n    print(\\\"No\\\")\\n\", \"import math\\n\\na, b = input().split()\\nnum = int(a+b)\\n\\nif math.sqrt(num).is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b =list(map(str,input().split()))\\nx = int(a+b)**0.5\\n\\nif x - int(x) == 0:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b = list(input().split())\\nnum = int(a+b)\\nans = round(num**0.5)\\nif ans**2 == num:\\n\\tprint(\\\"Yes\\\")\\nelse:\\n\\tprint(\\\"No\\\")\", \"import math\\na,b = list(map(int,input().split()))\\nnumber = int(str(a)+str(b))\\nroot = math.sqrt(number)\\nif int(root + 0.5) ** 2 == number:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na = input(\\\"\\\").split(\\\" \\\")\\na = [int(aa) for aa in a]\\nn = int(str(a[0])+str(a[1]))\\nr = math.sqrt(n)\\nif r**2 == int(r)**2:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b=list(map(str,input().split()))\\nc=a+b\\nc=int(c)\\nfor i in range(1001):\\n  if i**2==c:\\n    print(\\\"Yes\\\")\\n    return\\nprint(\\\"No\\\")\\n\", \"a, b = map(int, input().split())\\n\\nc = int(str(a)+str(b))\\n\\nl = []\\n\\nfor i in range(10, 100100):\\n    if (i ** .5).is_integer():\\n        l.append(i)\\n\\nfor i in l:\\n    if c == i:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"import math\\na, b = input().split()\\n\\nif math.sqrt(int(a + b)) == int(math.sqrt(int(a + b))):\\n  print('Yes')\\nelse:\\n  print('No')\", \"import math\\na,b = input().split()\\nq = int(a+b)\\nif math.sqrt(q)//1 == math.sqrt(q):\\n  print(\\\"Yes\\\")\\nelse:\\n  print('No')\", \"from math import sqrt\\na, b = input().split()\\nn = int(a+b)\\nprint(('Yes' if sqrt(n) == int(sqrt(n)) else 'No'))\\n\", \"import math\\ns = input()\\ns = int(s.replace(\\\" \\\", ''))\\nif math.sqrt(s) == int(math.sqrt(s)):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#!/usr/bin/env python3\\n\\ndef main():\\n    ab = int(input().replace(\\\" \\\", \\\"\\\"))\\n    print((\\\"Yes\\\" if int(ab**.5)**2 == ab else \\\"No\\\"))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"import math\\n\\n\\ndef answer(a: int, b: int) -> str:\\n    joined_value = int(str(a) + str(b))\\n    return 'Yes' if math.sqrt(joined_value) % 1 == 0 else 'No'\\n\\n\\ndef main():\\n    a, b = list(map(int, input().split()))\\n    print((answer(a, b)))\\n\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"# -*- coding:utf-8 -*-\\na, b = input().split()\\n\\njudge = int(a+b)\\n\\nif any(i**2 == judge for i in range(judge//2)):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import sys\\na,b=map(str,input().split())\\n\\nc=a+b\\nc=int(c)\\n\\nfor i in range(c//2):\\n    if c==i**2:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"#!/usr/bin/env python3\\nimport sys\\nsys.setrecursionlimit(10**6)\\n\\n\\na, b = list(map(str, input().split()))\\n\\n\\nnum = int(a+b)\\n\\nif num == int(num**0.5)**2:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"n=int(input().replace(\\\" \\\",\\\"\\\"))\\nprint(\\\"Yes\\\" if (n**0.5).is_integer() else \\\"No\\\")\", \"import math\\n\\na, b = input().split()\\nn = int(a + b)\\nprint('Yes') if math.sqrt(n) % 1 == 0 else print('No')\", \"a=int(input().replace(\\\" \\\",\\\"\\\"))\\nprint(\\\"Yes\\\" if int(a**0.5)==a**0.5 else 'No')\", \"a, b = map(str, input().split())\\nans = \\\"No\\\"\\nkey = int(a+b)\\nfor i in range(1000):\\n    if i**2 == key:\\n        ans =\\\"Yes\\\"\\n        break\\nprint(ans)\", \"import numpy as np\\n\\na, b = input().split(' ')\\n\\nc = int(a + b)\\n\\nsqrt_c = np.sqrt(c)//1\\n\\nif(sqrt_c**2 == c) :\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"x = int(''.join(input().split()))\\na = 1\\nwhile True:\\n    aa = a * a\\n    if aa == x:\\n        print(\\\"Yes\\\")\\n        return\\n    elif aa > x:\\n        print(\\\"No\\\")\\n        return\\n    a += 1\", \"from math import ceil, sqrt\\na, b = input().split()\\n\\nsq = sqrt(int(a+b))\\nf = sq - int(sq)\\nprint(('Yes' if ceil(f) == 0 else 'No'))\\n\", \"a, b = [i for i in input().split()]\\nt = int(a + b)\\nans = 'No'\\nn = 1\\nwhile n*n <= t:\\n    if n*n == t:\\n        ans = 'Yes'\\n    n += 1\\nprint(ans)\\n\", \"import math\\nab=list(input().split())\\ns=int(''.join(ab))\\n\\nroot=int(math.sqrt(s))\\nif root*root==s: print('Yes')\\nelse: print('No')\", \"import math\\na, b = list(map(str, input().split()))\\n\\ntarget = math.sqrt(int(a+b))\\n\\nif target.is_integer():\\n    print('Yes')\\nelse:\\n    print('No')\\n\\n\", \"import math\\n\\na, b = input().split()\\nn = int(a + b)\\n\\nif n == round(math.sqrt(n))**2:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na,b = input().split()\\nc = int(a + b)\\n\\nd = math.sqrt(c)\\nprint(\\\"Yes\\\" if d == int(d) else \\\"No\\\")\", \"a,b = map(str,input().split())\\nc = int(a + b)\\n\\nfor i in range(int(c ** 0.5), int(c ** 0.5) + 1 ):\\n    if i ** 2 == c:\\n        print('Yes')\\n        return\\n\\nprint('No')\", \"#!/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\nimport math\\n\\nIS = lambda: int(input())\\nIA = lambda: [int(x) for x in input().split()]\\n\\na, b = IA()\\n\\nab = int(str(a) + str(b))\\nrt = math.sqrt(ab)\\nprint((\\\"Yes\\\" if int(rt) ** 2 == ab else \\\"No\\\"))\\n\", \"#!/usr/bin/env python3\\nimport sys\\n\\nYES = \\\"Yes\\\"  # type: str\\nNO = \\\"No\\\"  # type: str\\n\\n\\ndef solve(a: int, b: int):\\n    c = int(str(a) + str(b))\\n    for i in range(400):\\n        if c == i*i:\\n            print(YES)\\n            break\\n    else:\\n        print(NO)\\n    return\\n\\n\\n# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)\\ndef main():\\n    def iterate_tokens():\\n        for line in sys.stdin:\\n            for word in line.split():\\n                yield word\\n    tokens = iterate_tokens()\\n    a = int(next(tokens))  # type: int\\n    b = int(next(tokens))  # type: int\\n    solve(a, b)\\n\\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"a=input().split()\\nb=int(\\\"\\\".join(a))\\n\\nnum=int(100100**1/2)\\n\\nans=\\\"No\\\"\\nfor i in range(num):\\n    if i**2==b:\\n        ans=\\\"Yes\\\"\\n        break\\n    \\nprint(ans)\", \"a,b = input().split()\\nab = int(a+b)\\nprint(\\\"Yes\\\" if (ab**0.5).is_integer() else \\\"No\\\")\", \"import math\\na, b = list(map(int, input().split()))\\nc = 0\\n\\nif b < 10:\\n    c = a*10 + b\\nelif 10 <= b <= 99:\\n    c = a*100 + b\\nelif b == 100:\\n    c = a*1000 + b\\n\\nd = math.sqrt(c)\\n\\nif d.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b = map(str,input().split())\\nc = int(a + b)\\nif c ** 0.5 ==int(c ** 0.5):\\n  print('Yes')\\nelse:\\n  print('No')\", \"print(('Yes' if int(''.join(input().split())) ** 0.5 % 1 == 0 else 'No'))\\n\\n\", \"a, b = input().split()\\nt = int(a + b)\\nans = 'No'\\nn = 1\\nwhile n*n <= t:\\n    if n*n == t:\\n        ans = 'Yes'\\n    n += 1\\nprint(ans)\", \"import math\\na,b = list(map(str,input().split()))\\nc = int(a+b)\\nif int(math.sqrt(c))**2 == c:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a, b = input().split()\\nt = int(a + b)\\nfor i in range(1,10 ** 3):\\n    if t == (i * i):\\n        print('Yes')\\n        return\\nprint('No')\\n\", \"import sys\\nc = [i for i in input().split()]\\nab = int(c[0]+c[1])\\nfor i in range(int(100100**0.5)+1):\\n    if i**2 == ab:\\n        print(\\\"Yes\\\")\\n        return\\n\\nprint(\\\"No\\\")\", \"import re\\nimport sys\\nimport math\\nimport itertools\\nimport bisect\\nfrom copy import copy\\nfrom collections import deque,Counter\\nfrom decimal import Decimal\\nimport functools\\ndef v(): return input()\\ndef k(): return int(input())\\ndef S(): return input().split()\\ndef I(): return map(int,input().split())\\ndef X(): return list(input())\\ndef L(): return list(input().split())\\ndef l(): return list(map(int,input().split()))\\ndef lcm(a,b): return a*b//math.gcd(a,b)\\nsys.setrecursionlimit(10 ** 6)\\nmod = 10**9+7\\ncnt = 0\\nans = 0\\ninf = float(\\\"inf\\\")\\nal = \\\"abcdefghijklmnopqrstuvwxyz\\\"\\nAL = al.upper()\\n\\na = L()\\nb = \\\"\\\".join(a)\\nb = int(b)\\nfor i in range(1000):\\n    if b == i**2:\\n        print(\\\"Yes\\\")\\n        return\\n \\nprint(\\\"No\\\")\", \"# import math\\n# import statistics\\n#a=input()\\n#b,c=int(input()),int(input())\\n# c=[]\\n# for i in a:\\n#    c.append(i)\\ne1,e2 = list(map(str,input().split()))\\n#K = input()\\n# f = list(map(int,input().split()))\\n#g = [input() for _ in range(a)]\\ncount=0\\na=e1+e2\\nfor i in range(1,int(a)):\\n\\tif int(a)/int(i)==int(i):\\n\\t\\tcount+=1\\nif count>0:\\n\\tprint('Yes')\\nelse:\\n\\tprint('No')\\n\", \"n = int(input().replace(' ', ''))\\nx = int(n ** 0.5)\\nprint('Yes' if x * x == n else 'No')\", \"ab = int(input().replace(\\\" \\\", \\\"\\\"))\\nans = False\\nfor i in range(320):\\n    if i * i == ab:\\n        ans = True\\n        break\\nprint(\\\"Yes\\\") if ans else print(\\\"No\\\")\", \"ab = int(\\\"\\\".join(input().split()))**0.5\\n\\nif ab.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\na, b = map(str, input().split( ))\\nA = int(a+b)\\n\\nif math.sqrt(A).is_integer() == True:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b=map(str,input().split())\\nab=int(a+b)\\n\\nans=\\\"No\\\"\\nfor i in range(1010):\\n    x=i**2\\n    if x==ab:\\n        ans=\\\"Yes\\\"\\n        break\\n\\nprint(ans)\", \"#!/usr/local/bin/python3\\n# https://atcoder.jp/contests/abc086/tasks/abc086_b\\nimport math\\n\\na, b = input().split()\\n\\nif math.sqrt(int(a+b)).is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b = map(int,input().split())\\nc = int(str(a) + str(b))\\nfor i in range(c):\\n    if i ** 2 == c:\\n        print('Yes')\\n        break\\n    elif i ** 2 > c:\\n        print('No')\\n        break\", \"n = int(\\\"\\\".join(input().split()))\\nx = n**0.5\\nif x == int(x):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b = input().split()\\na = int(a + b)\\n\\nfor i in range(1000):\\n    if i ** 2 == a:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\\n\", \"import math\\na,b=input().split()\\nc=int(a+b)\\nd=math.sqrt(c)\\ne=math.floor(d)\\nif e**2==c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na, b = list(map(int, input().split()))\\nc = 0\\n\\nif b < 10:\\n    c = a*10 + b\\nelif 10 <= b <= 99:\\n    c = a*100 + b\\nelif b == 100:\\n    c = a*1000 + b\\n\\nd = math.sqrt(c)\\n\\nif d.is_integer():\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#\\n# abc086 b\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"1 21\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"100 100\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"12 10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B = input().split()\\n\\n    C = int(A+B)\\n    for i in range(1, 100100):\\n        if i**2 == C:\\n            print(\\\"Yes\\\")\\n            break\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"a,b = map(str,input().split())\\nfrom math import sqrt\\nprint(\\\"Yes\\\" if sqrt(int(a+b)) == int(sqrt(int(a+b))) else \\\"No\\\")\", \"a,b=map(str,input().split())\\nc=a+b\\nfor i in range(1,350):\\n    if int(c)==i**2:\\n        print(\\\"Yes\\\")\\n        break\\nelse:\\n    print(\\\"No\\\")\", \"a,b = map(str,input().split())\\nc = int(a + b)\\nd = int(c ** 0.5)\\n\\n\\nif d ** 2 == c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import math\\na,b = map(str, input().split())\\nab = int(a+b)\\nsq = math.sqrt(ab)\\nif sq % 1 < 0.01:\\n  sq2 = sq**2\\n  if sq2 == ab:\\n    ans = 'Yes'\\n  else:\\n    ans = 'No'\\nelse:\\n  ans = 'No'\\nprint(ans)\", \"a, b = input().split()\\nab = int(a+b)\\nimport math\\nif math.sqrt(ab).is_integer():\\n  print('Yes')\\nelse:\\n  print('No')\", \"a,b=input().split()\\ns=0\\ns += int(b)\\ns += int(a)*(10**len(b))\\nfor i in range(320):\\n    if s==i*i:\\n        print('Yes')\\n        return\\nprint('No')\\n\", \"import math\\n\\na, b = map(int, input().split())\\nx = int(str(a) + str(b))\\nif math.sqrt(x) == math.ceil(math.sqrt(x)):\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"a, b = list(map(str, input().split(\\\" \\\")))\\n\\nans = False\\nfor i in range(1000):\\n    if int(a + b) == i ** 2:\\n        ans = True\\n\\nprint((\\\"Yes\\\" if ans else \\\"No\\\"))\\n\", \"from math import sqrt\\na,b=input().split()\\nc=int(a+b)\\nd=int(sqrt(c))\\nprint(\\\"Yes\\\" if d**2==c else \\\"No\\\")\", \"a, b = input().split()\\nab = int(a+b)\\ni = 0\\nwhile i**2 <= ab:\\n    flag = (i**2 == ab)\\n    i = i+1\\nif flag:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import math\\n\\na, b = map(str, input().split())\\n\\nX = int(a) * (10 ** len(b)) + int(b)\\n\\nif math.sqrt(X) % 1 == 0:\\n  print('Yes')\\nelse:\\n  print('No')\", \"from math import sqrt\\na, b = input().split()\\nc = a + b\\nif sqrt(int(c)) == int(sqrt(int(c))):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"from math import *\\nlst = input().split()\\n\\nif (sqrt(int(lst[0] + lst[1])) % 1) == 0:\\n   print('Yes')\\nelse:\\n   print('No')\", \"import math\\n\\na, b = input().split()\\nc = int(a + b)\\n\\nfor i in range(int(math.sqrt(c))+1):\\n  if c == i*i:\\n    print(\\\"Yes\\\")\\n    break\\nelse:\\n  print(\\\"No\\\")\\n  \\n\"]",
        "difficulty": "introductory",
        "input": "12 10\n",
        "output": "No\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc086/tasks/abc086_b"
    },
    {
        "id": 512,
        "task_id": 4562,
        "test_case_id": 1,
        "question": "Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - N is an integer.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the largest square number not exceeding N.\n\n-----Sample Input-----\n10\n\n-----Sample Output-----\n9\n\n10 is not square, but 9 = 3 × 3 is. Thus, we print 9.",
        "solutions": "[\"N = int (input ())\\nx = 1\\nwhile x**2 <= N:\\n  x += 1\\nx -= 1\\nprint (x**2)\", \"#\\n# abc077 b\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\nimport math\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"9\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"81\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"81\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"271828182\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"271821169\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n    print((math.floor(math.sqrt(N))**2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n = int(input())\\n\\ni=1\\nwhile i*i <= n:\\n    ans = i*i\\n    i+=1\\nprint(ans)\", \"n = int(input())\\nprint(int(n**(1/2))**2)\", \"N = int(input())\\ni = 1\\nif N == 1:\\n    print(i)\\nelse:\\n    while i <= N:\\n        if((i * i) > N):\\n            print((i-1) * (i-1))\\n            break\\n        i += 1\", \"from math import sqrt\\n\\nn = int(input())\\n\\nfor i in range(int(sqrt(n) + 1)):\\n    if i ** 2 <= n:\\n        ans = i ** 2\\nprint(ans)\", \"from math import sqrt\\nn = int(input())\\nprint(int(sqrt(n))**2)\", \"#!/usr/bin/env python3\\nN = int(input())\\n\\nans = 0\\nfor i in range(1, 10**5):\\n    n = i ** 2\\n    if n <= N:\\n        ans = n\\n    else:\\n        break\\nprint(ans)\\n\", \"print(int(int(input())**.5)**2)\", \"a=int(input())\\ni=0\\nwhile i**2<=a:\\n  i=i+1\\nprint((i-1)**2)\", \"n = int(input())\\n\\nfor i in range(n, 0, -1):\\n  j = int(i ** 0.5)\\n  if int(j) ** 2 == i:\\n    break\\nprint(i)\\n\", \"print((int(int(input())**0.5)**2))\\n\", \"import math\\nx=int(input())\\ny= math.sqrt(x)\\nz= y//1\\na=z**2\\nprint(int(a))\", \"n = int(input())\\nprint((int(n ** 0.5) ** 2))\\n\", \"n = int(input())\\nwhile (n ** 0.5) % 1 != 0:\\n    n -= 1\\nprint(n)\", \"print(int(int(input()) ** 0.5) ** 2)\", \"from math import sqrt\\n\\nn = int(input())\\n\\nans = int(sqrt(n))\\n\\nif (ans + 1) * (ans + 1) <= n:\\n    print((ans + 1) * (ans + 1))\\nelif ans * ans <= n:\\n    print(ans * ans)\\nelse:\\n    print((ans - 1) * (ans - 1))\", \"print(int(int(input())**0.5//1)**2)\", \"N=int(input())\\nans=1\\nfor i in range(N+1):\\n    if i*i<=N:\\n        ans=i\\n    else:\\n        break\\nprint((ans**2))\\n\", \"n = int(input())\\nx = 1\\nwhile x * x <= n:\\n    x += 1\\n \\nx -= 1\\nprint(x * x)\", \"n = int(input())\\nprint(int(n ** 0.5) ** 2)\", \"n = int(input())\\nfor i in range(100000):\\n  if n >= (10**5-i)**2:\\n    print((10**5-i)**2)\\n    return\", \"n=int(input())\\nprint(int(n**(1/2))**2)\", \"import math\\nprint(int(math.sqrt(int(input())))**2)\", \"from math import sqrt\\nn=int(input())\\nfor i in range(1,int(sqrt(n))+1):\\n  if i**2>n:\\n    print((i-1)**2)\\n    break\\nelse:\\n  print(i**2)\", \"import sys\\nN=int(input())\\nif N==1:\\n    print(\\\"1\\\")\\nelif N==2:\\n    print(\\\"1\\\")\\nelse:\\n    for i in range(N):\\n        if i**2>N:\\n            print((i-1)**2)\\n            return\\n        else:\\n            pass\", \"import math\\nN=int(input())\\nc=int(math.sqrt(N))\\nprint(c**2)\", \"n=int(input())\\ni=1\\ntmp=1\\nwhile True:\\n  if i**2 <= n:\\n    tmp = i**2\\n  else:\\n    break\\n  i += 1\\nprint(tmp)\", \"def multiple(n):\\n    a = []\\n    for i in range(1,int(n**.5)+1):\\n        a.append(i*i)\\n    return a\\nn = int(input())\\na = multiple(n)\\nans = 10**18\\nfor i in a:\\n    if n-i < 0:\\n        continue\\n    ans = min(ans,abs(n-i))\\nprint(n-ans)\", \"# coding = SJIS\\n\\nn = int(input())\\n\\nfor i in range(n):\\n    if int((n - i) ** 0.5) == (n - i) ** 0.5:\\n        print((n - i))\\n        return\\n\", \"import math\\na=int(input())\\nb=math.sqrt(a)\\nn=math.ceil(b)\\nm=math.floor(b)\\nprint(m**2)\", \"N=int(input())\\nfor i in range(int(N**0.5)+1):\\n    if N>=i**2:\\n        ans=i**2\\n    else:\\n        break\\nprint(ans)\", \"import math\\n\\n\\ndef answer(n: int) -> int:\\n    return int(math.sqrt(n)) ** 2\\n\\n\\ndef main():\\n    n = int(input())\\n    print(answer(n))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n=int(input())\\nfor i in range(1,10**5+2):\\n  if i**2>n:print(((i-1)**2));return\\n\", \"n = int(input())\\nfor i in range(100000):\\n  if i**2 > n:\\n    print((i-1)**2)\\n    break\", \"n = int(input())\\nfor i in range(1,n+2):\\n    if i*i > n:\\n        print((i-1)*(i-1))\\n        return\", \"print((int(int(input())**.5)**2))\\n\", \"n = int(input())\\nans=1\\nfor i in range(n+1):\\n    if i**2<=n:\\n        ans=i**2\\n    else:\\n        break\\n\\nprint(ans)\", \"import math\\nN = int(input())\\n\\nans = 1\\nfor i in range(1,math.floor(math.sqrt(N))+1):\\n  if i * i <= N:\\n    ans = i * i\\n    \\nprint(ans)\", \"def main():\\n    N = int(input())\\n    a = 1\\n    i = 0\\n    prev = 0\\n    while a <= N:\\n        i += 1\\n        prev = a\\n        if a > N:\\n            break\\n        else:\\n            a = i * i\\n    print(prev) \\nmain()\\n\", \"print(int(int(input())**.5)**2)\", \"import math\\nN = int(input())\\nfor i in range(N):\\n  x = N - i\\n  if int(math.sqrt(x)) == math.sqrt(x):\\n    print(x)\\n    break\\n\", \"N = int(input())\\n\\nfrom math import floor, sqrt\\nans = floor(sqrt(N))**2\\nprint(ans)\\n\", \"n = int(input())\\nprint(int(n**0.5)**2)\", \"N = int(input())\\nfor i in range(1, N+1):\\n    if i*i > N:\\n        print(((i-1)*(i-1)))\\n        return\\nprint((1))\\n\", \"N = int(input())\\n \\nprint(int(N**0.5)**2)\", \"N = int(input())\\nprint(int(N**(1/2))**2)\", \"N = int(input())\\nprint(int((N**(1/2)//1)**2))\", \"n=int(input())\\n\\nans=1\\nloop = 3\\nfor i in range (1,100000):\\n        if i**2 <= n:\\n                ans=i**2\\n        \\n        \\n\\nprint(ans)\", \"n=int(input())\\ni=1\\ntmp=1\\nwhile True:\\n  if i**2<=n:\\n    tmp=i**2\\n  else:\\n    break\\n  i+=1\\nprint(tmp)\", \"n = int(input())\\nprint((int(n ** 0.5)) ** 2)\", \"N = int(input())\\n\\nfor i in range(1, 10**9):\\n  if i**2 == N:\\n    print((i**2))\\n    break\\n  elif i**2 > N:\\n    print(((i-1)**2))\\n    break\\n\", \"N = int(input())\\nprint((int(N**(1/2))**2))\\n\", \"n = int(input())\\nprint((int(n**(1/2)))**2)\", \"n = int(input())\\n\\n\\nans = 1\\nfor i in range(1, n):\\n  if i**2 > n:\\n    ans = (i-1)**2\\n    break\\n\\n\\nprint(ans)\", \"import math\\nans=math.floor(int(input())**0.5)\\nprint (ans*ans)\", \"N = int(input())\\nans = 1\\nfor i in range(1, N):\\n    if i*i > N:\\n        break\\n    ans = max(ans, i*i)\\nprint(ans)\", \"print(int(int(input())**.5)**2)\", \"n = int(input())\\nans = 0\\nfor i in range(100001):\\n    if i **2 <= n:\\n        ans = i**2\\n    \\nprint(ans)\\n\", \"import math\\n\\nN=int(input())\\nn=math.floor(math.sqrt(N))**2\\n\\nprint(n)\\n\\n\", \"n = int(input())\\nprint(int(n ** 0.5) ** 2)\", \"from math import sqrt\\n\\nn = int(input())\\nprint(int(sqrt(n)) ** 2)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n))**2)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n))**2)\", \"n = int(input())\\nc = 1\\nfor i in range(10**5):\\n    if i**2 <= n:c = i**2\\n    else:break\\nprint(c)\", \"N = int(input())\\n\\nfor i in range(int(N**0.5)+3):\\n  if i**2 > N:\\n    print((i-1)**2)\\n    break\", \"n = int(input())\\nprint(int(n**.5) ** 2)\", \"import math\\nN=int(input())\\nans=N\\nfor i in range(N):\\n  if math.sqrt(ans).is_integer():\\n    print(ans)\\n    break\\n  ans-=1\", \"N=int(input())\\nimport math\\nprint((int(math.sqrt(N)))**2)\", \"n = int(input())\\n\\nfor i in range(1, 10**5):\\n    p = i**2\\n    if p > n:\\n        print((i-1)**2)\\n        break\", \"import math\\n\\nn = int(input())\\nprint(math.floor(math.sqrt(n)) ** 2)\", \"N=int(input())\\nprint(int(N**(1/2))**2)\", \"n = int(input())\\n\\nans = 0\\nmax = int(n**0.5)+1\\nfor i in range(1, max, 1):\\n    tmp = i**2\\n    if tmp <= n:\\n        ans = tmp\\nprint(ans)\", \"n=int(input())\\n\\nfor i in range(10**5):\\n    if i**2 > n:\\n        print((i-1)**2)\\n        break\", \"n = int(input())\\np = int(n**0.5)\\na = 1\\nans = 1\\nwhile a<=p:\\n    if a**2 <=n:\\n        ans = max(ans,a**2)\\n    a +=1\\nprint(ans)\", \"N = int(input())\\nprint(int(N**(0.5))**2)\", \"N=int(input())\\nif int((N+1)**.5)**2==N:print(N)\\nelse:print(int(N**.5)**2)\", \"N = int(input())\\nprint((int(N**.5)**2))\\n\", \"N = int(input())\\nprint(int(N**0.5)**2)\", \"N = int(input())\\nfrom math import sqrt, floor\\nfor i in range(1,floor(sqrt(N))+2):\\n    if i**2 > N:\\n        print((i-1)**2)\", \"import math\\nn = int(input())\\n\\nfor i in range(10**5):\\n    if n < i ** 2:\\n        print((i-1) ** 2)\\n        break\", \"n=int(input())\\nprint(int(n**0.5)**2)\", \"n=int(input())\\nres=1\\nfor i in range(100000):\\n    if i**2>n:\\n        break\\n    res=i*i\\nprint(res)\", \"n = int(input())\\nfor i in range(1, n):\\n    if i**2 > n:\\n        print((i-1)**2)\\n        break\\nelse:\\n    print(1)\", \"import math\\nn = int(input())\\nfor i in range(10**9):\\n  if math.sqrt(n) == int(math.sqrt(n)):\\n    print(n)\\n    break\\n  n -= 1\\n\", \"N=int(input())\\nif N==1 :\\n  print(1)\\n  return\\nfor i in range(1,N+1) :\\n  if i*i>N :\\n    print((i-1)*(i-1))\\n    return\", \"n = int(input())\\n\\nans = 0\\nfor i in range(1, 10 ** 5):\\n    if i ** 2 <= n:\\n        ans = i ** 2\\n\\nprint(ans)\\n\", \"import math\\n\\nn = int(input())\\nprint(math.floor(math.sqrt(n)) ** 2)\", \"x = int(input())\\nfor i in range(10**5):\\n  if i**2>x:\\n    a=((i-1)**2)\\n    break\\nprint(a)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n)) * int(math.sqrt(n)))\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nans = 1\\nfor i in range(1,n+1):\\n    if (i*i > n):\\n        ans =  (i-1)**2\\n        break\\nprint(ans)\\n\\n\\n\\n\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nimport heapq\\nimport re\\nimport numpy as np\\nfrom functools import reduce\\n\\nrr = lambda: sys.stdin.readline().rstrip()\\nrs = lambda: sys.stdin.readline().split()\\nri = lambda: int(sys.stdin.readline())\\nrm = lambda: list(map(int, sys.stdin.readline().split()))\\nrl = lambda: list(map(int, sys.stdin.readline().split()))\\ninf = float('inf')\\nmod = 10**9 + 7\\n\\nn = ri()\\na = int(n**0.5)\\nprint((a**2))\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\", \"N = int(input())\\nfor i in range(N+1):\\n    if i ** 2 == N:\\n        print((i**2))\\n        return\\n    elif i ** 2 > N:\\n        print((max((i-1)**2,1)))\\n        return\\n\", \"n = int(input())\\nans = 0\\nk = 1\\nwhile k ** 2 <= n:\\n  ans = k ** 2\\n  k += 1\\nprint(ans)\", \"#ABC077B\\nn = int(input())\\nwhile n>0:\\n    tmp = n**(1/2)\\n    if(tmp==int(tmp)):\\n        print(n)\\n        break\\n    n-=1\", \"#!/usr/bin/env python3\\nimport sys\\nsys.setrecursionlimit(10**6)\\n\\nn = int(input())\\n\\nans = 1\\nfor i in range(0, n):\\n    if (ans+1)**2 > n:\\n        break\\n    ans += 1\\nprint((ans**2))\\n\", \"import math\\nn = int(input())\\ntmp = int(math.sqrt(n))\\nprint(tmp**2)\", \"N = int(input())\\n\\ni = 1\\nwhile i*i <= N:\\n  i += 1\\n\\nprint((i-1)**2)\", \"N=int(input())\\nC=0\\nif N==1:\\n  print(1)\\n  return\\nfor i in range(1,N):\\n  if i**2<N:\\n    C=i**2\\n  elif i**2==N:\\n    C=i**2\\n    break\\n  elif i**2>N:\\n    break\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "10\n",
        "output": "9\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc077/tasks/abc077_b"
    },
    {
        "id": 513,
        "task_id": 4562,
        "test_case_id": 2,
        "question": "Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - N is an integer.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the largest square number not exceeding N.\n\n-----Sample Input-----\n10\n\n-----Sample Output-----\n9\n\n10 is not square, but 9 = 3 × 3 is. Thus, we print 9.",
        "solutions": "[\"N = int (input ())\\nx = 1\\nwhile x**2 <= N:\\n  x += 1\\nx -= 1\\nprint (x**2)\", \"#\\n# abc077 b\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\nimport math\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"9\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"81\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"81\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"271828182\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"271821169\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n    print((math.floor(math.sqrt(N))**2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n = int(input())\\n\\ni=1\\nwhile i*i <= n:\\n    ans = i*i\\n    i+=1\\nprint(ans)\", \"n = int(input())\\nprint(int(n**(1/2))**2)\", \"N = int(input())\\ni = 1\\nif N == 1:\\n    print(i)\\nelse:\\n    while i <= N:\\n        if((i * i) > N):\\n            print((i-1) * (i-1))\\n            break\\n        i += 1\", \"from math import sqrt\\n\\nn = int(input())\\n\\nfor i in range(int(sqrt(n) + 1)):\\n    if i ** 2 <= n:\\n        ans = i ** 2\\nprint(ans)\", \"from math import sqrt\\nn = int(input())\\nprint(int(sqrt(n))**2)\", \"#!/usr/bin/env python3\\nN = int(input())\\n\\nans = 0\\nfor i in range(1, 10**5):\\n    n = i ** 2\\n    if n <= N:\\n        ans = n\\n    else:\\n        break\\nprint(ans)\\n\", \"print(int(int(input())**.5)**2)\", \"a=int(input())\\ni=0\\nwhile i**2<=a:\\n  i=i+1\\nprint((i-1)**2)\", \"n = int(input())\\n\\nfor i in range(n, 0, -1):\\n  j = int(i ** 0.5)\\n  if int(j) ** 2 == i:\\n    break\\nprint(i)\\n\", \"print((int(int(input())**0.5)**2))\\n\", \"import math\\nx=int(input())\\ny= math.sqrt(x)\\nz= y//1\\na=z**2\\nprint(int(a))\", \"n = int(input())\\nprint((int(n ** 0.5) ** 2))\\n\", \"n = int(input())\\nwhile (n ** 0.5) % 1 != 0:\\n    n -= 1\\nprint(n)\", \"print(int(int(input()) ** 0.5) ** 2)\", \"from math import sqrt\\n\\nn = int(input())\\n\\nans = int(sqrt(n))\\n\\nif (ans + 1) * (ans + 1) <= n:\\n    print((ans + 1) * (ans + 1))\\nelif ans * ans <= n:\\n    print(ans * ans)\\nelse:\\n    print((ans - 1) * (ans - 1))\", \"print(int(int(input())**0.5//1)**2)\", \"N=int(input())\\nans=1\\nfor i in range(N+1):\\n    if i*i<=N:\\n        ans=i\\n    else:\\n        break\\nprint((ans**2))\\n\", \"n = int(input())\\nx = 1\\nwhile x * x <= n:\\n    x += 1\\n \\nx -= 1\\nprint(x * x)\", \"n = int(input())\\nprint(int(n ** 0.5) ** 2)\", \"n = int(input())\\nfor i in range(100000):\\n  if n >= (10**5-i)**2:\\n    print((10**5-i)**2)\\n    return\", \"n=int(input())\\nprint(int(n**(1/2))**2)\", \"import math\\nprint(int(math.sqrt(int(input())))**2)\", \"from math import sqrt\\nn=int(input())\\nfor i in range(1,int(sqrt(n))+1):\\n  if i**2>n:\\n    print((i-1)**2)\\n    break\\nelse:\\n  print(i**2)\", \"import sys\\nN=int(input())\\nif N==1:\\n    print(\\\"1\\\")\\nelif N==2:\\n    print(\\\"1\\\")\\nelse:\\n    for i in range(N):\\n        if i**2>N:\\n            print((i-1)**2)\\n            return\\n        else:\\n            pass\", \"import math\\nN=int(input())\\nc=int(math.sqrt(N))\\nprint(c**2)\", \"n=int(input())\\ni=1\\ntmp=1\\nwhile True:\\n  if i**2 <= n:\\n    tmp = i**2\\n  else:\\n    break\\n  i += 1\\nprint(tmp)\", \"def multiple(n):\\n    a = []\\n    for i in range(1,int(n**.5)+1):\\n        a.append(i*i)\\n    return a\\nn = int(input())\\na = multiple(n)\\nans = 10**18\\nfor i in a:\\n    if n-i < 0:\\n        continue\\n    ans = min(ans,abs(n-i))\\nprint(n-ans)\", \"# coding = SJIS\\n\\nn = int(input())\\n\\nfor i in range(n):\\n    if int((n - i) ** 0.5) == (n - i) ** 0.5:\\n        print((n - i))\\n        return\\n\", \"import math\\na=int(input())\\nb=math.sqrt(a)\\nn=math.ceil(b)\\nm=math.floor(b)\\nprint(m**2)\", \"N=int(input())\\nfor i in range(int(N**0.5)+1):\\n    if N>=i**2:\\n        ans=i**2\\n    else:\\n        break\\nprint(ans)\", \"import math\\n\\n\\ndef answer(n: int) -> int:\\n    return int(math.sqrt(n)) ** 2\\n\\n\\ndef main():\\n    n = int(input())\\n    print(answer(n))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n=int(input())\\nfor i in range(1,10**5+2):\\n  if i**2>n:print(((i-1)**2));return\\n\", \"n = int(input())\\nfor i in range(100000):\\n  if i**2 > n:\\n    print((i-1)**2)\\n    break\", \"n = int(input())\\nfor i in range(1,n+2):\\n    if i*i > n:\\n        print((i-1)*(i-1))\\n        return\", \"print((int(int(input())**.5)**2))\\n\", \"n = int(input())\\nans=1\\nfor i in range(n+1):\\n    if i**2<=n:\\n        ans=i**2\\n    else:\\n        break\\n\\nprint(ans)\", \"import math\\nN = int(input())\\n\\nans = 1\\nfor i in range(1,math.floor(math.sqrt(N))+1):\\n  if i * i <= N:\\n    ans = i * i\\n    \\nprint(ans)\", \"def main():\\n    N = int(input())\\n    a = 1\\n    i = 0\\n    prev = 0\\n    while a <= N:\\n        i += 1\\n        prev = a\\n        if a > N:\\n            break\\n        else:\\n            a = i * i\\n    print(prev) \\nmain()\\n\", \"print(int(int(input())**.5)**2)\", \"import math\\nN = int(input())\\nfor i in range(N):\\n  x = N - i\\n  if int(math.sqrt(x)) == math.sqrt(x):\\n    print(x)\\n    break\\n\", \"N = int(input())\\n\\nfrom math import floor, sqrt\\nans = floor(sqrt(N))**2\\nprint(ans)\\n\", \"n = int(input())\\nprint(int(n**0.5)**2)\", \"N = int(input())\\nfor i in range(1, N+1):\\n    if i*i > N:\\n        print(((i-1)*(i-1)))\\n        return\\nprint((1))\\n\", \"N = int(input())\\n \\nprint(int(N**0.5)**2)\", \"N = int(input())\\nprint(int(N**(1/2))**2)\", \"N = int(input())\\nprint(int((N**(1/2)//1)**2))\", \"n=int(input())\\n\\nans=1\\nloop = 3\\nfor i in range (1,100000):\\n        if i**2 <= n:\\n                ans=i**2\\n        \\n        \\n\\nprint(ans)\", \"n=int(input())\\ni=1\\ntmp=1\\nwhile True:\\n  if i**2<=n:\\n    tmp=i**2\\n  else:\\n    break\\n  i+=1\\nprint(tmp)\", \"n = int(input())\\nprint((int(n ** 0.5)) ** 2)\", \"N = int(input())\\n\\nfor i in range(1, 10**9):\\n  if i**2 == N:\\n    print((i**2))\\n    break\\n  elif i**2 > N:\\n    print(((i-1)**2))\\n    break\\n\", \"N = int(input())\\nprint((int(N**(1/2))**2))\\n\", \"n = int(input())\\nprint((int(n**(1/2)))**2)\", \"n = int(input())\\n\\n\\nans = 1\\nfor i in range(1, n):\\n  if i**2 > n:\\n    ans = (i-1)**2\\n    break\\n\\n\\nprint(ans)\", \"import math\\nans=math.floor(int(input())**0.5)\\nprint (ans*ans)\", \"N = int(input())\\nans = 1\\nfor i in range(1, N):\\n    if i*i > N:\\n        break\\n    ans = max(ans, i*i)\\nprint(ans)\", \"print(int(int(input())**.5)**2)\", \"n = int(input())\\nans = 0\\nfor i in range(100001):\\n    if i **2 <= n:\\n        ans = i**2\\n    \\nprint(ans)\\n\", \"import math\\n\\nN=int(input())\\nn=math.floor(math.sqrt(N))**2\\n\\nprint(n)\\n\\n\", \"n = int(input())\\nprint(int(n ** 0.5) ** 2)\", \"from math import sqrt\\n\\nn = int(input())\\nprint(int(sqrt(n)) ** 2)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n))**2)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n))**2)\", \"n = int(input())\\nc = 1\\nfor i in range(10**5):\\n    if i**2 <= n:c = i**2\\n    else:break\\nprint(c)\", \"N = int(input())\\n\\nfor i in range(int(N**0.5)+3):\\n  if i**2 > N:\\n    print((i-1)**2)\\n    break\", \"n = int(input())\\nprint(int(n**.5) ** 2)\", \"import math\\nN=int(input())\\nans=N\\nfor i in range(N):\\n  if math.sqrt(ans).is_integer():\\n    print(ans)\\n    break\\n  ans-=1\", \"N=int(input())\\nimport math\\nprint((int(math.sqrt(N)))**2)\", \"n = int(input())\\n\\nfor i in range(1, 10**5):\\n    p = i**2\\n    if p > n:\\n        print((i-1)**2)\\n        break\", \"import math\\n\\nn = int(input())\\nprint(math.floor(math.sqrt(n)) ** 2)\", \"N=int(input())\\nprint(int(N**(1/2))**2)\", \"n = int(input())\\n\\nans = 0\\nmax = int(n**0.5)+1\\nfor i in range(1, max, 1):\\n    tmp = i**2\\n    if tmp <= n:\\n        ans = tmp\\nprint(ans)\", \"n=int(input())\\n\\nfor i in range(10**5):\\n    if i**2 > n:\\n        print((i-1)**2)\\n        break\", \"n = int(input())\\np = int(n**0.5)\\na = 1\\nans = 1\\nwhile a<=p:\\n    if a**2 <=n:\\n        ans = max(ans,a**2)\\n    a +=1\\nprint(ans)\", \"N = int(input())\\nprint(int(N**(0.5))**2)\", \"N=int(input())\\nif int((N+1)**.5)**2==N:print(N)\\nelse:print(int(N**.5)**2)\", \"N = int(input())\\nprint((int(N**.5)**2))\\n\", \"N = int(input())\\nprint(int(N**0.5)**2)\", \"N = int(input())\\nfrom math import sqrt, floor\\nfor i in range(1,floor(sqrt(N))+2):\\n    if i**2 > N:\\n        print((i-1)**2)\", \"import math\\nn = int(input())\\n\\nfor i in range(10**5):\\n    if n < i ** 2:\\n        print((i-1) ** 2)\\n        break\", \"n=int(input())\\nprint(int(n**0.5)**2)\", \"n=int(input())\\nres=1\\nfor i in range(100000):\\n    if i**2>n:\\n        break\\n    res=i*i\\nprint(res)\", \"n = int(input())\\nfor i in range(1, n):\\n    if i**2 > n:\\n        print((i-1)**2)\\n        break\\nelse:\\n    print(1)\", \"import math\\nn = int(input())\\nfor i in range(10**9):\\n  if math.sqrt(n) == int(math.sqrt(n)):\\n    print(n)\\n    break\\n  n -= 1\\n\", \"N=int(input())\\nif N==1 :\\n  print(1)\\n  return\\nfor i in range(1,N+1) :\\n  if i*i>N :\\n    print((i-1)*(i-1))\\n    return\", \"n = int(input())\\n\\nans = 0\\nfor i in range(1, 10 ** 5):\\n    if i ** 2 <= n:\\n        ans = i ** 2\\n\\nprint(ans)\\n\", \"import math\\n\\nn = int(input())\\nprint(math.floor(math.sqrt(n)) ** 2)\", \"x = int(input())\\nfor i in range(10**5):\\n  if i**2>x:\\n    a=((i-1)**2)\\n    break\\nprint(a)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n)) * int(math.sqrt(n)))\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nans = 1\\nfor i in range(1,n+1):\\n    if (i*i > n):\\n        ans =  (i-1)**2\\n        break\\nprint(ans)\\n\\n\\n\\n\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nimport heapq\\nimport re\\nimport numpy as np\\nfrom functools import reduce\\n\\nrr = lambda: sys.stdin.readline().rstrip()\\nrs = lambda: sys.stdin.readline().split()\\nri = lambda: int(sys.stdin.readline())\\nrm = lambda: list(map(int, sys.stdin.readline().split()))\\nrl = lambda: list(map(int, sys.stdin.readline().split()))\\ninf = float('inf')\\nmod = 10**9 + 7\\n\\nn = ri()\\na = int(n**0.5)\\nprint((a**2))\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\", \"N = int(input())\\nfor i in range(N+1):\\n    if i ** 2 == N:\\n        print((i**2))\\n        return\\n    elif i ** 2 > N:\\n        print((max((i-1)**2,1)))\\n        return\\n\", \"n = int(input())\\nans = 0\\nk = 1\\nwhile k ** 2 <= n:\\n  ans = k ** 2\\n  k += 1\\nprint(ans)\", \"#ABC077B\\nn = int(input())\\nwhile n>0:\\n    tmp = n**(1/2)\\n    if(tmp==int(tmp)):\\n        print(n)\\n        break\\n    n-=1\", \"#!/usr/bin/env python3\\nimport sys\\nsys.setrecursionlimit(10**6)\\n\\nn = int(input())\\n\\nans = 1\\nfor i in range(0, n):\\n    if (ans+1)**2 > n:\\n        break\\n    ans += 1\\nprint((ans**2))\\n\", \"import math\\nn = int(input())\\ntmp = int(math.sqrt(n))\\nprint(tmp**2)\", \"N = int(input())\\n\\ni = 1\\nwhile i*i <= N:\\n  i += 1\\n\\nprint((i-1)**2)\", \"N=int(input())\\nC=0\\nif N==1:\\n  print(1)\\n  return\\nfor i in range(1,N):\\n  if i**2<N:\\n    C=i**2\\n  elif i**2==N:\\n    C=i**2\\n    break\\n  elif i**2>N:\\n    break\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "81\n",
        "output": "81\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc077/tasks/abc077_b"
    },
    {
        "id": 514,
        "task_id": 4562,
        "test_case_id": 3,
        "question": "Find the largest square number not exceeding N. Here, a square number is an integer that can be represented as the square of an integer.\n\n-----Constraints-----\n - 1 \\leq N \\leq 10^9\n - N is an integer.\n\n-----Input-----\nInput is given from Standard Input in the following format:\nN\n\n-----Output-----\nPrint the largest square number not exceeding N.\n\n-----Sample Input-----\n10\n\n-----Sample Output-----\n9\n\n10 is not square, but 9 = 3 × 3 is. Thus, we print 9.",
        "solutions": "[\"N = int (input ())\\nx = 1\\nwhile x**2 <= N:\\n  x += 1\\nx -= 1\\nprint (x**2)\", \"#\\n# abc077 b\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\nimport math\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"10\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"9\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"81\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"81\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"271828182\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"271821169\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    N = int(input())\\n    print((math.floor(math.sqrt(N))**2))\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"n = int(input())\\n\\ni=1\\nwhile i*i <= n:\\n    ans = i*i\\n    i+=1\\nprint(ans)\", \"n = int(input())\\nprint(int(n**(1/2))**2)\", \"N = int(input())\\ni = 1\\nif N == 1:\\n    print(i)\\nelse:\\n    while i <= N:\\n        if((i * i) > N):\\n            print((i-1) * (i-1))\\n            break\\n        i += 1\", \"from math import sqrt\\n\\nn = int(input())\\n\\nfor i in range(int(sqrt(n) + 1)):\\n    if i ** 2 <= n:\\n        ans = i ** 2\\nprint(ans)\", \"from math import sqrt\\nn = int(input())\\nprint(int(sqrt(n))**2)\", \"#!/usr/bin/env python3\\nN = int(input())\\n\\nans = 0\\nfor i in range(1, 10**5):\\n    n = i ** 2\\n    if n <= N:\\n        ans = n\\n    else:\\n        break\\nprint(ans)\\n\", \"print(int(int(input())**.5)**2)\", \"a=int(input())\\ni=0\\nwhile i**2<=a:\\n  i=i+1\\nprint((i-1)**2)\", \"n = int(input())\\n\\nfor i in range(n, 0, -1):\\n  j = int(i ** 0.5)\\n  if int(j) ** 2 == i:\\n    break\\nprint(i)\\n\", \"print((int(int(input())**0.5)**2))\\n\", \"import math\\nx=int(input())\\ny= math.sqrt(x)\\nz= y//1\\na=z**2\\nprint(int(a))\", \"n = int(input())\\nprint((int(n ** 0.5) ** 2))\\n\", \"n = int(input())\\nwhile (n ** 0.5) % 1 != 0:\\n    n -= 1\\nprint(n)\", \"print(int(int(input()) ** 0.5) ** 2)\", \"from math import sqrt\\n\\nn = int(input())\\n\\nans = int(sqrt(n))\\n\\nif (ans + 1) * (ans + 1) <= n:\\n    print((ans + 1) * (ans + 1))\\nelif ans * ans <= n:\\n    print(ans * ans)\\nelse:\\n    print((ans - 1) * (ans - 1))\", \"print(int(int(input())**0.5//1)**2)\", \"N=int(input())\\nans=1\\nfor i in range(N+1):\\n    if i*i<=N:\\n        ans=i\\n    else:\\n        break\\nprint((ans**2))\\n\", \"n = int(input())\\nx = 1\\nwhile x * x <= n:\\n    x += 1\\n \\nx -= 1\\nprint(x * x)\", \"n = int(input())\\nprint(int(n ** 0.5) ** 2)\", \"n = int(input())\\nfor i in range(100000):\\n  if n >= (10**5-i)**2:\\n    print((10**5-i)**2)\\n    return\", \"n=int(input())\\nprint(int(n**(1/2))**2)\", \"import math\\nprint(int(math.sqrt(int(input())))**2)\", \"from math import sqrt\\nn=int(input())\\nfor i in range(1,int(sqrt(n))+1):\\n  if i**2>n:\\n    print((i-1)**2)\\n    break\\nelse:\\n  print(i**2)\", \"import sys\\nN=int(input())\\nif N==1:\\n    print(\\\"1\\\")\\nelif N==2:\\n    print(\\\"1\\\")\\nelse:\\n    for i in range(N):\\n        if i**2>N:\\n            print((i-1)**2)\\n            return\\n        else:\\n            pass\", \"import math\\nN=int(input())\\nc=int(math.sqrt(N))\\nprint(c**2)\", \"n=int(input())\\ni=1\\ntmp=1\\nwhile True:\\n  if i**2 <= n:\\n    tmp = i**2\\n  else:\\n    break\\n  i += 1\\nprint(tmp)\", \"def multiple(n):\\n    a = []\\n    for i in range(1,int(n**.5)+1):\\n        a.append(i*i)\\n    return a\\nn = int(input())\\na = multiple(n)\\nans = 10**18\\nfor i in a:\\n    if n-i < 0:\\n        continue\\n    ans = min(ans,abs(n-i))\\nprint(n-ans)\", \"# coding = SJIS\\n\\nn = int(input())\\n\\nfor i in range(n):\\n    if int((n - i) ** 0.5) == (n - i) ** 0.5:\\n        print((n - i))\\n        return\\n\", \"import math\\na=int(input())\\nb=math.sqrt(a)\\nn=math.ceil(b)\\nm=math.floor(b)\\nprint(m**2)\", \"N=int(input())\\nfor i in range(int(N**0.5)+1):\\n    if N>=i**2:\\n        ans=i**2\\n    else:\\n        break\\nprint(ans)\", \"import math\\n\\n\\ndef answer(n: int) -> int:\\n    return int(math.sqrt(n)) ** 2\\n\\n\\ndef main():\\n    n = int(input())\\n    print(answer(n))\\n\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"n=int(input())\\nfor i in range(1,10**5+2):\\n  if i**2>n:print(((i-1)**2));return\\n\", \"n = int(input())\\nfor i in range(100000):\\n  if i**2 > n:\\n    print((i-1)**2)\\n    break\", \"n = int(input())\\nfor i in range(1,n+2):\\n    if i*i > n:\\n        print((i-1)*(i-1))\\n        return\", \"print((int(int(input())**.5)**2))\\n\", \"n = int(input())\\nans=1\\nfor i in range(n+1):\\n    if i**2<=n:\\n        ans=i**2\\n    else:\\n        break\\n\\nprint(ans)\", \"import math\\nN = int(input())\\n\\nans = 1\\nfor i in range(1,math.floor(math.sqrt(N))+1):\\n  if i * i <= N:\\n    ans = i * i\\n    \\nprint(ans)\", \"def main():\\n    N = int(input())\\n    a = 1\\n    i = 0\\n    prev = 0\\n    while a <= N:\\n        i += 1\\n        prev = a\\n        if a > N:\\n            break\\n        else:\\n            a = i * i\\n    print(prev) \\nmain()\\n\", \"print(int(int(input())**.5)**2)\", \"import math\\nN = int(input())\\nfor i in range(N):\\n  x = N - i\\n  if int(math.sqrt(x)) == math.sqrt(x):\\n    print(x)\\n    break\\n\", \"N = int(input())\\n\\nfrom math import floor, sqrt\\nans = floor(sqrt(N))**2\\nprint(ans)\\n\", \"n = int(input())\\nprint(int(n**0.5)**2)\", \"N = int(input())\\nfor i in range(1, N+1):\\n    if i*i > N:\\n        print(((i-1)*(i-1)))\\n        return\\nprint((1))\\n\", \"N = int(input())\\n \\nprint(int(N**0.5)**2)\", \"N = int(input())\\nprint(int(N**(1/2))**2)\", \"N = int(input())\\nprint(int((N**(1/2)//1)**2))\", \"n=int(input())\\n\\nans=1\\nloop = 3\\nfor i in range (1,100000):\\n        if i**2 <= n:\\n                ans=i**2\\n        \\n        \\n\\nprint(ans)\", \"n=int(input())\\ni=1\\ntmp=1\\nwhile True:\\n  if i**2<=n:\\n    tmp=i**2\\n  else:\\n    break\\n  i+=1\\nprint(tmp)\", \"n = int(input())\\nprint((int(n ** 0.5)) ** 2)\", \"N = int(input())\\n\\nfor i in range(1, 10**9):\\n  if i**2 == N:\\n    print((i**2))\\n    break\\n  elif i**2 > N:\\n    print(((i-1)**2))\\n    break\\n\", \"N = int(input())\\nprint((int(N**(1/2))**2))\\n\", \"n = int(input())\\nprint((int(n**(1/2)))**2)\", \"n = int(input())\\n\\n\\nans = 1\\nfor i in range(1, n):\\n  if i**2 > n:\\n    ans = (i-1)**2\\n    break\\n\\n\\nprint(ans)\", \"import math\\nans=math.floor(int(input())**0.5)\\nprint (ans*ans)\", \"N = int(input())\\nans = 1\\nfor i in range(1, N):\\n    if i*i > N:\\n        break\\n    ans = max(ans, i*i)\\nprint(ans)\", \"print(int(int(input())**.5)**2)\", \"n = int(input())\\nans = 0\\nfor i in range(100001):\\n    if i **2 <= n:\\n        ans = i**2\\n    \\nprint(ans)\\n\", \"import math\\n\\nN=int(input())\\nn=math.floor(math.sqrt(N))**2\\n\\nprint(n)\\n\\n\", \"n = int(input())\\nprint(int(n ** 0.5) ** 2)\", \"from math import sqrt\\n\\nn = int(input())\\nprint(int(sqrt(n)) ** 2)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n))**2)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n))**2)\", \"n = int(input())\\nc = 1\\nfor i in range(10**5):\\n    if i**2 <= n:c = i**2\\n    else:break\\nprint(c)\", \"N = int(input())\\n\\nfor i in range(int(N**0.5)+3):\\n  if i**2 > N:\\n    print((i-1)**2)\\n    break\", \"n = int(input())\\nprint(int(n**.5) ** 2)\", \"import math\\nN=int(input())\\nans=N\\nfor i in range(N):\\n  if math.sqrt(ans).is_integer():\\n    print(ans)\\n    break\\n  ans-=1\", \"N=int(input())\\nimport math\\nprint((int(math.sqrt(N)))**2)\", \"n = int(input())\\n\\nfor i in range(1, 10**5):\\n    p = i**2\\n    if p > n:\\n        print((i-1)**2)\\n        break\", \"import math\\n\\nn = int(input())\\nprint(math.floor(math.sqrt(n)) ** 2)\", \"N=int(input())\\nprint(int(N**(1/2))**2)\", \"n = int(input())\\n\\nans = 0\\nmax = int(n**0.5)+1\\nfor i in range(1, max, 1):\\n    tmp = i**2\\n    if tmp <= n:\\n        ans = tmp\\nprint(ans)\", \"n=int(input())\\n\\nfor i in range(10**5):\\n    if i**2 > n:\\n        print((i-1)**2)\\n        break\", \"n = int(input())\\np = int(n**0.5)\\na = 1\\nans = 1\\nwhile a<=p:\\n    if a**2 <=n:\\n        ans = max(ans,a**2)\\n    a +=1\\nprint(ans)\", \"N = int(input())\\nprint(int(N**(0.5))**2)\", \"N=int(input())\\nif int((N+1)**.5)**2==N:print(N)\\nelse:print(int(N**.5)**2)\", \"N = int(input())\\nprint((int(N**.5)**2))\\n\", \"N = int(input())\\nprint(int(N**0.5)**2)\", \"N = int(input())\\nfrom math import sqrt, floor\\nfor i in range(1,floor(sqrt(N))+2):\\n    if i**2 > N:\\n        print((i-1)**2)\", \"import math\\nn = int(input())\\n\\nfor i in range(10**5):\\n    if n < i ** 2:\\n        print((i-1) ** 2)\\n        break\", \"n=int(input())\\nprint(int(n**0.5)**2)\", \"n=int(input())\\nres=1\\nfor i in range(100000):\\n    if i**2>n:\\n        break\\n    res=i*i\\nprint(res)\", \"n = int(input())\\nfor i in range(1, n):\\n    if i**2 > n:\\n        print((i-1)**2)\\n        break\\nelse:\\n    print(1)\", \"import math\\nn = int(input())\\nfor i in range(10**9):\\n  if math.sqrt(n) == int(math.sqrt(n)):\\n    print(n)\\n    break\\n  n -= 1\\n\", \"N=int(input())\\nif N==1 :\\n  print(1)\\n  return\\nfor i in range(1,N+1) :\\n  if i*i>N :\\n    print((i-1)*(i-1))\\n    return\", \"n = int(input())\\n\\nans = 0\\nfor i in range(1, 10 ** 5):\\n    if i ** 2 <= n:\\n        ans = i ** 2\\n\\nprint(ans)\\n\", \"import math\\n\\nn = int(input())\\nprint(math.floor(math.sqrt(n)) ** 2)\", \"x = int(input())\\nfor i in range(10**5):\\n  if i**2>x:\\n    a=((i-1)**2)\\n    break\\nprint(a)\", \"import math\\nn = int(input())\\nprint(int(math.sqrt(n)) * int(math.sqrt(n)))\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n#a = [int(input()) for _ in range(n)]\\n\\nn = int(input())\\n\\nans = 1\\nfor i in range(1,n+1):\\n    if (i*i > n):\\n        ans =  (i-1)**2\\n        break\\nprint(ans)\\n\\n\\n\\n\", \"import sys\\nimport math\\nimport itertools\\nimport collections\\nimport heapq\\nimport re\\nimport numpy as np\\nfrom functools import reduce\\n\\nrr = lambda: sys.stdin.readline().rstrip()\\nrs = lambda: sys.stdin.readline().split()\\nri = lambda: int(sys.stdin.readline())\\nrm = lambda: list(map(int, sys.stdin.readline().split()))\\nrl = lambda: list(map(int, sys.stdin.readline().split()))\\ninf = float('inf')\\nmod = 10**9 + 7\\n\\nn = ri()\\na = int(n**0.5)\\nprint((a**2))\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\", \"N = int(input())\\nfor i in range(N+1):\\n    if i ** 2 == N:\\n        print((i**2))\\n        return\\n    elif i ** 2 > N:\\n        print((max((i-1)**2,1)))\\n        return\\n\", \"n = int(input())\\nans = 0\\nk = 1\\nwhile k ** 2 <= n:\\n  ans = k ** 2\\n  k += 1\\nprint(ans)\", \"#ABC077B\\nn = int(input())\\nwhile n>0:\\n    tmp = n**(1/2)\\n    if(tmp==int(tmp)):\\n        print(n)\\n        break\\n    n-=1\", \"#!/usr/bin/env python3\\nimport sys\\nsys.setrecursionlimit(10**6)\\n\\nn = int(input())\\n\\nans = 1\\nfor i in range(0, n):\\n    if (ans+1)**2 > n:\\n        break\\n    ans += 1\\nprint((ans**2))\\n\", \"import math\\nn = int(input())\\ntmp = int(math.sqrt(n))\\nprint(tmp**2)\", \"N = int(input())\\n\\ni = 1\\nwhile i*i <= N:\\n  i += 1\\n\\nprint((i-1)**2)\", \"N=int(input())\\nC=0\\nif N==1:\\n  print(1)\\n  return\\nfor i in range(1,N):\\n  if i**2<N:\\n    C=i**2\\n  elif i**2==N:\\n    C=i**2\\n    break\\n  elif i**2>N:\\n    break\\nprint(C)\"]",
        "difficulty": "introductory",
        "input": "271828182\n",
        "output": "271821169\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc077/tasks/abc077_b"
    },
    {
        "id": 515,
        "task_id": 4577,
        "test_case_id": 1,
        "question": "You are given three integers A, B and C.\nDetermine whether C is not less than A and not greater than B.\n\n-----Constraints-----\n - -100≤A,B,C≤100 \n - A, B and C are all integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:  \nA B C\n\n-----Output-----\nIf the condition is satisfied, print Yes; otherwise, print No.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\nYes\n\nC=2 is not less than A=1 and not greater than B=3, and thus the output should be Yes.",
        "solutions": "[\"# 3 \\u3064\\u306e\\u6574\\u6570 A , B , C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# \\u6574\\u6570 C \\u304c A \\u4ee5\\u4e0a \\u304b\\u3064 B \\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3057\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nA,B,C = map(int,input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\n\\nelse:\\n    print('No')\", \"A,B,C = map(int,input().split())\\n\\nif A <= C and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"# A - Between Two Integers\\n# https://atcoder.jp/contests/abc061/tasks/abc061_a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nresult = 'No'\\n\\nif A <= C <= B:\\n    result = 'Yes'\\n\\nprint(result)\\n\", \"a,b,c=map(int,input().split(\\\" \\\"))\\nprint(\\\"Yes\\\") if a<=c and c<=b else print(\\\"No\\\")\", \"a, b, c = map( int, input().split())\\n\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c<=b:print('Yes')\\nelse:print('No')\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"# 3\\u3064\\u306e\\u6574\\u6570 A, B, C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# \\u6574\\u6570 C \\u304c A \\u4ee5\\u4e0a \\u304b\\u3064 B \\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3057\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\n# \\u5236\\u7d04\\n# \\u2212100 \\u2266 A, B, C \\u2266 100\\n# A, B, C \\u306f\\u5168\\u3066\\u6574\\u6570\\n\\n# \\u6a19\\u6e96\\u5165\\u529b\\u304b\\u3089 A, B, C \\u3092\\u53d6\\u5f97\\u3059\\u308b\\na, b, c = list(map(int, input().split()))\\n\\n# \\u5224\\u5b9a\\u3057\\u3066\\u7d50\\u679c\\u3092\\u51fa\\u529b\\u3059\\u308b\\nresut = \\\"ret\\\"\\n\\nif a <= c and b >= c:\\n    result = \\\"Yes\\\"\\nelse:\\n    result = \\\"No\\\"\\n\\nprint(result)\\n\", \"a,b,c = map(int,input().split())\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"i = list(map(int,input().split()))\\n\\nif i[0]<=i[2]<=i[1]:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif a<=c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\"if a<=c<=b else \\\"No\\\")\", \"a,b,c = list(map(int,input().split()))\\nprint((\\\"Yes\\\" if a<=c<=b else \\\"No\\\"))\\n\", \"# \\u5404\\u6570\\u5024\\u306e\\u53d6\\u5f97\\nA,B,C = map(int,input().split())\\n\\n# \\u6570\\u5024\\u3092\\u6bd4\\u8f03\\u3057\\u3066\\u30e1\\u30c3\\u30bb\\u30fc\\u30b8\\u3092\\u51fa\\u529b\\nif C >= A \\\\\\nand C <=B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b, c = map(int, input().split())\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int, input().split())\\n\\nprint(\\\"Yes\\\" if A <= C and C <= B else \\\"No\\\")\", \"a,b,c = map(int,input().split())\\n\\nprint('Yes' if a <= c <= b else 'No')\", \"a,b,c = map(int,input().split())\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c = map(int,input().split())\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int, input().split())\\nans = 'Yes' if c >= a and c <= b else 'No'\\nprint(ans)\", \"# 061_a\\nA, B, C = list(map(int, input().split()))\\nif (-100 <= A <= 100) and (-100 <= B <= 100) and (-100 <= C <= 100):\\n    if A <= C and C <= B:\\n        print('Yes')\\n    else:\\n        print('No')\\n\", \"A,B,C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b\\n      else \\\"No\\\")\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a <= c and c <= b else \\\"No\\\")\", \"# 3\\u3064\\u306e\\u6574\\u6570A,B,C\\u3002C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u304b\\u5224\\u5b9a\\u3002\\n\\nA, B, C = map(int, input().split())\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C =map(int,input().split())\\nif C >= A and C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"#   AtCoder abc061 a\\n#   \\u30b9\\u30c8\\u30ec\\u30c3\\u30c1\\u8ab2\\u984c\\n\\n#   \\u5165\\u529b\\na, b, c = list(map(int, input().split()))\\n\\n#   \\u5224\\u5b9a\\nif (c >= a) and (c <= b):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif c>=a and c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c = list(map(int,input().split()))\\n#lis = list(map(int,input().split()))\\nprint((\\\"Yes\\\" if a<=c<=b else \\\"No\\\"))\\n\\n\\n\\n\\n\", \"A,B,C=list(map(int,input().split()))\\nif C>=A and B>=C:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif (a<=c and c<=b):\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c=map(int,input().split())\\nif (a<=c)and(c<=b):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split());print('NYoe s'[a<=c<=b::2])\", \"A,B,C=map(int,input().split())\\nif C>=A and C<=B :\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"A, B, C = [int(i) for i in input().split()]\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"A, B, C = map(int, input().split())\\n\\nif A <= C and B >= C:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nprint('Yes' if a<=c<=b else 'No')\", \"A,B,C=list(map(int,input().split()))\\nif A<=C and C<=B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a, b, c = map(int, input().split())\\n\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nprint('Yes' if a <= c <= b else 'No')\", \"a, b, c=map(int, input().split())\\nif a<=c<=b:\\n  print('Yes')\\nelse:\\n  print('No')\", \"A,B,C = map(int,input().split())\\nprint(\\\"Yes\\\") if A<=C<=B else print(\\\"No\\\")\", \"a,b,c=map(int, input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"A, B, C = list(map(int, input().split()))\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = [int(x) for x in input().split()]\\nif a <= c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = list(map(int, input().split()))\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b,c=map(int,input().split())\\n\\nif c>=a and c<=b:\\n    ans=\\\"Yes\\\"\\nelse:\\n    ans=\\\"No\\\"\\nprint(ans)\", \"A, B, C = map(int, input().split())\\n\\nif (C >= A) and (C <= B):\\n    print( \\\"Yes\\\" )\\nelse :\\n    print( \\\"No\\\" )\", \"A, B, C = map(int,input().split())\\nprint(\\\"Yes\\\" if A <= C <= B else \\\"No\\\")\", \"A,B,C = map(int, input().split())\\nprint('Yes' if A<=C<=B else 'No')\", \"a, b, c = map(int, input().split())\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int,input().split())\\n\\nif a<= c and b>=c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import sys\\n\\ndef I(): return int(sys.stdin.readline())\\ndef MI(): return map(int, sys.stdin.readline().split())\\ndef LI(): return list(map(int, sys.stdin.readline().split()))\\ndef main():\\n    a, b, c = MI()\\n    if a <= c and c <= b:\\n        print('Yes')\\n    else:\\n        print('No')\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# 061a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a = list(map(int,input().split()))\\n\\nprint('Yes' if a[0] <= a[2] <= a[1] else 'No')\", \"A,B,C=map(int,input().split())\\nif (C>=A) & (C<=B):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A,B,C = map(int,input().split())\\nprint(['No','Yes'][C>=A and B>=C])\", \"#\\n# abc061 a\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"1 3 2\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"6 5 4\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"2 2 2\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B, C = list(map(int, input().split()))\\n    if A <= C <= B:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"a, b, c = map(int, input().split())\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"A,B,C = map(int,input().split())\\n\\nif A <= C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int,input().split())\\n\\nif B >= C >= A:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"A,B,C = list(map(int, input().split()))\\n\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# \\u51fa\\u529b\\nif -100 <= A and B and C <= 100:\\n    if C >= A and C <= B:\\n        print('Yes')\\n    else:\\n        print('No')\", \"a,b,c = map(int,input().split())\\nif c >= a and c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b, c = list(map(int, input().split()))\\n\\nif (c >= a) and (c <= b):\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"A, B, C = map(int, input().split())\\nif C >= A and C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"# \\u5165\\u529b\\nA, B, C =map(int,input().split())\\n\\n# \\u51e6\\u7406\\nif C >=A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int,input().split())\\nif (C>=A) and (C<=B):\\n  print('Yes')\\nelse:\\n  print('No')\", \"a, b, c = map(int,input().split())\\nprint('Yes') if a <= c <= b else print('No')\\n\", \"S_list = list(map(int,input().split()))\\n\\nif  S_list[1] - S_list[0] >= 0 and S_list[2]- S_list[0] >=0 and S_list[1] - S_list[2] >=0:\\n    result = \\\"Yes\\\"\\nelse:\\n    result = \\\"No\\\"\\nprint(result)\\n\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if c>=a and c<=b else \\\"No\\\")\", \"a,b,c = map(int, input().split())\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = list(map(int, input().split()))\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#n = int(input())\\na, b, c = list(map(int, input().split()))\\n#l = list(map(int,input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b,c = map(int,input().split())\\nif a<=c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a = list(map(int,input().split()))\\n# b = list(map(int,input().split()))\\n\\nif a[0]<=a[2]<=a[1]:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import sys, math\\nfrom itertools import combinations as c, product as p\\nfrom collections import deque\\nsys.setrecursionlimit(10**9)\\nINF = float('inf')\\nMOD = 10**9 + 7\\n#MOD = 998244353\\n\\n\\ndef si(): return input()\\ndef ii(): return int(input())\\ndef fi(): return float(input())\\ndef lstr(): return input().split()\\ndef lint(): return list(map(int, input().split()))\\ndef lintdec(): return list(map(lambda x:int(x) - 1, input().split()))\\ndef lnstr(n): return [input() for _ in range(n)]\\ndef lnint(n): return [int(input()) for _ in range(n)]\\ndef lint_list(n): return [lint() for _ in range(n)]\\n\\n\\n\\n############################################################\\nA, B, C = lint()\\nprint('Yes' if A <= C <= B else 'No')\", \"# A - Between Two Integers\\n\\n# \\u6574\\u6570A,B,C\\u304c\\u5165\\u529b\\u3055\\u308c\\u308b\\n# C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n\\n\\nA,B,C = list(map(int,input().split()))\\n\\nif A<=C and B>=C:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a <= c and c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int, input().split())\\nprint(\\\"Yes\\\" if C >= A and C <= B else \\\"No\\\")\", \"def iroha():\\n    a, b, c = list(map(int, input().split()))\\n\\n    if a <= c and b >= c:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    iroha()\\n\\n\\n__starting_point()\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u306a\\u3089Yes\\u3001\\u9055\\u3046\\u306a\\u3089No\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b: print('Yes')\\nelse: print('No')\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"a=list(map(int,input().split()))\\n\\nif (a[2]>=a[0]) and (a[2]<=a[1]):\\n  print('Yes')\\n  \\nelse:\\n  print('No')\", \"A, B, C = map(int, open(0).readline().split())\\nprint('Yes' if A <= C <= B else 'No')\", \"a,b,c = map(int, input().split())\\n\\nif b >= c >= a:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"'''\\nabc061 A - Between Two Integers\\nhttps://atcoder.jp/contests/abc061/tasks/abc061_a\\n'''\\n\\ni = list(map(int, input().split()))\\nif i[2] >= i[0] and i[1] >= i[2]:\\n    ans = 'Yes'\\nelse:\\n    ans = 'No'\\nprint(ans)\\n\", \"a, b, c = map(int, input().split())\\n\\nif c>=a and c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b:\\n  print('Yes')\\nelse:\\n  print('No')\", \"A, B, C = map(int, input().split())\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\"]",
        "difficulty": "introductory",
        "input": "1 3 2\n",
        "output": "Yes\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc061/tasks/abc061_a"
    },
    {
        "id": 516,
        "task_id": 4577,
        "test_case_id": 2,
        "question": "You are given three integers A, B and C.\nDetermine whether C is not less than A and not greater than B.\n\n-----Constraints-----\n - -100≤A,B,C≤100 \n - A, B and C are all integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:  \nA B C\n\n-----Output-----\nIf the condition is satisfied, print Yes; otherwise, print No.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\nYes\n\nC=2 is not less than A=1 and not greater than B=3, and thus the output should be Yes.",
        "solutions": "[\"# 3 \\u3064\\u306e\\u6574\\u6570 A , B , C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# \\u6574\\u6570 C \\u304c A \\u4ee5\\u4e0a \\u304b\\u3064 B \\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3057\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nA,B,C = map(int,input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\n\\nelse:\\n    print('No')\", \"A,B,C = map(int,input().split())\\n\\nif A <= C and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"# A - Between Two Integers\\n# https://atcoder.jp/contests/abc061/tasks/abc061_a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nresult = 'No'\\n\\nif A <= C <= B:\\n    result = 'Yes'\\n\\nprint(result)\\n\", \"a,b,c=map(int,input().split(\\\" \\\"))\\nprint(\\\"Yes\\\") if a<=c and c<=b else print(\\\"No\\\")\", \"a, b, c = map( int, input().split())\\n\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c<=b:print('Yes')\\nelse:print('No')\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"# 3\\u3064\\u306e\\u6574\\u6570 A, B, C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# \\u6574\\u6570 C \\u304c A \\u4ee5\\u4e0a \\u304b\\u3064 B \\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3057\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\n# \\u5236\\u7d04\\n# \\u2212100 \\u2266 A, B, C \\u2266 100\\n# A, B, C \\u306f\\u5168\\u3066\\u6574\\u6570\\n\\n# \\u6a19\\u6e96\\u5165\\u529b\\u304b\\u3089 A, B, C \\u3092\\u53d6\\u5f97\\u3059\\u308b\\na, b, c = list(map(int, input().split()))\\n\\n# \\u5224\\u5b9a\\u3057\\u3066\\u7d50\\u679c\\u3092\\u51fa\\u529b\\u3059\\u308b\\nresut = \\\"ret\\\"\\n\\nif a <= c and b >= c:\\n    result = \\\"Yes\\\"\\nelse:\\n    result = \\\"No\\\"\\n\\nprint(result)\\n\", \"a,b,c = map(int,input().split())\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"i = list(map(int,input().split()))\\n\\nif i[0]<=i[2]<=i[1]:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif a<=c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\"if a<=c<=b else \\\"No\\\")\", \"a,b,c = list(map(int,input().split()))\\nprint((\\\"Yes\\\" if a<=c<=b else \\\"No\\\"))\\n\", \"# \\u5404\\u6570\\u5024\\u306e\\u53d6\\u5f97\\nA,B,C = map(int,input().split())\\n\\n# \\u6570\\u5024\\u3092\\u6bd4\\u8f03\\u3057\\u3066\\u30e1\\u30c3\\u30bb\\u30fc\\u30b8\\u3092\\u51fa\\u529b\\nif C >= A \\\\\\nand C <=B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b, c = map(int, input().split())\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int, input().split())\\n\\nprint(\\\"Yes\\\" if A <= C and C <= B else \\\"No\\\")\", \"a,b,c = map(int,input().split())\\n\\nprint('Yes' if a <= c <= b else 'No')\", \"a,b,c = map(int,input().split())\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c = map(int,input().split())\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int, input().split())\\nans = 'Yes' if c >= a and c <= b else 'No'\\nprint(ans)\", \"# 061_a\\nA, B, C = list(map(int, input().split()))\\nif (-100 <= A <= 100) and (-100 <= B <= 100) and (-100 <= C <= 100):\\n    if A <= C and C <= B:\\n        print('Yes')\\n    else:\\n        print('No')\\n\", \"A,B,C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b\\n      else \\\"No\\\")\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a <= c and c <= b else \\\"No\\\")\", \"# 3\\u3064\\u306e\\u6574\\u6570A,B,C\\u3002C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u304b\\u5224\\u5b9a\\u3002\\n\\nA, B, C = map(int, input().split())\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C =map(int,input().split())\\nif C >= A and C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"#   AtCoder abc061 a\\n#   \\u30b9\\u30c8\\u30ec\\u30c3\\u30c1\\u8ab2\\u984c\\n\\n#   \\u5165\\u529b\\na, b, c = list(map(int, input().split()))\\n\\n#   \\u5224\\u5b9a\\nif (c >= a) and (c <= b):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif c>=a and c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c = list(map(int,input().split()))\\n#lis = list(map(int,input().split()))\\nprint((\\\"Yes\\\" if a<=c<=b else \\\"No\\\"))\\n\\n\\n\\n\\n\", \"A,B,C=list(map(int,input().split()))\\nif C>=A and B>=C:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif (a<=c and c<=b):\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c=map(int,input().split())\\nif (a<=c)and(c<=b):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split());print('NYoe s'[a<=c<=b::2])\", \"A,B,C=map(int,input().split())\\nif C>=A and C<=B :\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"A, B, C = [int(i) for i in input().split()]\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"A, B, C = map(int, input().split())\\n\\nif A <= C and B >= C:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nprint('Yes' if a<=c<=b else 'No')\", \"A,B,C=list(map(int,input().split()))\\nif A<=C and C<=B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a, b, c = map(int, input().split())\\n\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nprint('Yes' if a <= c <= b else 'No')\", \"a, b, c=map(int, input().split())\\nif a<=c<=b:\\n  print('Yes')\\nelse:\\n  print('No')\", \"A,B,C = map(int,input().split())\\nprint(\\\"Yes\\\") if A<=C<=B else print(\\\"No\\\")\", \"a,b,c=map(int, input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"A, B, C = list(map(int, input().split()))\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = [int(x) for x in input().split()]\\nif a <= c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = list(map(int, input().split()))\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b,c=map(int,input().split())\\n\\nif c>=a and c<=b:\\n    ans=\\\"Yes\\\"\\nelse:\\n    ans=\\\"No\\\"\\nprint(ans)\", \"A, B, C = map(int, input().split())\\n\\nif (C >= A) and (C <= B):\\n    print( \\\"Yes\\\" )\\nelse :\\n    print( \\\"No\\\" )\", \"A, B, C = map(int,input().split())\\nprint(\\\"Yes\\\" if A <= C <= B else \\\"No\\\")\", \"A,B,C = map(int, input().split())\\nprint('Yes' if A<=C<=B else 'No')\", \"a, b, c = map(int, input().split())\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int,input().split())\\n\\nif a<= c and b>=c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import sys\\n\\ndef I(): return int(sys.stdin.readline())\\ndef MI(): return map(int, sys.stdin.readline().split())\\ndef LI(): return list(map(int, sys.stdin.readline().split()))\\ndef main():\\n    a, b, c = MI()\\n    if a <= c and c <= b:\\n        print('Yes')\\n    else:\\n        print('No')\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# 061a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a = list(map(int,input().split()))\\n\\nprint('Yes' if a[0] <= a[2] <= a[1] else 'No')\", \"A,B,C=map(int,input().split())\\nif (C>=A) & (C<=B):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A,B,C = map(int,input().split())\\nprint(['No','Yes'][C>=A and B>=C])\", \"#\\n# abc061 a\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"1 3 2\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"6 5 4\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"2 2 2\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B, C = list(map(int, input().split()))\\n    if A <= C <= B:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"a, b, c = map(int, input().split())\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"A,B,C = map(int,input().split())\\n\\nif A <= C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int,input().split())\\n\\nif B >= C >= A:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"A,B,C = list(map(int, input().split()))\\n\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# \\u51fa\\u529b\\nif -100 <= A and B and C <= 100:\\n    if C >= A and C <= B:\\n        print('Yes')\\n    else:\\n        print('No')\", \"a,b,c = map(int,input().split())\\nif c >= a and c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b, c = list(map(int, input().split()))\\n\\nif (c >= a) and (c <= b):\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"A, B, C = map(int, input().split())\\nif C >= A and C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"# \\u5165\\u529b\\nA, B, C =map(int,input().split())\\n\\n# \\u51e6\\u7406\\nif C >=A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int,input().split())\\nif (C>=A) and (C<=B):\\n  print('Yes')\\nelse:\\n  print('No')\", \"a, b, c = map(int,input().split())\\nprint('Yes') if a <= c <= b else print('No')\\n\", \"S_list = list(map(int,input().split()))\\n\\nif  S_list[1] - S_list[0] >= 0 and S_list[2]- S_list[0] >=0 and S_list[1] - S_list[2] >=0:\\n    result = \\\"Yes\\\"\\nelse:\\n    result = \\\"No\\\"\\nprint(result)\\n\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if c>=a and c<=b else \\\"No\\\")\", \"a,b,c = map(int, input().split())\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = list(map(int, input().split()))\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#n = int(input())\\na, b, c = list(map(int, input().split()))\\n#l = list(map(int,input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b,c = map(int,input().split())\\nif a<=c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a = list(map(int,input().split()))\\n# b = list(map(int,input().split()))\\n\\nif a[0]<=a[2]<=a[1]:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import sys, math\\nfrom itertools import combinations as c, product as p\\nfrom collections import deque\\nsys.setrecursionlimit(10**9)\\nINF = float('inf')\\nMOD = 10**9 + 7\\n#MOD = 998244353\\n\\n\\ndef si(): return input()\\ndef ii(): return int(input())\\ndef fi(): return float(input())\\ndef lstr(): return input().split()\\ndef lint(): return list(map(int, input().split()))\\ndef lintdec(): return list(map(lambda x:int(x) - 1, input().split()))\\ndef lnstr(n): return [input() for _ in range(n)]\\ndef lnint(n): return [int(input()) for _ in range(n)]\\ndef lint_list(n): return [lint() for _ in range(n)]\\n\\n\\n\\n############################################################\\nA, B, C = lint()\\nprint('Yes' if A <= C <= B else 'No')\", \"# A - Between Two Integers\\n\\n# \\u6574\\u6570A,B,C\\u304c\\u5165\\u529b\\u3055\\u308c\\u308b\\n# C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n\\n\\nA,B,C = list(map(int,input().split()))\\n\\nif A<=C and B>=C:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a <= c and c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int, input().split())\\nprint(\\\"Yes\\\" if C >= A and C <= B else \\\"No\\\")\", \"def iroha():\\n    a, b, c = list(map(int, input().split()))\\n\\n    if a <= c and b >= c:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    iroha()\\n\\n\\n__starting_point()\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u306a\\u3089Yes\\u3001\\u9055\\u3046\\u306a\\u3089No\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b: print('Yes')\\nelse: print('No')\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"a=list(map(int,input().split()))\\n\\nif (a[2]>=a[0]) and (a[2]<=a[1]):\\n  print('Yes')\\n  \\nelse:\\n  print('No')\", \"A, B, C = map(int, open(0).readline().split())\\nprint('Yes' if A <= C <= B else 'No')\", \"a,b,c = map(int, input().split())\\n\\nif b >= c >= a:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"'''\\nabc061 A - Between Two Integers\\nhttps://atcoder.jp/contests/abc061/tasks/abc061_a\\n'''\\n\\ni = list(map(int, input().split()))\\nif i[2] >= i[0] and i[1] >= i[2]:\\n    ans = 'Yes'\\nelse:\\n    ans = 'No'\\nprint(ans)\\n\", \"a, b, c = map(int, input().split())\\n\\nif c>=a and c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b:\\n  print('Yes')\\nelse:\\n  print('No')\", \"A, B, C = map(int, input().split())\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\"]",
        "difficulty": "introductory",
        "input": "6 5 4\n",
        "output": "No\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc061/tasks/abc061_a"
    },
    {
        "id": 517,
        "task_id": 4577,
        "test_case_id": 3,
        "question": "You are given three integers A, B and C.\nDetermine whether C is not less than A and not greater than B.\n\n-----Constraints-----\n - -100≤A,B,C≤100 \n - A, B and C are all integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:  \nA B C\n\n-----Output-----\nIf the condition is satisfied, print Yes; otherwise, print No.\n\n-----Sample Input-----\n1 3 2\n\n-----Sample Output-----\nYes\n\nC=2 is not less than A=1 and not greater than B=3, and thus the output should be Yes.",
        "solutions": "[\"# 3 \\u3064\\u306e\\u6574\\u6570 A , B , C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# \\u6574\\u6570 C \\u304c A \\u4ee5\\u4e0a \\u304b\\u3064 B \\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3057\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nA,B,C = map(int,input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\n\\nelse:\\n    print('No')\", \"A,B,C = map(int,input().split())\\n\\nif A <= C and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"# A - Between Two Integers\\n# https://atcoder.jp/contests/abc061/tasks/abc061_a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nresult = 'No'\\n\\nif A <= C <= B:\\n    result = 'Yes'\\n\\nprint(result)\\n\", \"a,b,c=map(int,input().split(\\\" \\\"))\\nprint(\\\"Yes\\\") if a<=c and c<=b else print(\\\"No\\\")\", \"a, b, c = map( int, input().split())\\n\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c<=b:print('Yes')\\nelse:print('No')\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"# 3\\u3064\\u306e\\u6574\\u6570 A, B, C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# \\u6574\\u6570 C \\u304c A \\u4ee5\\u4e0a \\u304b\\u3064 B \\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3057\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\n# \\u5236\\u7d04\\n# \\u2212100 \\u2266 A, B, C \\u2266 100\\n# A, B, C \\u306f\\u5168\\u3066\\u6574\\u6570\\n\\n# \\u6a19\\u6e96\\u5165\\u529b\\u304b\\u3089 A, B, C \\u3092\\u53d6\\u5f97\\u3059\\u308b\\na, b, c = list(map(int, input().split()))\\n\\n# \\u5224\\u5b9a\\u3057\\u3066\\u7d50\\u679c\\u3092\\u51fa\\u529b\\u3059\\u308b\\nresut = \\\"ret\\\"\\n\\nif a <= c and b >= c:\\n    result = \\\"Yes\\\"\\nelse:\\n    result = \\\"No\\\"\\n\\nprint(result)\\n\", \"a,b,c = map(int,input().split())\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"i = list(map(int,input().split()))\\n\\nif i[0]<=i[2]<=i[1]:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif a<=c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\"if a<=c<=b else \\\"No\\\")\", \"a,b,c = list(map(int,input().split()))\\nprint((\\\"Yes\\\" if a<=c<=b else \\\"No\\\"))\\n\", \"# \\u5404\\u6570\\u5024\\u306e\\u53d6\\u5f97\\nA,B,C = map(int,input().split())\\n\\n# \\u6570\\u5024\\u3092\\u6bd4\\u8f03\\u3057\\u3066\\u30e1\\u30c3\\u30bb\\u30fc\\u30b8\\u3092\\u51fa\\u529b\\nif C >= A \\\\\\nand C <=B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b, c = map(int, input().split())\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int, input().split())\\n\\nprint(\\\"Yes\\\" if A <= C and C <= B else \\\"No\\\")\", \"a,b,c = map(int,input().split())\\n\\nprint('Yes' if a <= c <= b else 'No')\", \"a,b,c = map(int,input().split())\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c = map(int,input().split())\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int, input().split())\\nans = 'Yes' if c >= a and c <= b else 'No'\\nprint(ans)\", \"# 061_a\\nA, B, C = list(map(int, input().split()))\\nif (-100 <= A <= 100) and (-100 <= B <= 100) and (-100 <= C <= 100):\\n    if A <= C and C <= B:\\n        print('Yes')\\n    else:\\n        print('No')\\n\", \"A,B,C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b\\n      else \\\"No\\\")\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a <= c and c <= b else \\\"No\\\")\", \"# 3\\u3064\\u306e\\u6574\\u6570A,B,C\\u3002C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u304b\\u5224\\u5b9a\\u3002\\n\\nA, B, C = map(int, input().split())\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C =map(int,input().split())\\nif C >= A and C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"#   AtCoder abc061 a\\n#   \\u30b9\\u30c8\\u30ec\\u30c3\\u30c1\\u8ab2\\u984c\\n\\n#   \\u5165\\u529b\\na, b, c = list(map(int, input().split()))\\n\\n#   \\u5224\\u5b9a\\nif (c >= a) and (c <= b):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif c>=a and c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c = list(map(int,input().split()))\\n#lis = list(map(int,input().split()))\\nprint((\\\"Yes\\\" if a<=c<=b else \\\"No\\\"))\\n\\n\\n\\n\\n\", \"A,B,C=list(map(int,input().split()))\\nif C>=A and B>=C:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif (a<=c and c<=b):\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c=map(int,input().split())\\nif (a<=c)and(c<=b):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b,c=map(int,input().split());print('NYoe s'[a<=c<=b::2])\", \"A,B,C=map(int,input().split())\\nif C>=A and C<=B :\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"A, B, C = [int(i) for i in input().split()]\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"A, B, C = map(int, input().split())\\n\\nif A <= C and B >= C:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nprint('Yes' if a<=c<=b else 'No')\", \"A,B,C=list(map(int,input().split()))\\nif A<=C and C<=B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a, b, c = map(int, input().split())\\n\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nprint('Yes' if a <= c <= b else 'No')\", \"a, b, c=map(int, input().split())\\nif a<=c<=b:\\n  print('Yes')\\nelse:\\n  print('No')\", \"A,B,C = map(int,input().split())\\nprint(\\\"Yes\\\") if A<=C<=B else print(\\\"No\\\")\", \"a,b,c=map(int, input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"A, B, C = list(map(int, input().split()))\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = [int(x) for x in input().split()]\\nif a <= c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = list(map(int, input().split()))\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b,c=map(int,input().split())\\n\\nif c>=a and c<=b:\\n    ans=\\\"Yes\\\"\\nelse:\\n    ans=\\\"No\\\"\\nprint(ans)\", \"A, B, C = map(int, input().split())\\n\\nif (C >= A) and (C <= B):\\n    print( \\\"Yes\\\" )\\nelse :\\n    print( \\\"No\\\" )\", \"A, B, C = map(int,input().split())\\nprint(\\\"Yes\\\" if A <= C <= B else \\\"No\\\")\", \"A,B,C = map(int, input().split())\\nprint('Yes' if A<=C<=B else 'No')\", \"a, b, c = map(int, input().split())\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c = map(int,input().split())\\n\\nif a<= c and b>=c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int, input().split())\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"import sys\\n\\ndef I(): return int(sys.stdin.readline())\\ndef MI(): return map(int, sys.stdin.readline().split())\\ndef LI(): return list(map(int, sys.stdin.readline().split()))\\ndef main():\\n    a, b, c = MI()\\n    if a <= c and c <= b:\\n        print('Yes')\\n    else:\\n        print('No')\\n\\ndef __starting_point():\\n    main()\\n__starting_point()\", \"# 061a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nif C >= A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a = list(map(int,input().split()))\\n\\nprint('Yes' if a[0] <= a[2] <= a[1] else 'No')\", \"A,B,C=map(int,input().split())\\nif (C>=A) & (C<=B):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A,B,C = map(int,input().split())\\nprint(['No','Yes'][C>=A and B>=C])\", \"#\\n# abc061 a\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"1 3 2\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"6 5 4\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"No\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"2 2 2\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"Yes\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B, C = list(map(int, input().split()))\\n    if A <= C <= B:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"a, b, c = map(int, input().split())\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"A,B,C = map(int,input().split())\\n\\nif A <= C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int,input().split())\\n\\nif B >= C >= A:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"A,B,C = list(map(int, input().split()))\\n\\nif C >= A and C <= B:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# \\u51fa\\u529b\\nif -100 <= A and B and C <= 100:\\n    if C >= A and C <= B:\\n        print('Yes')\\n    else:\\n        print('No')\", \"a,b,c = map(int,input().split())\\nif c >= a and c <= b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b, c = list(map(int, input().split()))\\n\\nif (c >= a) and (c <= b):\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"A, B, C = map(int, input().split())\\nif C >= A and C <= B:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"# \\u5165\\u529b\\nA, B, C =map(int,input().split())\\n\\n# \\u51e6\\u7406\\nif C >=A and C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"A, B, C = map(int,input().split())\\nif (C>=A) and (C<=B):\\n  print('Yes')\\nelse:\\n  print('No')\", \"a, b, c = map(int,input().split())\\nprint('Yes') if a <= c <= b else print('No')\\n\", \"S_list = list(map(int,input().split()))\\n\\nif  S_list[1] - S_list[0] >= 0 and S_list[2]- S_list[0] >=0 and S_list[1] - S_list[2] >=0:\\n    result = \\\"Yes\\\"\\nelse:\\n    result = \\\"No\\\"\\nprint(result)\\n\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if c>=a and c<=b else \\\"No\\\")\", \"a,b,c = map(int, input().split())\\nif a <= c and c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = list(map(int, input().split()))\\nif a <= c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"#n = int(input())\\na, b, c = list(map(int, input().split()))\\n#l = list(map(int,input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n\\nif a <= c <= b:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b,c = map(int,input().split())\\nif a<=c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a = list(map(int,input().split()))\\n# b = list(map(int,input().split()))\\n\\nif a[0]<=a[2]<=a[1]:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"import sys, math\\nfrom itertools import combinations as c, product as p\\nfrom collections import deque\\nsys.setrecursionlimit(10**9)\\nINF = float('inf')\\nMOD = 10**9 + 7\\n#MOD = 998244353\\n\\n\\ndef si(): return input()\\ndef ii(): return int(input())\\ndef fi(): return float(input())\\ndef lstr(): return input().split()\\ndef lint(): return list(map(int, input().split()))\\ndef lintdec(): return list(map(lambda x:int(x) - 1, input().split()))\\ndef lnstr(n): return [input() for _ in range(n)]\\ndef lnint(n): return [int(input()) for _ in range(n)]\\ndef lint_list(n): return [lint() for _ in range(n)]\\n\\n\\n\\n############################################################\\nA, B, C = lint()\\nprint('Yes' if A <= C <= B else 'No')\", \"# A - Between Two Integers\\n\\n# \\u6574\\u6570A,B,C\\u304c\\u5165\\u529b\\u3055\\u308c\\u308b\\n# C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u3067\\u3042\\u308b\\u304b\\u3092\\u5224\\u5b9a\\u3059\\u308b\\n\\n\\nA,B,C = list(map(int,input().split()))\\n\\nif A<=C and B>=C:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a <= c and c <= b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a,b,c=map(int,input().split())\\nif a<=c and c<=b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"A, B, C = map(int, input().split())\\nprint(\\\"Yes\\\" if C >= A and C <= B else \\\"No\\\")\", \"def iroha():\\n    a, b, c = list(map(int, input().split()))\\n\\n    if a <= c and b >= c:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    iroha()\\n\\n\\n__starting_point()\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# C\\u304cA\\u4ee5\\u4e0a\\u304b\\u3064B\\u4ee5\\u4e0b\\u306a\\u3089Yes\\u3001\\u9055\\u3046\\u306a\\u3089No\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b: print('Yes')\\nelse: print('No')\", \"a,b,c = map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\", \"a=list(map(int,input().split()))\\n\\nif (a[2]>=a[0]) and (a[2]<=a[1]):\\n  print('Yes')\\n  \\nelse:\\n  print('No')\", \"A, B, C = map(int, open(0).readline().split())\\nprint('Yes' if A <= C <= B else 'No')\", \"a,b,c = map(int, input().split())\\n\\nif b >= c >= a:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"'''\\nabc061 A - Between Two Integers\\nhttps://atcoder.jp/contests/abc061/tasks/abc061_a\\n'''\\n\\ni = list(map(int, input().split()))\\nif i[2] >= i[0] and i[1] >= i[2]:\\n    ans = 'Yes'\\nelse:\\n    ans = 'No'\\nprint(ans)\\n\", \"a, b, c = map(int, input().split())\\n\\nif c>=a and c<=b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a, b, c = map(int, input().split())\\nif c >= a and c <= b:\\n  print('Yes')\\nelse:\\n  print('No')\", \"A, B, C = map(int, input().split())\\n\\nif A <= C <= B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"a,b,c=map(int,input().split())\\nprint(\\\"Yes\\\" if a<=c<=b else \\\"No\\\")\"]",
        "difficulty": "introductory",
        "input": "2 2 2\n",
        "output": "Yes\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc061/tasks/abc061_a"
    },
    {
        "id": 518,
        "task_id": 4614,
        "test_case_id": 1,
        "question": "You are given three integers, A, B and C.\n\nAmong them, two are the same, but the remaining one is different from the rest.\n\nFor example, when A=5,B=7,C=5, A and C are the same, but B is different.\n\nFind the one that is different from the rest among the given three integers.  \n\n-----Constraints-----\n - -100 \\leq A,B,C \\leq 100 \n - A, B and C are integers.\n - The input satisfies the condition in the statement.\n\n-----Input-----\nInput is given from Standard Input in the following format:  \nA B C\n\n-----Output-----\nAmong A, B and C, print the integer that is different from the rest.\n\n-----Sample Input-----\n5 7 5\n\n-----Sample Output-----\n7\n\nThis is the same case as the one in the statement.",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,string\\nimport sys\\ndef I():\\n    #1 line 1 int\\n     return int(sys.stdin.readline().rstrip())\\ndef LI():\\n    #1 line n int\\n     return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S():\\n    #1 line 1 string\\n     return sys.stdin.readline().rstrip()\\ndef LS():\\n    #1 line n strings\\n     return list(sys.stdin.readline().rstrip().split())\\n\\n\\nxs=LI()\\n\\nif xs[0] == xs[1]:\\n    print(xs[2])\\nelif xs[0] == xs[2]:\\n    print(xs[1])\\nelse:\\n    print(xs[0])\", \"A, B, C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a = input().split(' ')\\n\\nfor i in a:\\n    if (a.count(i)==1):\\n        print(i)\", \"a, b, c = map(int, input().split())\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"#\\n# abc075 a\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"5 7 5\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"7\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"1 1 7\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"7\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"-100 100 100\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"-100\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B, C = list(map(int, input().split()))\\n\\n    if A == B:\\n        print(C)\\n    elif A == C:\\n        print(B)\\n    else:\\n        print(A)\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"#75\\na,b,c=map(int,input().split())\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"a, b, c = input().split()\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c=map(int, input().split())\\nprint(a if b==c else b if c==a else c)\", \"a=list(map(int,input().split()))\\nb=set(a)\\n\\nfor i in b:\\n  if (a.count(i))==1:\\n    print(i)\", \"# 3\\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u30611\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u5024\\u3092\\u51fa\\u529b\\nA, B, C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"import collections\\nl=list(map(int,input().split()))\\ncounted = collections.Counter(l)\\nprint(counted.most_common()[1][0])\", \"l=list(map(int,input().split()))\\nfrom collections import Counter\\nl=list(Counter(l).most_common())\\nprint(l[1][0])\", \"a,b,c = input().split()\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelif b == c:\\n    print(a)\", \"A,B,C=map(int,input().split())\\nif A==B :\\n  print(C)\\nelif B==C :\\n  print(A)\\nelse :\\n  print(B)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif b==c:\\n  print(a)\\nelse:\\n  print(b)\", \"a,b,c = map(int,input().split())\\n\\nif a == b:\\n  print(c)\\n  \\nelif a == c:\\n  print(b)\\n  \\nelse:\\n  print(a)\", \"A, B, C = [int(i) for i in input().split()]\\n\\nif A == B:\\n  print(C)\\nelif A == C:\\n  print(B)\\nelif B == C:\\n  print(A)\\n\", \"a,b,c = map(int,input().split())\\nprint(a if b==c else b if a==c else c)\", \"a, b, c = map(int, input().split())\\nprint(a ^ b ^ c)\", \"A,B,C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a, b, c = list(map(int, input().split()))\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a,b,c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"A,B,C = map(int,input().split())\\n\\nprint(A if B == C else B if A == C else C)\", \"A, B, C = sorted(map(int, input().split()))\\n\\nprint((A if B == C else C))\\n\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"A, B, C = list(map(int, input().split()))\\n\\nif A - B == 0:\\n    print(C)\\nelif A - C == 0:\\n    print(B)\\nelse:\\n    print(A)\\n\", \"a, b, c = map(int, input().split())\\nif a == b: print(c)\\nif b == c: print(a)\\nif c == a: print(b)\", \"A, B, C = map(int, input().split())\\n\\nif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\nelse:\\n    print(C)\", \"a,b,c = map(int,input().split())\\nif a != b and a == c:\\n    print(b)\\nelif a != b and a != c:\\n    print(a)\\nelse:\\n    print(c)\", \"def main():\\n  a = list(map(int,input().split()))\\n  if a[0] == a[1]:\\n    print((a[2]))\\n  elif a[1] == a[2]:\\n    print((a[0]))\\n  else:\\n    print((a[1]))\\n    \\ndef __starting_point():\\n  main()\\n\\n__starting_point()\", \"integer1, integer2, integer3 = map(int, input().split())\\nif integer2 == integer3:\\n    print(integer1)\\nelif integer1 == integer3:\\n    print(integer2)\\nelse:\\n    print(integer3)\", \"a,b,c=map(int,input().split())\\n\\nprint(c) if a == b else print(b) if a == c else print(a)\", \"# A - One out of Three\\n# https://atcoder.jp/contests/abc075/tasks/abc075_a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nif A == B and A != C:\\n    print(C)\\nelif A == C and A != B:\\n    print(B)\\nelif B == C and A != C:\\n    print(A)\\n\", \"A,B,C = map(int, input().split())\\nif A == C:\\n   print(B)\\nelif A == B:\\n    print(C)\\nelse:\\n    print(A)\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# \\u6bd4\\u8f03\\u3057\\u3066\\u51fa\\u529b\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\", \"# \\u5165\\u529b\\nA, B, C = map(int,input().split())\\n\\n# \\u51e6\\u7406\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a,b,c= map(int,input().split())\\nprint(a^b^c)\", \"x,y,z=map(int,input().split())\\nprint(z if x == y else y if x == z else x)\", \"a,b,c = map(int,input().split())\\n\\nif a == c:\\n\\tprint(b)\\nelif a == b:\\n\\tprint(c)\\nelif b == c:\\n\\tprint(a)\", \"a,b,c = map(int,input().split())\\nif a == b:\\n    print(c)\\nif a == c:\\n    print(b)\\nif b == c:\\n    print(a)\", \"ls = list(map(int,input().split()))\\nif ls[1] != ls[2] and ls[2] == ls[0]:\\n  print((ls[1]))\\nif ls[0] != ls[1] and ls[1] == ls[2]:\\n  print((ls[0]))\\nif ls[2] != ls[1] and ls[1] == ls[0]:\\n  print((ls[2]))\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a = [int(x) for x in input().split()]\\nif a[0] == a[1]:\\n  print(a[2])\\nelif a[1] == a[2]:\\n  print(a[0])\\nelse:\\n  print(a[1])\", \"a,b,c = map(int,input().split())\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n  print(C)\\nelif B == C:\\n  print(A)\\nelse:\\n  print(B)\", \"a,b,c=list(map(int,input().split()))\\nif a==b & b != c:\\n    print(c)\\nelif a==c & c !=b:\\n    print(b)\\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif C == A:\\n    print(B)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"a,b,c = map(int, input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"import sys, collections\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = 10**20\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef S(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LS(): return input().split()\\n\\ndef resolve():\\n    ABC = LI()\\n\\n    cnt = collections.Counter(ABC)\\n    ans = [k for k, v in list(cnt.items()) if v == 1]\\n    print((ans[0]))\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"# 3 \\u3064\\u306e\\u6574\\u6570 A, B, C\\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# A, B, C \\u306e\\u3046\\u3061 2\\u3064\\u306f \\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\n# \\u6b8b\\u308a\\u306e 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# \\u4f8b\\u3048\\u3070\\u3001A = 5, B = 7, C = 5\\u306e\\u5834\\u5408\\u3001\\n# A, C \\u306e 2\\u3064\\u306f\\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\n# B \\u306f 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# 3\\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u3061\\u30011\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\n# \\u5236\\u7d04\\n# -100 \\u2266 A, B, C \\u2266 100\\n# A, B, C \\u306f\\u6574\\u6570\\n# \\u5165\\u529b\\u306f\\u554f\\u984c\\u6587\\u306e\\u6761\\u4ef6\\u3092\\u6e80\\u305f\\u3059\\n\\n# \\u6a19\\u6e96\\u5165\\u529b\\u304b\\u3089 A, B, C \\u306e\\u5024\\u3092\\u53d6\\u5f97\\u3059\\u308b\\na, b, c = list(map(int, input().split()))\\n\\n# \\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u63a2\\u3057\\u3066\\u51fa\\u529b\\u3059\\u308b\\nresult = 0\\n\\nif a == b:\\n    result = c\\nelif b == c:\\n    result = a\\nelif a == c:\\n    result = b\\nelse:\\n    result = \\\"Error\\\"\\n\\nprint(result)\\n\", \"a, b, c = map(int, input().split())\\nif a == b:\\n  print(c)\\nelif b == c:\\n  print(a)\\nelse:\\n  print(b)\", \"a,b,c = input().split()\\n\\nif(a==b):\\n    print(c)\\nelif(a == c):\\n    print(b)\\nelse:\\n    print(a)\", \"from collections import Counter\\n\\nABC = list(map(int, input().split()))\\n\\ncnt = Counter(ABC)\\nvalues, counts = zip(*cnt.most_common(2))\\n\\nprint(values[1])\", \"num = list(map(int, input().split()))\\nnum = sorted(num)\\nprint((num[0] if num[0] != num[1] else num[2]))\\n\", \"a,b,c = map(int,input().split())\\nif a==b:\\n    print(c)\\nelif b==c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c = map(int,input().split())\\nif a == c:\\n  print(b)\\nelif a == b:\\n  print(c)\\nelse:\\n  print(a)\", \"def mapt(fn, *args):\\n    return tuple(map(fn, *args))\\n\\n\\ndef Input():\\n    return mapt(int, input().split(\\\" \\\"))\\n\\n\\ndef main():\\n    abc = sorted(Input())\\n    if abc[0] == abc[1]:\\n        print(abc[2])\\n    else:\\n        print(abc[0])\\n\\n\\nmain()\", \"a,b,c=input().split()\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"# A - One out of Three\\n\\n# \\u5165\\u529b\\u3055\\u308c\\u305f\\u6574\\u6570A,B,C\\u306e\\u3046\\u3061\\u30012\\u3064\\u306f\\u7b49\\u3057\\u304f1\\u3064\\u306f\\u7570\\u306a\\u308b\\n# 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u306e\\u5024\\u3092\\u51fa\\u529b\\u3059\\u308b\\n\\n\\nA,B,C = list(map(int,input().split()))\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a, b, c =map(int, input().split())\\n\\n\\nif a==b:\\n    print(c)\\nelif b ==c:\\n    print(a)\\nelse:\\n    print(b)\", \"# 3 \\u3064\\u306e\\u6574\\u6570 A , B , C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002 A , B , C \\u306e\\u3046\\u3061 2 \\u3064\\u306f \\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\u6b8b\\u308a\\u306e 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# \\u4f8b\\u3048\\u3070\\u3001 A = 5 , B = 7 , C = 5 \\u306e\\u5834\\u5408\\u3001 A , C \\u306e 2 \\u3064\\u306f\\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001 B \\u306f 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# 3 \\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u3061\\u3001 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nA,B,C =map(int,input().split())\\n\\nif A == B:\\n    print(C)\\n\\nelif A == C:\\n    print(B)\\n\\nelif B == C:\\n    print(A)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif C == A:\\n    print(B)\", \"a,b,c = map(int,input().split())\\n\\nif a == b:\\n  print(c)\\nelif a == c:\\n  print(b)\\nelse:\\n  print(a)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"A,B,C=list(map(int,input().split()))\\nif A==B:\\n    print(C)\\nelif B==C:\\n    print(A)\\nelse:\\n    print(B)\\n\", \"#!/usr/bin/env python3\\n\\nA, B, C = list(map(int, input().split()))\\nif A == B: print(C)\\nelif A == C: print(B)\\nelse: print(A)\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nprint((a ^ b ^ c))\\n\", \"A, B, C = map(int, input().split())\\nprint(A if B == C else B if A == C else C)\", \"a, b, c = map(int,input().split())\\n\\nif int(a) == int(b):\\n  print(c)\\nif int(a) == int(c):\\n  print(b)\\nif int(b) == int(c):\\n  print(a)\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby, product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil,pi,factorial\\n    from operator import itemgetter\\n    def I(): return int(input())\\n    def MI(): return list(map(int, input().split()))\\n    def LI(): return list(map(int, input().split()))\\n    def LI2(): return [int(input()) for i in range(n)]\\n    def MXI(): return [[LI()]for i in range(n)]\\n    def SI(): return input().rstrip()\\n    def printns(x): print(('\\\\n'.join(x)))\\n    def printni(x): print(('\\\\n'.join(list(map(str,x)))))\\n    inf = 10**17\\n    mod = 10**9 + 7\\n#main code here!\\n    a,b,c=MI()\\n    if a==b:\\n        print(c)\\n    elif b==c:\\n        print(a)\\n    else:\\n        print(b)\\n        \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"lst = input().split()\\n\\nfor i in range(3):\\n   if lst.count(lst[i]) == 1:\\n      print(lst[i])\\n      break\", \"a, b, c = map(int, input().split())\\nif a == b:\\n  print(c)\\nelif b == c:\\n  print(a)\\nelse:\\n  print(b)\", \"A,B,C=list(map(int,input().split()))\\nif A==B:\\n  print(C)\\nelif A==C:\\n  print(B)\\nelif B==C:\\n  print(A)\\n\", \"a,b,c = list(map(int,input().split()))\\n\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b) \\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\nprint(A ^ B ^ C)\", \"l=sorted(map(int,input().split()))\\nprint(sum(l)-l[1]*2)\", \"#   AtCoder abc075 a\\n#   \\u30b9\\u30c8\\u30ec\\u30c3\\u30c1\\u8ab2\\u984c\\n\\n#   \\u5165\\u529b\\na, b, c =list(map(int, input().split()))\\n\\n#   \\u5224\\u5b9a\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif A == C:\\n    print(B)\", \"A,B,C = list(map(int,input().split()))\\nif A==B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelse:\\n    print(B)\", \"a,b,c = sorted(map(int,input().split()))\\nprint( c if a == b else a)\", \"a,b,c=map(int,input().split())\\nif a==c:\\n    print(b)\\nelif a==b:\\n    print(c)\\nelse:\\n    print(a)\", \"l = list(map(int, input().split()))\\nfor ll in l:\\n    if l.count(ll)==1:\\n        print(ll)\\n        break\", \"def iroha():\\n    a,b,c = list(map(int, input().split()))\\n    if a == b:\\n        print(c)\\n    elif a == c:\\n        print(b)\\n    else:\\n        print(a)\\n\\n\\n\\ndef __starting_point():\\n    iroha()\\n\\n\\n__starting_point()\", \"a,b,c=list(map(int,input().split()))\\n\\nif a==b:\\n    ans=c\\nelif b==c:\\n    ans=a\\nelse:\\n    ans=b\\nprint(ans)\\n\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif c == b:\\n    print(a)\\nelse:\\n    print(b)\", \"# 075_a\\nA,B,C=list(map(int,input().split()))\\nif (-100<=A and A<=100) and (-100<=B and B<=100) and (-100<=C and C<=100):\\n    if A==B:\\n        print(C)\\n    elif B==C:\\n        print(A)\\n    elif C==A:\\n        print(B)\\n\", \"s=list(map(int,input().split()))\\ni=set(s)\\nprint(sum(i)-(sum(s)-sum(i)))\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"a, b, c = map(int, input().split())\\n\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelse:\\n    print(a)\", \"a,b,c=map(int,input().split())\\nprint(a if b==c else b if a==c else c)\", \"a=list(map(int,input().split()))\\na.sort()\\n\\nif a[0]==a[1]:\\n  print(a[2])\\nelse:\\n  print(a[0])\", \"a, b, c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif c==b:\\n  print(a)\\nelse:\\n  print(b)\"]",
        "difficulty": "introductory",
        "input": "5 7 5\n",
        "output": "7\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc075/tasks/abc075_a"
    },
    {
        "id": 519,
        "task_id": 4614,
        "test_case_id": 2,
        "question": "You are given three integers, A, B and C.\n\nAmong them, two are the same, but the remaining one is different from the rest.\n\nFor example, when A=5,B=7,C=5, A and C are the same, but B is different.\n\nFind the one that is different from the rest among the given three integers.  \n\n-----Constraints-----\n - -100 \\leq A,B,C \\leq 100 \n - A, B and C are integers.\n - The input satisfies the condition in the statement.\n\n-----Input-----\nInput is given from Standard Input in the following format:  \nA B C\n\n-----Output-----\nAmong A, B and C, print the integer that is different from the rest.\n\n-----Sample Input-----\n5 7 5\n\n-----Sample Output-----\n7\n\nThis is the same case as the one in the statement.",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,string\\nimport sys\\ndef I():\\n    #1 line 1 int\\n     return int(sys.stdin.readline().rstrip())\\ndef LI():\\n    #1 line n int\\n     return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S():\\n    #1 line 1 string\\n     return sys.stdin.readline().rstrip()\\ndef LS():\\n    #1 line n strings\\n     return list(sys.stdin.readline().rstrip().split())\\n\\n\\nxs=LI()\\n\\nif xs[0] == xs[1]:\\n    print(xs[2])\\nelif xs[0] == xs[2]:\\n    print(xs[1])\\nelse:\\n    print(xs[0])\", \"A, B, C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a = input().split(' ')\\n\\nfor i in a:\\n    if (a.count(i)==1):\\n        print(i)\", \"a, b, c = map(int, input().split())\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"#\\n# abc075 a\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"5 7 5\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"7\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"1 1 7\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"7\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"-100 100 100\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"-100\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B, C = list(map(int, input().split()))\\n\\n    if A == B:\\n        print(C)\\n    elif A == C:\\n        print(B)\\n    else:\\n        print(A)\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"#75\\na,b,c=map(int,input().split())\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"a, b, c = input().split()\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c=map(int, input().split())\\nprint(a if b==c else b if c==a else c)\", \"a=list(map(int,input().split()))\\nb=set(a)\\n\\nfor i in b:\\n  if (a.count(i))==1:\\n    print(i)\", \"# 3\\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u30611\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u5024\\u3092\\u51fa\\u529b\\nA, B, C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"import collections\\nl=list(map(int,input().split()))\\ncounted = collections.Counter(l)\\nprint(counted.most_common()[1][0])\", \"l=list(map(int,input().split()))\\nfrom collections import Counter\\nl=list(Counter(l).most_common())\\nprint(l[1][0])\", \"a,b,c = input().split()\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelif b == c:\\n    print(a)\", \"A,B,C=map(int,input().split())\\nif A==B :\\n  print(C)\\nelif B==C :\\n  print(A)\\nelse :\\n  print(B)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif b==c:\\n  print(a)\\nelse:\\n  print(b)\", \"a,b,c = map(int,input().split())\\n\\nif a == b:\\n  print(c)\\n  \\nelif a == c:\\n  print(b)\\n  \\nelse:\\n  print(a)\", \"A, B, C = [int(i) for i in input().split()]\\n\\nif A == B:\\n  print(C)\\nelif A == C:\\n  print(B)\\nelif B == C:\\n  print(A)\\n\", \"a,b,c = map(int,input().split())\\nprint(a if b==c else b if a==c else c)\", \"a, b, c = map(int, input().split())\\nprint(a ^ b ^ c)\", \"A,B,C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a, b, c = list(map(int, input().split()))\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a,b,c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"A,B,C = map(int,input().split())\\n\\nprint(A if B == C else B if A == C else C)\", \"A, B, C = sorted(map(int, input().split()))\\n\\nprint((A if B == C else C))\\n\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"A, B, C = list(map(int, input().split()))\\n\\nif A - B == 0:\\n    print(C)\\nelif A - C == 0:\\n    print(B)\\nelse:\\n    print(A)\\n\", \"a, b, c = map(int, input().split())\\nif a == b: print(c)\\nif b == c: print(a)\\nif c == a: print(b)\", \"A, B, C = map(int, input().split())\\n\\nif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\nelse:\\n    print(C)\", \"a,b,c = map(int,input().split())\\nif a != b and a == c:\\n    print(b)\\nelif a != b and a != c:\\n    print(a)\\nelse:\\n    print(c)\", \"def main():\\n  a = list(map(int,input().split()))\\n  if a[0] == a[1]:\\n    print((a[2]))\\n  elif a[1] == a[2]:\\n    print((a[0]))\\n  else:\\n    print((a[1]))\\n    \\ndef __starting_point():\\n  main()\\n\\n__starting_point()\", \"integer1, integer2, integer3 = map(int, input().split())\\nif integer2 == integer3:\\n    print(integer1)\\nelif integer1 == integer3:\\n    print(integer2)\\nelse:\\n    print(integer3)\", \"a,b,c=map(int,input().split())\\n\\nprint(c) if a == b else print(b) if a == c else print(a)\", \"# A - One out of Three\\n# https://atcoder.jp/contests/abc075/tasks/abc075_a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nif A == B and A != C:\\n    print(C)\\nelif A == C and A != B:\\n    print(B)\\nelif B == C and A != C:\\n    print(A)\\n\", \"A,B,C = map(int, input().split())\\nif A == C:\\n   print(B)\\nelif A == B:\\n    print(C)\\nelse:\\n    print(A)\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# \\u6bd4\\u8f03\\u3057\\u3066\\u51fa\\u529b\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\", \"# \\u5165\\u529b\\nA, B, C = map(int,input().split())\\n\\n# \\u51e6\\u7406\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a,b,c= map(int,input().split())\\nprint(a^b^c)\", \"x,y,z=map(int,input().split())\\nprint(z if x == y else y if x == z else x)\", \"a,b,c = map(int,input().split())\\n\\nif a == c:\\n\\tprint(b)\\nelif a == b:\\n\\tprint(c)\\nelif b == c:\\n\\tprint(a)\", \"a,b,c = map(int,input().split())\\nif a == b:\\n    print(c)\\nif a == c:\\n    print(b)\\nif b == c:\\n    print(a)\", \"ls = list(map(int,input().split()))\\nif ls[1] != ls[2] and ls[2] == ls[0]:\\n  print((ls[1]))\\nif ls[0] != ls[1] and ls[1] == ls[2]:\\n  print((ls[0]))\\nif ls[2] != ls[1] and ls[1] == ls[0]:\\n  print((ls[2]))\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a = [int(x) for x in input().split()]\\nif a[0] == a[1]:\\n  print(a[2])\\nelif a[1] == a[2]:\\n  print(a[0])\\nelse:\\n  print(a[1])\", \"a,b,c = map(int,input().split())\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n  print(C)\\nelif B == C:\\n  print(A)\\nelse:\\n  print(B)\", \"a,b,c=list(map(int,input().split()))\\nif a==b & b != c:\\n    print(c)\\nelif a==c & c !=b:\\n    print(b)\\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif C == A:\\n    print(B)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"a,b,c = map(int, input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"import sys, collections\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = 10**20\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef S(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LS(): return input().split()\\n\\ndef resolve():\\n    ABC = LI()\\n\\n    cnt = collections.Counter(ABC)\\n    ans = [k for k, v in list(cnt.items()) if v == 1]\\n    print((ans[0]))\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"# 3 \\u3064\\u306e\\u6574\\u6570 A, B, C\\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# A, B, C \\u306e\\u3046\\u3061 2\\u3064\\u306f \\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\n# \\u6b8b\\u308a\\u306e 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# \\u4f8b\\u3048\\u3070\\u3001A = 5, B = 7, C = 5\\u306e\\u5834\\u5408\\u3001\\n# A, C \\u306e 2\\u3064\\u306f\\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\n# B \\u306f 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# 3\\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u3061\\u30011\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\n# \\u5236\\u7d04\\n# -100 \\u2266 A, B, C \\u2266 100\\n# A, B, C \\u306f\\u6574\\u6570\\n# \\u5165\\u529b\\u306f\\u554f\\u984c\\u6587\\u306e\\u6761\\u4ef6\\u3092\\u6e80\\u305f\\u3059\\n\\n# \\u6a19\\u6e96\\u5165\\u529b\\u304b\\u3089 A, B, C \\u306e\\u5024\\u3092\\u53d6\\u5f97\\u3059\\u308b\\na, b, c = list(map(int, input().split()))\\n\\n# \\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u63a2\\u3057\\u3066\\u51fa\\u529b\\u3059\\u308b\\nresult = 0\\n\\nif a == b:\\n    result = c\\nelif b == c:\\n    result = a\\nelif a == c:\\n    result = b\\nelse:\\n    result = \\\"Error\\\"\\n\\nprint(result)\\n\", \"a, b, c = map(int, input().split())\\nif a == b:\\n  print(c)\\nelif b == c:\\n  print(a)\\nelse:\\n  print(b)\", \"a,b,c = input().split()\\n\\nif(a==b):\\n    print(c)\\nelif(a == c):\\n    print(b)\\nelse:\\n    print(a)\", \"from collections import Counter\\n\\nABC = list(map(int, input().split()))\\n\\ncnt = Counter(ABC)\\nvalues, counts = zip(*cnt.most_common(2))\\n\\nprint(values[1])\", \"num = list(map(int, input().split()))\\nnum = sorted(num)\\nprint((num[0] if num[0] != num[1] else num[2]))\\n\", \"a,b,c = map(int,input().split())\\nif a==b:\\n    print(c)\\nelif b==c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c = map(int,input().split())\\nif a == c:\\n  print(b)\\nelif a == b:\\n  print(c)\\nelse:\\n  print(a)\", \"def mapt(fn, *args):\\n    return tuple(map(fn, *args))\\n\\n\\ndef Input():\\n    return mapt(int, input().split(\\\" \\\"))\\n\\n\\ndef main():\\n    abc = sorted(Input())\\n    if abc[0] == abc[1]:\\n        print(abc[2])\\n    else:\\n        print(abc[0])\\n\\n\\nmain()\", \"a,b,c=input().split()\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"# A - One out of Three\\n\\n# \\u5165\\u529b\\u3055\\u308c\\u305f\\u6574\\u6570A,B,C\\u306e\\u3046\\u3061\\u30012\\u3064\\u306f\\u7b49\\u3057\\u304f1\\u3064\\u306f\\u7570\\u306a\\u308b\\n# 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u306e\\u5024\\u3092\\u51fa\\u529b\\u3059\\u308b\\n\\n\\nA,B,C = list(map(int,input().split()))\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a, b, c =map(int, input().split())\\n\\n\\nif a==b:\\n    print(c)\\nelif b ==c:\\n    print(a)\\nelse:\\n    print(b)\", \"# 3 \\u3064\\u306e\\u6574\\u6570 A , B , C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002 A , B , C \\u306e\\u3046\\u3061 2 \\u3064\\u306f \\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\u6b8b\\u308a\\u306e 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# \\u4f8b\\u3048\\u3070\\u3001 A = 5 , B = 7 , C = 5 \\u306e\\u5834\\u5408\\u3001 A , C \\u306e 2 \\u3064\\u306f\\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001 B \\u306f 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# 3 \\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u3061\\u3001 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nA,B,C =map(int,input().split())\\n\\nif A == B:\\n    print(C)\\n\\nelif A == C:\\n    print(B)\\n\\nelif B == C:\\n    print(A)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif C == A:\\n    print(B)\", \"a,b,c = map(int,input().split())\\n\\nif a == b:\\n  print(c)\\nelif a == c:\\n  print(b)\\nelse:\\n  print(a)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"A,B,C=list(map(int,input().split()))\\nif A==B:\\n    print(C)\\nelif B==C:\\n    print(A)\\nelse:\\n    print(B)\\n\", \"#!/usr/bin/env python3\\n\\nA, B, C = list(map(int, input().split()))\\nif A == B: print(C)\\nelif A == C: print(B)\\nelse: print(A)\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nprint((a ^ b ^ c))\\n\", \"A, B, C = map(int, input().split())\\nprint(A if B == C else B if A == C else C)\", \"a, b, c = map(int,input().split())\\n\\nif int(a) == int(b):\\n  print(c)\\nif int(a) == int(c):\\n  print(b)\\nif int(b) == int(c):\\n  print(a)\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby, product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil,pi,factorial\\n    from operator import itemgetter\\n    def I(): return int(input())\\n    def MI(): return list(map(int, input().split()))\\n    def LI(): return list(map(int, input().split()))\\n    def LI2(): return [int(input()) for i in range(n)]\\n    def MXI(): return [[LI()]for i in range(n)]\\n    def SI(): return input().rstrip()\\n    def printns(x): print(('\\\\n'.join(x)))\\n    def printni(x): print(('\\\\n'.join(list(map(str,x)))))\\n    inf = 10**17\\n    mod = 10**9 + 7\\n#main code here!\\n    a,b,c=MI()\\n    if a==b:\\n        print(c)\\n    elif b==c:\\n        print(a)\\n    else:\\n        print(b)\\n        \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"lst = input().split()\\n\\nfor i in range(3):\\n   if lst.count(lst[i]) == 1:\\n      print(lst[i])\\n      break\", \"a, b, c = map(int, input().split())\\nif a == b:\\n  print(c)\\nelif b == c:\\n  print(a)\\nelse:\\n  print(b)\", \"A,B,C=list(map(int,input().split()))\\nif A==B:\\n  print(C)\\nelif A==C:\\n  print(B)\\nelif B==C:\\n  print(A)\\n\", \"a,b,c = list(map(int,input().split()))\\n\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b) \\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\nprint(A ^ B ^ C)\", \"l=sorted(map(int,input().split()))\\nprint(sum(l)-l[1]*2)\", \"#   AtCoder abc075 a\\n#   \\u30b9\\u30c8\\u30ec\\u30c3\\u30c1\\u8ab2\\u984c\\n\\n#   \\u5165\\u529b\\na, b, c =list(map(int, input().split()))\\n\\n#   \\u5224\\u5b9a\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif A == C:\\n    print(B)\", \"A,B,C = list(map(int,input().split()))\\nif A==B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelse:\\n    print(B)\", \"a,b,c = sorted(map(int,input().split()))\\nprint( c if a == b else a)\", \"a,b,c=map(int,input().split())\\nif a==c:\\n    print(b)\\nelif a==b:\\n    print(c)\\nelse:\\n    print(a)\", \"l = list(map(int, input().split()))\\nfor ll in l:\\n    if l.count(ll)==1:\\n        print(ll)\\n        break\", \"def iroha():\\n    a,b,c = list(map(int, input().split()))\\n    if a == b:\\n        print(c)\\n    elif a == c:\\n        print(b)\\n    else:\\n        print(a)\\n\\n\\n\\ndef __starting_point():\\n    iroha()\\n\\n\\n__starting_point()\", \"a,b,c=list(map(int,input().split()))\\n\\nif a==b:\\n    ans=c\\nelif b==c:\\n    ans=a\\nelse:\\n    ans=b\\nprint(ans)\\n\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif c == b:\\n    print(a)\\nelse:\\n    print(b)\", \"# 075_a\\nA,B,C=list(map(int,input().split()))\\nif (-100<=A and A<=100) and (-100<=B and B<=100) and (-100<=C and C<=100):\\n    if A==B:\\n        print(C)\\n    elif B==C:\\n        print(A)\\n    elif C==A:\\n        print(B)\\n\", \"s=list(map(int,input().split()))\\ni=set(s)\\nprint(sum(i)-(sum(s)-sum(i)))\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"a, b, c = map(int, input().split())\\n\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelse:\\n    print(a)\", \"a,b,c=map(int,input().split())\\nprint(a if b==c else b if a==c else c)\", \"a=list(map(int,input().split()))\\na.sort()\\n\\nif a[0]==a[1]:\\n  print(a[2])\\nelse:\\n  print(a[0])\", \"a, b, c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif c==b:\\n  print(a)\\nelse:\\n  print(b)\"]",
        "difficulty": "introductory",
        "input": "1 1 7\n",
        "output": "7\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc075/tasks/abc075_a"
    },
    {
        "id": 520,
        "task_id": 4614,
        "test_case_id": 3,
        "question": "You are given three integers, A, B and C.\n\nAmong them, two are the same, but the remaining one is different from the rest.\n\nFor example, when A=5,B=7,C=5, A and C are the same, but B is different.\n\nFind the one that is different from the rest among the given three integers.  \n\n-----Constraints-----\n - -100 \\leq A,B,C \\leq 100 \n - A, B and C are integers.\n - The input satisfies the condition in the statement.\n\n-----Input-----\nInput is given from Standard Input in the following format:  \nA B C\n\n-----Output-----\nAmong A, B and C, print the integer that is different from the rest.\n\n-----Sample Input-----\n5 7 5\n\n-----Sample Output-----\n7\n\nThis is the same case as the one in the statement.",
        "solutions": "[\"import bisect,collections,copy,heapq,itertools,math,string\\nimport sys\\ndef I():\\n    #1 line 1 int\\n     return int(sys.stdin.readline().rstrip())\\ndef LI():\\n    #1 line n int\\n     return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S():\\n    #1 line 1 string\\n     return sys.stdin.readline().rstrip()\\ndef LS():\\n    #1 line n strings\\n     return list(sys.stdin.readline().rstrip().split())\\n\\n\\nxs=LI()\\n\\nif xs[0] == xs[1]:\\n    print(xs[2])\\nelif xs[0] == xs[2]:\\n    print(xs[1])\\nelse:\\n    print(xs[0])\", \"A, B, C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a = input().split(' ')\\n\\nfor i in a:\\n    if (a.count(i)==1):\\n        print(i)\", \"a, b, c = map(int, input().split())\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"#\\n# abc075 a\\n#\\nimport sys\\nfrom io import StringIO\\nimport unittest\\n\\n\\nclass TestClass(unittest.TestCase):\\n    def assertIO(self, input, output):\\n        stdout, stdin = sys.stdout, sys.stdin\\n        sys.stdout, sys.stdin = StringIO(), StringIO(input)\\n        resolve()\\n        sys.stdout.seek(0)\\n        out = sys.stdout.read()[:-1]\\n        sys.stdout, sys.stdin = stdout, stdin\\n        self.assertEqual(out, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_1(self):\\n        input = \\\"\\\"\\\"5 7 5\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"7\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_2(self):\\n        input = \\\"\\\"\\\"1 1 7\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"7\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n    def test_\\u5165\\u529b\\u4f8b_3(self):\\n        input = \\\"\\\"\\\"-100 100 100\\\"\\\"\\\"\\n        output = \\\"\\\"\\\"-100\\\"\\\"\\\"\\n        self.assertIO(input, output)\\n\\n\\ndef resolve():\\n    A, B, C = list(map(int, input().split()))\\n\\n    if A == B:\\n        print(C)\\n    elif A == C:\\n        print(B)\\n    else:\\n        print(A)\\n\\n\\ndef __starting_point():\\n    # unittest.main()\\n    resolve()\\n\\n__starting_point()\", \"#75\\na,b,c=map(int,input().split())\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"a, b, c = input().split()\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c=map(int, input().split())\\nprint(a if b==c else b if c==a else c)\", \"a=list(map(int,input().split()))\\nb=set(a)\\n\\nfor i in b:\\n  if (a.count(i))==1:\\n    print(i)\", \"# 3\\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u30611\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u5024\\u3092\\u51fa\\u529b\\nA, B, C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"import collections\\nl=list(map(int,input().split()))\\ncounted = collections.Counter(l)\\nprint(counted.most_common()[1][0])\", \"l=list(map(int,input().split()))\\nfrom collections import Counter\\nl=list(Counter(l).most_common())\\nprint(l[1][0])\", \"a,b,c = input().split()\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelif b == c:\\n    print(a)\", \"A,B,C=map(int,input().split())\\nif A==B :\\n  print(C)\\nelif B==C :\\n  print(A)\\nelse :\\n  print(B)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif b==c:\\n  print(a)\\nelse:\\n  print(b)\", \"a,b,c = map(int,input().split())\\n\\nif a == b:\\n  print(c)\\n  \\nelif a == c:\\n  print(b)\\n  \\nelse:\\n  print(a)\", \"A, B, C = [int(i) for i in input().split()]\\n\\nif A == B:\\n  print(C)\\nelif A == C:\\n  print(B)\\nelif B == C:\\n  print(A)\\n\", \"a,b,c = map(int,input().split())\\nprint(a if b==c else b if a==c else c)\", \"a, b, c = map(int, input().split())\\nprint(a ^ b ^ c)\", \"A,B,C = map(int,input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a, b, c = list(map(int, input().split()))\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a,b,c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"A,B,C = map(int,input().split())\\n\\nprint(A if B == C else B if A == C else C)\", \"A, B, C = sorted(map(int, input().split()))\\n\\nprint((A if B == C else C))\\n\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"A, B, C = list(map(int, input().split()))\\n\\nif A - B == 0:\\n    print(C)\\nelif A - C == 0:\\n    print(B)\\nelse:\\n    print(A)\\n\", \"a, b, c = map(int, input().split())\\nif a == b: print(c)\\nif b == c: print(a)\\nif c == a: print(b)\", \"A, B, C = map(int, input().split())\\n\\nif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\nelse:\\n    print(C)\", \"a,b,c = map(int,input().split())\\nif a != b and a == c:\\n    print(b)\\nelif a != b and a != c:\\n    print(a)\\nelse:\\n    print(c)\", \"def main():\\n  a = list(map(int,input().split()))\\n  if a[0] == a[1]:\\n    print((a[2]))\\n  elif a[1] == a[2]:\\n    print((a[0]))\\n  else:\\n    print((a[1]))\\n    \\ndef __starting_point():\\n  main()\\n\\n__starting_point()\", \"integer1, integer2, integer3 = map(int, input().split())\\nif integer2 == integer3:\\n    print(integer1)\\nelif integer1 == integer3:\\n    print(integer2)\\nelse:\\n    print(integer3)\", \"a,b,c=map(int,input().split())\\n\\nprint(c) if a == b else print(b) if a == c else print(a)\", \"# A - One out of Three\\n# https://atcoder.jp/contests/abc075/tasks/abc075_a\\n\\nA, B, C = list(map(int, input().split()))\\n\\nif A == B and A != C:\\n    print(C)\\nelif A == C and A != B:\\n    print(B)\\nelif B == C and A != C:\\n    print(A)\\n\", \"A,B,C = map(int, input().split())\\nif A == C:\\n   print(B)\\nelif A == B:\\n    print(C)\\nelse:\\n    print(A)\", \"# \\u5165\\u529b\\nA, B, C = map(int, input().split())\\n\\n# \\u6bd4\\u8f03\\u3057\\u3066\\u51fa\\u529b\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\", \"# \\u5165\\u529b\\nA, B, C = map(int,input().split())\\n\\n# \\u51e6\\u7406\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a,b,c= map(int,input().split())\\nprint(a^b^c)\", \"x,y,z=map(int,input().split())\\nprint(z if x == y else y if x == z else x)\", \"a,b,c = map(int,input().split())\\n\\nif a == c:\\n\\tprint(b)\\nelif a == b:\\n\\tprint(c)\\nelif b == c:\\n\\tprint(a)\", \"a,b,c = map(int,input().split())\\nif a == b:\\n    print(c)\\nif a == c:\\n    print(b)\\nif b == c:\\n    print(a)\", \"ls = list(map(int,input().split()))\\nif ls[1] != ls[2] and ls[2] == ls[0]:\\n  print((ls[1]))\\nif ls[0] != ls[1] and ls[1] == ls[2]:\\n  print((ls[0]))\\nif ls[2] != ls[1] and ls[1] == ls[0]:\\n  print((ls[2]))\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a = [int(x) for x in input().split()]\\nif a[0] == a[1]:\\n  print(a[2])\\nelif a[1] == a[2]:\\n  print(a[0])\\nelse:\\n  print(a[1])\", \"a,b,c = map(int,input().split())\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n  print(C)\\nelif B == C:\\n  print(A)\\nelse:\\n  print(B)\", \"a,b,c=list(map(int,input().split()))\\nif a==b & b != c:\\n    print(c)\\nelif a==c & c !=b:\\n    print(b)\\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif C == A:\\n    print(B)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelse:\\n    print(A)\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"a,b,c = map(int, input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"import sys, collections\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = 10**20\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef S(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LS(): return input().split()\\n\\ndef resolve():\\n    ABC = LI()\\n\\n    cnt = collections.Counter(ABC)\\n    ans = [k for k, v in list(cnt.items()) if v == 1]\\n    print((ans[0]))\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"# 3 \\u3064\\u306e\\u6574\\u6570 A, B, C\\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002\\n# A, B, C \\u306e\\u3046\\u3061 2\\u3064\\u306f \\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\n# \\u6b8b\\u308a\\u306e 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# \\u4f8b\\u3048\\u3070\\u3001A = 5, B = 7, C = 5\\u306e\\u5834\\u5408\\u3001\\n# A, C \\u306e 2\\u3064\\u306f\\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\n# B \\u306f 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# 3\\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u3061\\u30011\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\n# \\u5236\\u7d04\\n# -100 \\u2266 A, B, C \\u2266 100\\n# A, B, C \\u306f\\u6574\\u6570\\n# \\u5165\\u529b\\u306f\\u554f\\u984c\\u6587\\u306e\\u6761\\u4ef6\\u3092\\u6e80\\u305f\\u3059\\n\\n# \\u6a19\\u6e96\\u5165\\u529b\\u304b\\u3089 A, B, C \\u306e\\u5024\\u3092\\u53d6\\u5f97\\u3059\\u308b\\na, b, c = list(map(int, input().split()))\\n\\n# \\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u63a2\\u3057\\u3066\\u51fa\\u529b\\u3059\\u308b\\nresult = 0\\n\\nif a == b:\\n    result = c\\nelif b == c:\\n    result = a\\nelif a == c:\\n    result = b\\nelse:\\n    result = \\\"Error\\\"\\n\\nprint(result)\\n\", \"a, b, c = map(int, input().split())\\nif a == b:\\n  print(c)\\nelif b == c:\\n  print(a)\\nelse:\\n  print(b)\", \"a,b,c = input().split()\\n\\nif(a==b):\\n    print(c)\\nelif(a == c):\\n    print(b)\\nelse:\\n    print(a)\", \"from collections import Counter\\n\\nABC = list(map(int, input().split()))\\n\\ncnt = Counter(ABC)\\nvalues, counts = zip(*cnt.most_common(2))\\n\\nprint(values[1])\", \"num = list(map(int, input().split()))\\nnum = sorted(num)\\nprint((num[0] if num[0] != num[1] else num[2]))\\n\", \"a,b,c = map(int,input().split())\\nif a==b:\\n    print(c)\\nelif b==c:\\n    print(a)\\nelse:\\n    print(b)\", \"a,b,c = map(int,input().split())\\nif a == c:\\n  print(b)\\nelif a == b:\\n  print(c)\\nelse:\\n  print(a)\", \"def mapt(fn, *args):\\n    return tuple(map(fn, *args))\\n\\n\\ndef Input():\\n    return mapt(int, input().split(\\\" \\\"))\\n\\n\\ndef main():\\n    abc = sorted(Input())\\n    if abc[0] == abc[1]:\\n        print(abc[2])\\n    else:\\n        print(abc[0])\\n\\n\\nmain()\", \"a,b,c=input().split()\\nif a==b:\\n    print(c)\\nelif a==c:\\n    print(b)\\nelse:\\n    print(a)\", \"# A - One out of Three\\n\\n# \\u5165\\u529b\\u3055\\u308c\\u305f\\u6574\\u6570A,B,C\\u306e\\u3046\\u3061\\u30012\\u3064\\u306f\\u7b49\\u3057\\u304f1\\u3064\\u306f\\u7570\\u306a\\u308b\\n# 1\\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u306e\\u5024\\u3092\\u51fa\\u529b\\u3059\\u308b\\n\\n\\nA,B,C = list(map(int,input().split()))\\n\\nif A == B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\\n\", \"a, b, c =map(int, input().split())\\n\\n\\nif a==b:\\n    print(c)\\nelif b ==c:\\n    print(a)\\nelse:\\n    print(b)\", \"# 3 \\u3064\\u306e\\u6574\\u6570 A , B , C \\u304c\\u4e0e\\u3048\\u3089\\u308c\\u307e\\u3059\\u3002 A , B , C \\u306e\\u3046\\u3061 2 \\u3064\\u306f \\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001\\u6b8b\\u308a\\u306e 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# \\u4f8b\\u3048\\u3070\\u3001 A = 5 , B = 7 , C = 5 \\u306e\\u5834\\u5408\\u3001 A , C \\u306e 2 \\u3064\\u306f\\u540c\\u3058\\u6574\\u6570\\u3067\\u3042\\u308a\\u3001 B \\u306f 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3067\\u3059\\u3002\\n# 3 \\u3064\\u306e\\u6574\\u6570\\u306e\\u3046\\u3061\\u3001 1 \\u3064\\u3060\\u3051\\u7570\\u306a\\u308b\\u6574\\u6570\\u3092\\u6c42\\u3081\\u3066\\u304f\\u3060\\u3055\\u3044\\u3002\\n\\nA,B,C =map(int,input().split())\\n\\nif A == B:\\n    print(C)\\n\\nelif A == C:\\n    print(B)\\n\\nelif B == C:\\n    print(A)\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif C == A:\\n    print(B)\", \"a,b,c = map(int,input().split())\\n\\nif a == b:\\n  print(c)\\nelif a == c:\\n  print(b)\\nelse:\\n  print(a)\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"A,B,C=list(map(int,input().split()))\\nif A==B:\\n    print(C)\\nelif B==C:\\n    print(A)\\nelse:\\n    print(B)\\n\", \"#!/usr/bin/env python3\\n\\nA, B, C = list(map(int, input().split()))\\nif A == B: print(C)\\nelif A == C: print(B)\\nelse: print(A)\\n\", \"a, b, c = list(map(int, input().split()))\\n\\nprint((a ^ b ^ c))\\n\", \"A, B, C = map(int, input().split())\\nprint(A if B == C else B if A == C else C)\", \"a, b, c = map(int,input().split())\\n\\nif int(a) == int(b):\\n  print(c)\\nif int(a) == int(c):\\n  print(b)\\nif int(b) == int(c):\\n  print(a)\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif b == c:\\n    print(a)\\nelse:\\n    print(b)\", \"def main():\\n    import sys\\n    input = sys.stdin.readline\\n    sys.setrecursionlimit(10**7)\\n    from collections import Counter, deque\\n    from collections import defaultdict\\n    from itertools import combinations, permutations, accumulate, groupby, product\\n    from bisect import bisect_left,bisect_right\\n    from heapq import heapify, heappop, heappush\\n    from math import floor, ceil,pi,factorial\\n    from operator import itemgetter\\n    def I(): return int(input())\\n    def MI(): return list(map(int, input().split()))\\n    def LI(): return list(map(int, input().split()))\\n    def LI2(): return [int(input()) for i in range(n)]\\n    def MXI(): return [[LI()]for i in range(n)]\\n    def SI(): return input().rstrip()\\n    def printns(x): print(('\\\\n'.join(x)))\\n    def printni(x): print(('\\\\n'.join(list(map(str,x)))))\\n    inf = 10**17\\n    mod = 10**9 + 7\\n#main code here!\\n    a,b,c=MI()\\n    if a==b:\\n        print(c)\\n    elif b==c:\\n        print(a)\\n    else:\\n        print(b)\\n        \\ndef __starting_point():\\n    main()\\n\\n__starting_point()\", \"lst = input().split()\\n\\nfor i in range(3):\\n   if lst.count(lst[i]) == 1:\\n      print(lst[i])\\n      break\", \"a, b, c = map(int, input().split())\\nif a == b:\\n  print(c)\\nelif b == c:\\n  print(a)\\nelse:\\n  print(b)\", \"A,B,C=list(map(int,input().split()))\\nif A==B:\\n  print(C)\\nelif A==C:\\n  print(B)\\nelif B==C:\\n  print(A)\\n\", \"a,b,c = list(map(int,input().split()))\\n\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b) \\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\nprint(A ^ B ^ C)\", \"l=sorted(map(int,input().split()))\\nprint(sum(l)-l[1]*2)\", \"#   AtCoder abc075 a\\n#   \\u30b9\\u30c8\\u30ec\\u30c3\\u30c1\\u8ab2\\u984c\\n\\n#   \\u5165\\u529b\\na, b, c =list(map(int, input().split()))\\n\\n#   \\u5224\\u5b9a\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelse:\\n    print(a)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelif A == C:\\n    print(B)\", \"A,B,C = list(map(int,input().split()))\\nif A==B:\\n    print(C)\\nelif A == C:\\n    print(B)\\nelif B == C:\\n    print(A)\\n\", \"A, B, C = map(int, input().split())\\n\\nif A == B:\\n    print(C)\\nelif B == C:\\n    print(A)\\nelse:\\n    print(B)\", \"a,b,c = sorted(map(int,input().split()))\\nprint( c if a == b else a)\", \"a,b,c=map(int,input().split())\\nif a==c:\\n    print(b)\\nelif a==b:\\n    print(c)\\nelse:\\n    print(a)\", \"l = list(map(int, input().split()))\\nfor ll in l:\\n    if l.count(ll)==1:\\n        print(ll)\\n        break\", \"def iroha():\\n    a,b,c = list(map(int, input().split()))\\n    if a == b:\\n        print(c)\\n    elif a == c:\\n        print(b)\\n    else:\\n        print(a)\\n\\n\\n\\ndef __starting_point():\\n    iroha()\\n\\n\\n__starting_point()\", \"a,b,c=list(map(int,input().split()))\\n\\nif a==b:\\n    ans=c\\nelif b==c:\\n    ans=a\\nelse:\\n    ans=b\\nprint(ans)\\n\", \"a, b, c = map(int, input().split())\\nif a == b:\\n    print(c)\\nelif c == b:\\n    print(a)\\nelse:\\n    print(b)\", \"# 075_a\\nA,B,C=list(map(int,input().split()))\\nif (-100<=A and A<=100) and (-100<=B and B<=100) and (-100<=C and C<=100):\\n    if A==B:\\n        print(C)\\n    elif B==C:\\n        print(A)\\n    elif C==A:\\n        print(B)\\n\", \"s=list(map(int,input().split()))\\ni=set(s)\\nprint(sum(i)-(sum(s)-sum(i)))\", \"a,b,c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif a==c:\\n  print(b)\\nelse:\\n  print(a)\", \"a, b, c = map(int, input().split())\\n\\nif a == b:\\n    print(c)\\nelif a == c:\\n    print(b)\\nelse:\\n    print(a)\", \"a,b,c=map(int,input().split())\\nprint(a if b==c else b if a==c else c)\", \"a=list(map(int,input().split()))\\na.sort()\\n\\nif a[0]==a[1]:\\n  print(a[2])\\nelse:\\n  print(a[0])\", \"a, b, c=map(int,input().split())\\nif a==b:\\n  print(c)\\nelif c==b:\\n  print(a)\\nelse:\\n  print(b)\"]",
        "difficulty": "introductory",
        "input": "-100 100 100\n",
        "output": "-100\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc075/tasks/abc075_a"
    },
    {
        "id": 521,
        "task_id": 4695,
        "test_case_id": 1,
        "question": "Based on some criterion, Snuke divided the integers from 1 through 12 into three groups as shown in the figure below.\nGiven two integers x and y (1 ≤ x < y ≤ 12), determine whether they belong to the same group.\n\n-----Constraints-----\n - x and y are integers.\n - 1 ≤ x < y ≤ 12\n\n-----Input-----\nInput is given from Standard Input in the following format:\nx y\n\n-----Output-----\nIf x and y belong to the same group, print Yes; otherwise, print No.\n\n-----Sample Input-----\n1 3\n\n-----Sample Output-----\nYes\n",
        "solutions": "[\"n1 = [1, 3, 5, 7, 8, 10, 12]\\nn2 = [4, 6, 9, 11]\\n\\na, b = list(map(int, input().split()))\\nprint((\\\"Yes\\\" if a in n1 and b in n1 or a in n2 and b in n2 else \\\"No\\\"))\\n\", \"lst1 = [4,6,9,11]\\nlst2 = [2]\\nlst3 = [1,3,5,7,8,10,12]\\nx,y = map(int,input().split())\\nif x in lst1 and y in lst1:\\n    print('Yes')\\nelif x in lst2 and y in lst2:\\n    print('Yes')\\nelif x in lst3 and y in lst3:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=map(int,input().split())\\nA=[2]\\nB=[4,6,9,11]\\nC=[1,3,5,7,8,10,12]\\nif x in B and y in B:\\n  print(\\\"Yes\\\")\\nelif x in C and y in C:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a,b,c=[1,3,5,7,8,10,12],[4,6,9,11],[2]\\nprint('YNeos'[len(set([0 if i in a else [1,2][i in b] for i in list(map(int,input().split()))]))!=1::2])\", \"X,Y=map(int,input().split())\\nA=1,3,5,7,8,10,12\\nB=4,6,9,11\\nC=2\\nans=\\\"No\\\"\\nif X in A and Y in A:\\n    ans=\\\"Yes\\\"\\nelif X in B and Y in B:\\n    ans=\\\"Yes\\\"\\nelif X==Y==2:\\n    ans=\\\"Yes\\\"\\nprint(ans)\", \"x,y=map(int,input().split())\\ngrp1=[1,3,5,7,8,10,12]\\ngrp2=[4,6,9,11]\\n\\nif x in grp1 and y in grp1: print(\\\"Yes\\\")\\nelif x in grp2 and y in grp2: print(\\\"Yes\\\")\\nelse: print(\\\"No\\\")\", \"a = map(int, input().split())\\ninput_list = list(a)\\n\\ngroup_a = [1, 3, 5, 7, 8, 10, 12]\\ngroup_b = [4, 6, 9, 11]\\ngroup_c = [2]\\nlist_of_list = [group_a, group_b, group_c]\\n\\ncount_match = 0\\n\\nfor list_i in list_of_list:\\n    if input_list[0] in list_i and input_list[1] in list_i:\\n        count_match += 1\\n        break\\n\\nif count_match == 1:\\n    print('Yes')\\nelse:\\n    print('No')\", \"data_1 =[1,3,5,7,8,10,12]\\ndata_2 =[4,6,9,11]\\nx,y = map(int,input().split())\\nif x in data_1 and y in data_1:\\n    print('Yes')\\nelif x in data_2 and y in data_2:\\n    print('Yes')\\nelse:\\n    print('No')\", \"#!/usr/bin/env python3\\nx, y = list(map(int, input().split()))\\n\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\n\\nif x in a and y in a:\\n    print('Yes')\\nelif x in b and y in b:\\n    print('Yes')\\nelif x in c and y in c:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b = map(int,input().split())\\n\\nx = [1,3,5,7,8,10,12]\\ny = [4,6,9,11]\\n\\nif a in x and b in x or a in y and b in y:\\n  print('Yes')\\n  \\nelse:\\n  print('No')\", \"x,y=map(int,input().split())\\ns1 = [1,3,5,7,8,10,12]\\ns2 = [4,6,9,11]\\ns3 = [2]\\nif x in s1 and y in s1:\\n    print('Yes')\\nelif x in s2 and y in s2:\\n    print('Yes')\\nelif x in s3 and y in s3:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y = map(int, input().split())\\na = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\nc = [2]\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\", \"x, y = map(int, input().split())\\n\\nA = [1, 3, 5, 7, 8, 10, 12]\\nB = [4, 6, 9, 11]\\nC = [2, ]\\n\\nif x in A and y in A:\\n    print('Yes')\\nelif x in B and y in B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=map(int,input().split())\\n\\nn=[0,1,3,1,2,1,2,1,1,2,1,2,1]\\n\\nif n[x]==n[y]:\\n    ans=\\\"Yes\\\"\\nelse:\\n    ans=\\\"No\\\"\\n            \\nprint(ans)\", \"A=[1,3,5,7,8,10,12]\\nB=[4,6,9,11]\\nC=[2]\\nx,y = map(int,input().split())\\nif x in A and y in A:\\n    print('Yes')  \\nelif x in B and y in B:\\n    print('Yes')\\nelse:\\n    print('No') \", \"x, y = map(int,input().split())\\nS1 = [1, 3, 5, 7, 8, 10, 12]\\nS2 = [4, 6, 9, 11]\\nans = False\\nfor i in range(len(S1)):\\n  for j in range(len(S1)):\\n    if S1[i] == x and S1[j] == y:\\n      ans = True\\nfor i in range(len(S2)):\\n  for j in range(len(S2)):\\n    if S2[i] == x and S2[j] == y:\\n      ans = True\\nif ans:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"c = [['1', '3', '5', '7', '8', '10', '12'], ['4', '6', '9', '11'], ['2']]\\n\\na, b = input().split(' ')\\n\\nif a in c[0] and b in c[0]:\\n  print(\\\"Yes\\\")\\nelif a in c[1] and b in c[1]:\\n  print(\\\"Yes\\\")\\nelif a in c[2] and b in c[2]:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"x, y = map(int, input().split())\\ngroup1 = [1, 3, 5, 7, 8, 10, 12]\\ngroup2 = [4, 6, 9, 11]\\n\\nflag = False\\nif x in group1 and y in group1:\\n    flag = True\\nelif x in group2 and y in group2:\\n    flag = True\\n    \\nif flag:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x, y = list(map(int, input().split()))\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\n\\nif x in a and x not in b and x not in c and y in a and y not in b and y not in c:\\n  print('Yes')\\nelif x not in a and x in b and x not in c and y not in a and y in b and y not in c :\\n  print('Yes')\\nelse:\\n  print('No')\\n\", \"x,y = map(int,input().split())\\ngr_a = [1,3,5,7,8,10,12]\\ngr_b = [4,6,9,11]\\ngr_c = [2]\\n\\nif x in gr_a and y in gr_a:\\n  print(\\\"Yes\\\")\\nelif x in gr_b and y in gr_b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"g1 = [4, 6, 9, 11]\\ng2 = [2]\\n\\nx, y = list(map(int, input().split()))\\ngx = 1 if x in g1 else 2 if x in g2 else 0\\ngy = 1 if y in g1 else 2 if y in g2 else 0\\nprint((\\\"Yes\\\" if gx == gy else \\\"No\\\"))\\n\", \"a = map(int, input().split())\\ninput_set = set(a)\\n\\ngroup_a = {1, 3, 5, 7, 8, 10, 12}\\ngroup_b = {4, 6, 9, 11}\\ngroup_c = {2}\\n\\nlist_of_list = [group_a, group_b, group_c]\\n\\ncount_match = 0\\n\\nfor set_i in list_of_list:\\n    if set_i.issuperset(input_set):\\n        count_match += 1\\n        print('Yes')\\n        break\\n\\nif not count_match >= 1:\\n    print('No')\", \"a=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=list(map(int,input().split(\\\" \\\")))\\nprint(\\\"Yes\\\") if (c[0] in a and c[1] in a) or (c[0] in b and c[1] in b) else print(\\\"No\\\")\", \"x, y = list(map(int,input().split()))\\n\\na= [1,3,5,7,8,10,12]\\nb= [4,6,9,11]\\nc= [2]\\n\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=map(int,input().split())\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=[2]\\n\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"l = ((1,3,5,7,8,10,12),(4,6,9,11),(0,2))\\nx,y = map(int, input().split())\\np = 0\\nfor i in l:\\n\\tif x in i and y in i:\\n\\t\\tp = 1\\n\\t\\tbreak\\nans = 'Yes' if p == 1 else 'No'\\nprint(ans)\", \"group1 = [1, 3, 5, 7, 8, 10, 12]\\ngroup2 = [4, 6, 9, 11]\\n\\nx, y = map(int, input().split())\\n\\nif (x in group1 and y in group1) or (x in group2 and y in group2) or (x == y == 2):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"print('YNeos'[len(set([0 if i==2 else [1,2][i in [4,6,9,11]] for i in [*map(int,input().split())]]))!=1::2])\", \"G1 = [1,3,5,7,8,10,12]\\nG2 = [4,6,9,11]\\nx,y = map(int, input().split())\\n\\nif x in G1 and y in G1:\\n  print('Yes')\\nelif x in G2 and y in G2:\\n  print('Yes')\\nelse:\\n  print('No')\", \"x,y=map(int,input().split())\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nif x in a and y in a :\\n  print(\\\"Yes\\\")\\nelif x in b and y in b :\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"x,y=list(map(int,input().split()))\\nfor l in [[1,3,5,7,8,10,12],[4,6,9,11],[2]]:\\n    if x in l and y in l:\\n        print('Yes')\\n        return\\nprint('No')\\n\", \"x, y = map(int, input().split())\\n\\ng1 = [1, 3, 5, 7, 8, 10, 12]\\ng2 = [4, 6, 9, 11]\\ng3 = [2]\\n\\nif (x in g1 and y in g1) or (x in g2 and y in g2) or (x in g3 and y in g3):\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b = list(map(int, input().split()))\\n\\nlis = [4, 6, 9, 11]\\nlis2 = [1, 3, 5, 7, 8, 10, 12]\\n\\nif a == b == 2:\\n    print('Yes')\\nelif a in lis and b in lis:\\n    print('Yes')\\nelif a in lis2 and b in lis2:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"def solve():\\n    x, y = list(map(int, input().split()))\\n    a = [1, 3, 5, 7, 8, 10, 12]\\n    b = [4, 6, 9, 11]\\n    c = [2]\\n\\n    if (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    solve()\\n\\n__starting_point()\", \"array1 = [1,3,5,7,8,10,12]\\narray2 = [4,6,9,11]\\narray3 = [2]\\nx,y = map(int,input().split())\\nif (x in array1 and y in array1) or (x in array2 and y in array2) or (x in array3 and y in array3):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"x,y=map(int,input().split())\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nif x in a and y in a:\\n    print(\\\"Yes\\\")\\nelif x in b and y in b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"s1 =set([1,3,5,7,8,10,12])\\ns2 =set([4,6,9,11])\\ns3 =set([2])\\na,b =map(int,input().split())\\nfor i in [s1,s2,s3]:\\n  if a in i and b in i:\\n    print(\\\"Yes\\\")\\n    break\\nelse:\\n  print(\\\"No\\\")\", \"a = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\nx, y = map(int, input().split())\\nif a.count(x) * a.count(y) > 0 or b.count(x) * b.count(y) > 0 or c.count(x) * c.count(y) > 0:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b = [int(x) for x in input().split()]\\ng = [[] for x in range(3)]\\ng[0] = [1,3,5,7,8,10,12]\\ng[1] = [4,6,9,11]\\ng[2] = [2]\\nres = \\\"No\\\"\\nfor i in range(3):\\n  if a in g[i] and b in g[i]:\\n    res = \\\"Yes\\\"\\n    \\nprint(res)\", \"a, b = map(int, input().split())\\n\\nif a == 4 or a == 6 or a == 9 or a == 11:\\n  if b == 1 or b == 2 or b == 3 or b == 5 or b == 7 or b == 8 or b == 10 or b == 12:\\n    print(\\\"No\\\")\\n  else:\\n    print(\\\"Yes\\\")\\n    \\nelif a == 2:\\n  print(\\\"No\\\")\\n  \\nelse:\\n  if b == 2 or b == 4 or b == 6 or b == 9 or b == 11:\\n    print(\\\"No\\\")\\n  else:\\n    print(\\\"Yes\\\")\", \"a=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=[2]\\np=0\\nq=0\\n\\ns=list(map(int,input().split()))\\n\\nfor i in a:\\n  if s[0]==i:\\n    p=0\\n  elif s[0]==2:\\n    p=2\\n  else:\\n    p=1\\n\\nfor i in a:\\n  if s[1]==i:\\n    q=0\\n  elif s[1]==2:\\n    q=2\\n  else:\\n    q=1\\n\\nif p==q:\\n  print('Yes')\\nelse:\\n  print('No')\\n\", \"a,b=map(int,input().split())\\nl1=[1,3,5,7,8,10,12]\\nl2=[4,6,9,11] \\nif a==2 or b==2:\\n  print(\\\"No\\\")\\nelif a in l1 and b in l1:\\n  print(\\\"Yes\\\")\\nelif a in l2 and b in l2:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b = map(int, input().split())\\ns = {1, 3, 5, 8, 7, 10, 12}\\nt = {4, 6, 9, 11}\\nu = {2}\\nif a in s and b in s:\\n    print(\\\"Yes\\\")\\nelif a in t and b in t:\\n    print(\\\"Yes\\\")\\nelif a in u and b in u:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"x, y = list(map(int, input().split()))\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\n\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"x, y=map(int, input().split())\\nA=set([1, 3, 5, 7, 8, 10, 12])\\nB=set([4, 6, 9, 11])\\nif x in A and y in A:\\n  print('Yes')\\nelif x in B and y in B:\\n  print('Yes')\\nelse:\\n  print('No')\", \"x,y=map(int,input().split())\\n \\nA=[1,3,5,7,8,10,12]\\nB=[4,6,9,11]\\n \\nif x==2 or y==2:\\n  print('No')\\nelif (x in A and y in A) or (x in B and y in B):\\n  print('Yes')\\nelse:\\n  print('No')\", \"x,y=map(int, input().split())  \\ng=[[1,3,5,7,8,10,12],[4,6,9,11]]\\nprint(\\\"Yes\\\" if any(x in g[i] and y in g[i] for i in range(2)) else \\\"No\\\")\", \"gr = [0,1,3,1,2,1,2,1,1,2,1,2,1]\\nx, y = map(int, input().split())\\nans = 'Yes' if gr[x] == gr[y] else 'No'\\nprint(ans)\", \"x,y = map(int,input().split())\\n\\ngrp1=[1,3,5,7,8,10,12]\\ngrp2=[4,6,9,11]\\n\\nif x in grp1 and y in grp1: print('Yes')\\nelif x in grp2 and y in grp2: print('Yes')\\nelse: print('No')\", \"a=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nx,y=map(int,input().split())\\nif (x in a and y in a) or (x in b and y in b):print('Yes')\\nelse:print('No')\", \"x,y=map(int,input().split())\\ngroup_A=[1,3,5,7,8,10,12]\\ngroup_B=[4,6,9,11]\\nif x in group_A and y in group_A :\\n  print(\\\"Yes\\\")\\nelif x in group_B and y in group_B :\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"L=[1,0,1,2,1,2,1,1,2,1,2,1]\\na,b=map(int,input().split())\\nif L[a-1]==L[b-1]:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\nx, y = map(int, input().split())\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=list(map(int,input().split()))\\nA={1,3,5,7,8,10,13}\\nB={4,6,9,11}\\nC={2}\\n\\nif (x in A and y in A) or (x in B and y in B) or (x in C and y in C):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"g = [-1, 0, 2, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]\\nx, y = map(int, input().split())\\nif g[x] == g[y]: print('Yes')\\nelse: print('No')\", \"x, y = list(map(int, input().split()))\\n\\nga = [4,6,9,11]\\ngb = [1,3,5,7,8,10,12]\\ngc = [2]\\n\\nxg = yg = \\\"\\\"\\ndef group(x):\\n  if x in ga:\\n    return \\\"ga\\\"\\n  if x in gb:\\n    return \\\"gb\\\"\\n  if x in gc:\\n    return \\\"gc\\\"\\nxg = group(x)\\nyg = group(y)\\nif xg == yg:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"x, y = map(int, input().split())\\n\\ng1 = [1, 3, 5, 7, 8, 10, 12]\\ng2 = [4, 6, 9, 11]\\n\\n\\nif x == 2 and y == 2:\\n    print(\\\"Yes\\\")\\nelif x in g1 and y in g1:\\n    print(\\\"Yes\\\")\\nelif x in g2 and y in g2:\\n    print(\\\"Yes\\\")\\nelse:\\n print(\\\"No\\\")\", \"a,b=map(int,input().split())\\ns=[1,3,5,7,8,10,12]\\nt=[4,6,9,11]\\nif a in s:\\n    a = 0\\nelif a in t:\\n    a = 1\\nelse:\\n    a = 2\\nif b in s:\\n    b = 0\\nelif b in t:\\n    b = 1\\nelse:\\n    b = 2\\nprint(\\\"Yes\\\" if a==b else \\\"No\\\")\", \"N = 12\\nParent = [I for I in range(N+1)]\\nRank = [0]*(N+1)\\ndef FindParent(X):\\n    if Parent[X]==X:\\n        return X\\n    else:\\n        Parent[X] = FindParent(Parent[X])\\n        return Parent[X]\\n\\ndef CheckParent(X,Y):\\n    return FindParent(X)==FindParent(Y)\\n\\ndef UniteParent(X,Y):\\n    X = FindParent(X)\\n    Y = FindParent(Y)\\n    if X==Y:\\n        return 0\\n    if Rank[X]<Rank[Y]:\\n        Parent[X] = Y\\n    else:\\n        Parent[Y] = X\\n        if Rank[X]==Rank[Y]:\\n            Rank[X] += 1\\n            \\nfor GA in [3,5,7,8,10,12]:\\n    UniteParent(1,GA)\\nfor GB in [6,9,11]:\\n    UniteParent(4,GB)\\nX,Y = (int(T) for T in input().split())\\nprint(['No','Yes'][CheckParent(X,Y)])\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    x, y = LI()\\n    d = {1: 0, 2: 2, 3: 0, 4: 1, 5: 0, 6: 1, 7: 0, 8: 0, 9: 1, 10: 0, 11: 1, 12: 0}\\n\\n    if d[x] == d[y]:\\n        print('Yes')\\n    else:\\n        print('No')\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"a = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\nc = [2]\\nx,y=map(int,input().split())\\nif x in a and y in a:\\n  print(\\\"Yes\\\")\\nelif x in b and y in b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"x,y=map(int,input().split())\\ns1={1,3,5,7,8,10,12}\\ns2={4,6,9,11}\\nprint([\\\"No\\\",\\\"Yes\\\"][(x in s1 and y in s1) or (x in s2 and y in s2)]) \", \"x, y = map(int, input().split())\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\n\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\", \"g = [0,1,3,1,2,1,2,1,1,2,1,2,1]\\nx, y = map(int,input().split())\\n\\nprint('Yes') if g[x] == g[y] else print('No')\", \"x,y=map(int,input().split())\\ndata=[1,3,1,2,1,2,1,1,2,1,2,1]\\nif data[x-1]==data[y-1]:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=list(map(int,input().split()))\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=[2]\\nif x in a and y in a:\\n    print(\\\"Yes\\\")\\nelif x in b and y in b:\\n    print(\\\"Yes\\\")\\nelif x in c and y in c:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\nx,y = list(map(int,input().split()))\\nprint((\\\"Yes\\\" if (x in a and y in a) or (x in b and y in b) else \\\"No\\\"))\\n\", \"x, y = map(int, input().split())\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nif (x==y or (x in a and y in a) or (x in b and y in b)):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b = map(int,input().split())\\nx = [1,3,5,7,8,10,12]\\ny = [4,6,9,11]\\nif a == 2 or b == 2:\\n    print(\\\"No\\\")\\nelse:\\n    if a in x and b in x:\\n        print(\\\"Yes\\\")\\n    elif a in y and b in y:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\", \"x,y = map(int,input().split())\\nA = [1,3,5,7,8,10,12]\\nB = [4,6,9,11]\\nC = [2]\\n\\nif x in A and y in A:\\n  check = True\\nelif x in B and y in B:\\n  check = True\\nelif x in C and y in C:\\n  check = True\\nelse:\\n  check = False\\n  \\nprint(\\\"Yes\\\" if check else \\\"No\\\")\", \"import sys, math\\nfrom itertools import combinations as c, product as p\\nfrom collections import deque\\nsys.setrecursionlimit(10**9)\\nINF = float('inf')\\nMOD = 10**9 + 7\\n#MOD = 998244353\\n\\n\\ndef si(): return input()\\ndef ii(): return int(input())\\ndef fi(): return float(input())\\ndef lstr(): return input().split()\\ndef lint(): return list(map(int, input().split()))\\ndef lintdec(): return list(map(lambda x:int(x) - 1, input().split()))\\ndef lnstr(n): return [input() for _ in range(n)]\\ndef lnint(n): return [int(input()) for _ in range(n)]\\ndef lint_list(n): return [lint() for _ in range(n)]\\n\\n\\n\\n############################################################\\nc = set(lint())\\na = set([1, 3, 5, 7, 8, 10, 12])\\nb = set([4, 6, 9, 11])\\n\\nif c & a == c or c & b == c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y = list(map(int,input().split()))\\n\\na = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\n\\nif x == 2 or y == 2:\\n  print('No')\\nelif x in a and y in a:\\n  print('Yes')\\nelif x in b and y in b:\\n  print('Yes')\\nelse:\\n  print('No')\\n\", \"x, y = map(int, input().split())\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc =[2]\\nif x in a and y in a:\\n  print(\\\"Yes\\\")\\nelif x in b and y in b:\\n  print(\\\"Yes\\\")\\nelif x in c and y in c:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"x, y = map(int, input().split())\\na = [4, 6, 9, 11]\\nb = 0\\nc = 0\\nif x == 2 or y == 2:\\n    print(\\\"No\\\")\\nelse:\\n    if x in a:\\n        b = 1\\n    if y in a:\\n        c = 1\\n    if (b + c) % 2 == 0:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\", \"x, y = list(map(int, input().split()))\\n\\ngroup_1 = {1, 3, 5, 7, 8, 10, 12}\\ngroup_2 = {4, 6, 9, 11}\\n\\nif (x in group_1) and (y in group_1):\\n    print('Yes')\\nelif (x in group_2) and (y in group_2):\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"x,y=map(int,input().split())\\nG=\\\"121313113131\\\"\\nprint([\\\"No\\\",\\\"Yes\\\"][G[x-1]==G[y-1]])\", \"x, y = map(int, input().split())\\nd = {1:1, 3:1, 5:1, 7:1, 8:1, 10:1, 12:1, 4:2, 6:2, 9:2, 11:2, 2:3}\\nif d[x]==d[y]:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"s = \\\"0131212112121\\\"\\nx,y = map(int,input().split())\\nprint(\\\"Yes\\\" if s[x]==s[y] else \\\"No\\\")\", \"x,y = map(int,input().split())\\ng = [[1,3,5,7,8,10,12],[4,6,9,11],[2]]\\ns = 0\\nfor i in range(3):\\n    if x in g[i] and y in g[i]:\\n        print(\\\"Yes\\\")\\n        s = 1\\nif s == 0:\\n    print(\\\"No\\\")\", \"x,y = map(int, input().split())\\na = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\nif (x in a and y in a) or (x in b and y in b):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"print('YNeos'[len(set([0 if i==2 else [1,2][i in [4,6,9,11]] for i in list(map(int,input().split()))]))!=1::2])\", \"group = [0,2,0,1,0,1,0,0,1,0,1,0]\\nx,y = map(int, open(0).readline().split())\\nprint('Yes' if group[x-1] == group[y-1] else 'No')\", \"a, b = list(map(int, input().split()))\\ns = {1, 3, 5, 8, 7, 10, 12}\\nt = {4, 6, 9, 11}\\nu = {2}\\nif a in s and b in s:\\n    print(\\\"Yes\\\")\\nelif a in t and b in t:\\n    print(\\\"Yes\\\")\\nelif a in u and b in u:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"x,y = list(map(int,input().split()))\\n\\ns = [1,3,5,7,8,10,12]\\ns1 = [4,6,9,11]\\ns2 = [2]\\n\\nif x in s:\\n    if y in s:\\n        print('Yes')\\n        return\\nelif x in s1:\\n    if y in s1:\\n        print('Yes')\\n        return\\nelif x in s2:\\n    if y in s2:\\n        print('Yes')\\n        return\\n\\nprint('No')\\n\", \"G = [set([1,3,5,7,8,10,12]), set([4,6,9,11]), set([2])]\\ndef check(x, y):\\n  for g in G:\\n    if x in g and y in g:\\n      return True\\n  return False\\nx, y = list(map(int, input().split()))\\nprint((\\\"Yes\\\" if check(x, y) else \\\"No\\\"))\\n\", \"lst = input().split()\\n\\nx = int(lst[0])\\ny = int(lst[1])\\n\\nA = [1, 3, 5, 7, 8, 10, 12]\\nB = [4, 6, 9, 11]\\nC = [2]\\n\\ndef judge(L):\\n   if (x in L) and (y in L):\\n      return True\\n   else:\\n      return False\\n\\nif judge(A) or judge(B) or judge(C):\\n   print('Yes')\\nelse:\\n   print('No')\", \"r = list(map(int,input().split()))\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=[2]\\nif r[0]==2 or r[0]==2:\\n  print('No')\\nelif len(list(set(r) & set(a))) == 2:\\n  print('Yes')\\nelif len(list(set(r) & set(b))) == 2:\\n  print('Yes')\\nelse:\\n  print('No')\", \"lisa=[1,3,5,7,8,10,12]\\nlisb=[4,6,9,11]\\nlisc=[2]\\nx,y=map(int,input().split())\\nif (x in lisa)and(y in lisa):\\n    print(\\\"Yes\\\")\\nelif (x in lisb)and(y in lisb):\\n    print(\\\"Yes\\\")\\nelif (x in lisc)and(y in lisc):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"x, y = map(int, input().split())\\n\\ng1 = [1, 3, 5, 7, 8, 10, 12]\\ng2 = [4, 6, 9, 11]\\n\\nprint(\\\"Yes\\\" if (x in g1 and y in g1) or (x in g2 and y in g2) else \\\"No\\\")\", \"a = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\nacount = 0\\nbcount = 0\\nccount = 0\\n\\nx, y = input().split()\\n\\nfor i in range(0, 7):\\n    if int(x) == a[i] or int(y) == a[i]:\\n        acount += 1\\n\\nfor i in range(0, 4):\\n    if int(x) == b[i] or int(y) == b[i]:\\n        bcount += 1\\n\\nif int(x) == c[0]:\\n    ccount += 1\\nif int(y) == c[0]:\\n    ccount += 1\\n\\n\\nif acount == 2 or bcount == 2 or ccount == 2:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\\n\\n\", \"g = [[1, 3, 5, 7, 8, 10, 12], [4, 6, 9, 11], [2]]\\nx, y = map(int, input().split())\\nfor i in range(len(g)):\\n    if x in g[i]:\\n        xg = i\\n    if y in g[i]:\\n        yg = i\\nif xg == yg:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x, y = map(int, input().split())\\n\\ngr1=[1,3,5,7,8,10,12]\\ngr2=[4,6,9,11]\\ngr3=[2]\\n\\nif x in gr1 and y in gr1:\\n    print('Yes')\\nelif x in gr2 and y in gr2:\\n    print('Yes')\\nelif x in gr3 and y in gr3:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x, y =map(int, input().split())\\nif x in {1,3,5,7,8,10,12}:\\n    x= 1\\nelif x in {4,6,9,11}:\\n    x =2\\nelse:\\n    x = 3\\nif y in {1,3,5,7,8,10,12}:\\n    y= 1\\nelif y in {4,6,9,11}:\\n    y =2\\nelse:\\n    y = 3\\nprint(\\\"Yes\\\" if x == y else \\\"No\\\")\", \"x,y=map(int,input().split())\\ng1 = {1,3,5,7,8,10,12}\\ng2 = {4,6,9,11}\\ng3 = {2}\\n\\ndef group(z):\\n  if z in g1:return 1\\n  elif z in g2:return 2\\n  else: return 3\\n  \\nif group(x)==group(y):print('Yes')\\nelse:print('No')\", \"'''\\nabc062 A - Grouping\\nhttps://atcoder.jp/contests/abc062/tasks/abc062_a\\n'''\\n\\ndirs = [{1, 3, 5, 7, 8, 10, 12}, {4, 6, 9, 11}, {2}]\\n\\ni = list(map(int, input().split()))\\n\\nfor dir in dirs:\\n    if i[0] in dir and i[1] in dir:\\n        print('Yes')\\n        return\\nelse:\\n    print('No')\\n\", \"a,b=input().split()\\na=int(a)\\nb=int(b)\\nl1=[1,3,5,7,8,10,12]\\nl2=[4,6,9,11]\\nif a in l1 and b in l1:\\n  print(\\\"Yes\\\")\\nelif a in l2 and b in l2:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n\\nx,y = list(map(int, input().split()))\\n\\ng1 = [1,3,5,7,8,10,12]\\ng2 = [4,6,9,11]\\ng3 = [2]\\n\\n\\nif (x in g1 and y in g1):\\n    print(\\\"Yes\\\")\\nelif (x in g2 and y in g2):\\n    print(\\\"Yes\\\")\\nelif (x in g3 and y in g3):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\\n\\n\"]",
        "difficulty": "introductory",
        "input": "1 3\n",
        "output": "Yes\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc062/tasks/abc062_a"
    },
    {
        "id": 522,
        "task_id": 4695,
        "test_case_id": 2,
        "question": "Based on some criterion, Snuke divided the integers from 1 through 12 into three groups as shown in the figure below.\nGiven two integers x and y (1 ≤ x < y ≤ 12), determine whether they belong to the same group.\n\n-----Constraints-----\n - x and y are integers.\n - 1 ≤ x < y ≤ 12\n\n-----Input-----\nInput is given from Standard Input in the following format:\nx y\n\n-----Output-----\nIf x and y belong to the same group, print Yes; otherwise, print No.\n\n-----Sample Input-----\n1 3\n\n-----Sample Output-----\nYes\n",
        "solutions": "[\"n1 = [1, 3, 5, 7, 8, 10, 12]\\nn2 = [4, 6, 9, 11]\\n\\na, b = list(map(int, input().split()))\\nprint((\\\"Yes\\\" if a in n1 and b in n1 or a in n2 and b in n2 else \\\"No\\\"))\\n\", \"lst1 = [4,6,9,11]\\nlst2 = [2]\\nlst3 = [1,3,5,7,8,10,12]\\nx,y = map(int,input().split())\\nif x in lst1 and y in lst1:\\n    print('Yes')\\nelif x in lst2 and y in lst2:\\n    print('Yes')\\nelif x in lst3 and y in lst3:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=map(int,input().split())\\nA=[2]\\nB=[4,6,9,11]\\nC=[1,3,5,7,8,10,12]\\nif x in B and y in B:\\n  print(\\\"Yes\\\")\\nelif x in C and y in C:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a,b,c=[1,3,5,7,8,10,12],[4,6,9,11],[2]\\nprint('YNeos'[len(set([0 if i in a else [1,2][i in b] for i in list(map(int,input().split()))]))!=1::2])\", \"X,Y=map(int,input().split())\\nA=1,3,5,7,8,10,12\\nB=4,6,9,11\\nC=2\\nans=\\\"No\\\"\\nif X in A and Y in A:\\n    ans=\\\"Yes\\\"\\nelif X in B and Y in B:\\n    ans=\\\"Yes\\\"\\nelif X==Y==2:\\n    ans=\\\"Yes\\\"\\nprint(ans)\", \"x,y=map(int,input().split())\\ngrp1=[1,3,5,7,8,10,12]\\ngrp2=[4,6,9,11]\\n\\nif x in grp1 and y in grp1: print(\\\"Yes\\\")\\nelif x in grp2 and y in grp2: print(\\\"Yes\\\")\\nelse: print(\\\"No\\\")\", \"a = map(int, input().split())\\ninput_list = list(a)\\n\\ngroup_a = [1, 3, 5, 7, 8, 10, 12]\\ngroup_b = [4, 6, 9, 11]\\ngroup_c = [2]\\nlist_of_list = [group_a, group_b, group_c]\\n\\ncount_match = 0\\n\\nfor list_i in list_of_list:\\n    if input_list[0] in list_i and input_list[1] in list_i:\\n        count_match += 1\\n        break\\n\\nif count_match == 1:\\n    print('Yes')\\nelse:\\n    print('No')\", \"data_1 =[1,3,5,7,8,10,12]\\ndata_2 =[4,6,9,11]\\nx,y = map(int,input().split())\\nif x in data_1 and y in data_1:\\n    print('Yes')\\nelif x in data_2 and y in data_2:\\n    print('Yes')\\nelse:\\n    print('No')\", \"#!/usr/bin/env python3\\nx, y = list(map(int, input().split()))\\n\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\n\\nif x in a and y in a:\\n    print('Yes')\\nelif x in b and y in b:\\n    print('Yes')\\nelif x in c and y in c:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"a,b = map(int,input().split())\\n\\nx = [1,3,5,7,8,10,12]\\ny = [4,6,9,11]\\n\\nif a in x and b in x or a in y and b in y:\\n  print('Yes')\\n  \\nelse:\\n  print('No')\", \"x,y=map(int,input().split())\\ns1 = [1,3,5,7,8,10,12]\\ns2 = [4,6,9,11]\\ns3 = [2]\\nif x in s1 and y in s1:\\n    print('Yes')\\nelif x in s2 and y in s2:\\n    print('Yes')\\nelif x in s3 and y in s3:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y = map(int, input().split())\\na = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\nc = [2]\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\", \"x, y = map(int, input().split())\\n\\nA = [1, 3, 5, 7, 8, 10, 12]\\nB = [4, 6, 9, 11]\\nC = [2, ]\\n\\nif x in A and y in A:\\n    print('Yes')\\nelif x in B and y in B:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=map(int,input().split())\\n\\nn=[0,1,3,1,2,1,2,1,1,2,1,2,1]\\n\\nif n[x]==n[y]:\\n    ans=\\\"Yes\\\"\\nelse:\\n    ans=\\\"No\\\"\\n            \\nprint(ans)\", \"A=[1,3,5,7,8,10,12]\\nB=[4,6,9,11]\\nC=[2]\\nx,y = map(int,input().split())\\nif x in A and y in A:\\n    print('Yes')  \\nelif x in B and y in B:\\n    print('Yes')\\nelse:\\n    print('No') \", \"x, y = map(int,input().split())\\nS1 = [1, 3, 5, 7, 8, 10, 12]\\nS2 = [4, 6, 9, 11]\\nans = False\\nfor i in range(len(S1)):\\n  for j in range(len(S1)):\\n    if S1[i] == x and S1[j] == y:\\n      ans = True\\nfor i in range(len(S2)):\\n  for j in range(len(S2)):\\n    if S2[i] == x and S2[j] == y:\\n      ans = True\\nif ans:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"c = [['1', '3', '5', '7', '8', '10', '12'], ['4', '6', '9', '11'], ['2']]\\n\\na, b = input().split(' ')\\n\\nif a in c[0] and b in c[0]:\\n  print(\\\"Yes\\\")\\nelif a in c[1] and b in c[1]:\\n  print(\\\"Yes\\\")\\nelif a in c[2] and b in c[2]:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"x, y = map(int, input().split())\\ngroup1 = [1, 3, 5, 7, 8, 10, 12]\\ngroup2 = [4, 6, 9, 11]\\n\\nflag = False\\nif x in group1 and y in group1:\\n    flag = True\\nelif x in group2 and y in group2:\\n    flag = True\\n    \\nif flag:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x, y = list(map(int, input().split()))\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\n\\nif x in a and x not in b and x not in c and y in a and y not in b and y not in c:\\n  print('Yes')\\nelif x not in a and x in b and x not in c and y not in a and y in b and y not in c :\\n  print('Yes')\\nelse:\\n  print('No')\\n\", \"x,y = map(int,input().split())\\ngr_a = [1,3,5,7,8,10,12]\\ngr_b = [4,6,9,11]\\ngr_c = [2]\\n\\nif x in gr_a and y in gr_a:\\n  print(\\\"Yes\\\")\\nelif x in gr_b and y in gr_b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"g1 = [4, 6, 9, 11]\\ng2 = [2]\\n\\nx, y = list(map(int, input().split()))\\ngx = 1 if x in g1 else 2 if x in g2 else 0\\ngy = 1 if y in g1 else 2 if y in g2 else 0\\nprint((\\\"Yes\\\" if gx == gy else \\\"No\\\"))\\n\", \"a = map(int, input().split())\\ninput_set = set(a)\\n\\ngroup_a = {1, 3, 5, 7, 8, 10, 12}\\ngroup_b = {4, 6, 9, 11}\\ngroup_c = {2}\\n\\nlist_of_list = [group_a, group_b, group_c]\\n\\ncount_match = 0\\n\\nfor set_i in list_of_list:\\n    if set_i.issuperset(input_set):\\n        count_match += 1\\n        print('Yes')\\n        break\\n\\nif not count_match >= 1:\\n    print('No')\", \"a=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=list(map(int,input().split(\\\" \\\")))\\nprint(\\\"Yes\\\") if (c[0] in a and c[1] in a) or (c[0] in b and c[1] in b) else print(\\\"No\\\")\", \"x, y = list(map(int,input().split()))\\n\\na= [1,3,5,7,8,10,12]\\nb= [4,6,9,11]\\nc= [2]\\n\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=map(int,input().split())\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=[2]\\n\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"l = ((1,3,5,7,8,10,12),(4,6,9,11),(0,2))\\nx,y = map(int, input().split())\\np = 0\\nfor i in l:\\n\\tif x in i and y in i:\\n\\t\\tp = 1\\n\\t\\tbreak\\nans = 'Yes' if p == 1 else 'No'\\nprint(ans)\", \"group1 = [1, 3, 5, 7, 8, 10, 12]\\ngroup2 = [4, 6, 9, 11]\\n\\nx, y = map(int, input().split())\\n\\nif (x in group1 and y in group1) or (x in group2 and y in group2) or (x == y == 2):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"print('YNeos'[len(set([0 if i==2 else [1,2][i in [4,6,9,11]] for i in [*map(int,input().split())]]))!=1::2])\", \"G1 = [1,3,5,7,8,10,12]\\nG2 = [4,6,9,11]\\nx,y = map(int, input().split())\\n\\nif x in G1 and y in G1:\\n  print('Yes')\\nelif x in G2 and y in G2:\\n  print('Yes')\\nelse:\\n  print('No')\", \"x,y=map(int,input().split())\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nif x in a and y in a :\\n  print(\\\"Yes\\\")\\nelif x in b and y in b :\\n  print(\\\"Yes\\\")\\nelse :\\n  print(\\\"No\\\")\", \"x,y=list(map(int,input().split()))\\nfor l in [[1,3,5,7,8,10,12],[4,6,9,11],[2]]:\\n    if x in l and y in l:\\n        print('Yes')\\n        return\\nprint('No')\\n\", \"x, y = map(int, input().split())\\n\\ng1 = [1, 3, 5, 7, 8, 10, 12]\\ng2 = [4, 6, 9, 11]\\ng3 = [2]\\n\\nif (x in g1 and y in g1) or (x in g2 and y in g2) or (x in g3 and y in g3):\\n    print('Yes')\\nelse:\\n    print('No')\", \"a, b = list(map(int, input().split()))\\n\\nlis = [4, 6, 9, 11]\\nlis2 = [1, 3, 5, 7, 8, 10, 12]\\n\\nif a == b == 2:\\n    print('Yes')\\nelif a in lis and b in lis:\\n    print('Yes')\\nelif a in lis2 and b in lis2:\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"def solve():\\n    x, y = list(map(int, input().split()))\\n    a = [1, 3, 5, 7, 8, 10, 12]\\n    b = [4, 6, 9, 11]\\n    c = [2]\\n\\n    if (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\\n\\n\\ndef __starting_point():\\n    solve()\\n\\n__starting_point()\", \"array1 = [1,3,5,7,8,10,12]\\narray2 = [4,6,9,11]\\narray3 = [2]\\nx,y = map(int,input().split())\\nif (x in array1 and y in array1) or (x in array2 and y in array2) or (x in array3 and y in array3):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"x,y=map(int,input().split())\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nif x in a and y in a:\\n    print(\\\"Yes\\\")\\nelif x in b and y in b:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"s1 =set([1,3,5,7,8,10,12])\\ns2 =set([4,6,9,11])\\ns3 =set([2])\\na,b =map(int,input().split())\\nfor i in [s1,s2,s3]:\\n  if a in i and b in i:\\n    print(\\\"Yes\\\")\\n    break\\nelse:\\n  print(\\\"No\\\")\", \"a = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\nx, y = map(int, input().split())\\nif a.count(x) * a.count(y) > 0 or b.count(x) * b.count(y) > 0 or c.count(x) * c.count(y) > 0:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b = [int(x) for x in input().split()]\\ng = [[] for x in range(3)]\\ng[0] = [1,3,5,7,8,10,12]\\ng[1] = [4,6,9,11]\\ng[2] = [2]\\nres = \\\"No\\\"\\nfor i in range(3):\\n  if a in g[i] and b in g[i]:\\n    res = \\\"Yes\\\"\\n    \\nprint(res)\", \"a, b = map(int, input().split())\\n\\nif a == 4 or a == 6 or a == 9 or a == 11:\\n  if b == 1 or b == 2 or b == 3 or b == 5 or b == 7 or b == 8 or b == 10 or b == 12:\\n    print(\\\"No\\\")\\n  else:\\n    print(\\\"Yes\\\")\\n    \\nelif a == 2:\\n  print(\\\"No\\\")\\n  \\nelse:\\n  if b == 2 or b == 4 or b == 6 or b == 9 or b == 11:\\n    print(\\\"No\\\")\\n  else:\\n    print(\\\"Yes\\\")\", \"a=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=[2]\\np=0\\nq=0\\n\\ns=list(map(int,input().split()))\\n\\nfor i in a:\\n  if s[0]==i:\\n    p=0\\n  elif s[0]==2:\\n    p=2\\n  else:\\n    p=1\\n\\nfor i in a:\\n  if s[1]==i:\\n    q=0\\n  elif s[1]==2:\\n    q=2\\n  else:\\n    q=1\\n\\nif p==q:\\n  print('Yes')\\nelse:\\n  print('No')\\n\", \"a,b=map(int,input().split())\\nl1=[1,3,5,7,8,10,12]\\nl2=[4,6,9,11] \\nif a==2 or b==2:\\n  print(\\\"No\\\")\\nelif a in l1 and b in l1:\\n  print(\\\"Yes\\\")\\nelif a in l2 and b in l2:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a, b = map(int, input().split())\\ns = {1, 3, 5, 8, 7, 10, 12}\\nt = {4, 6, 9, 11}\\nu = {2}\\nif a in s and b in s:\\n    print(\\\"Yes\\\")\\nelif a in t and b in t:\\n    print(\\\"Yes\\\")\\nelif a in u and b in u:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"x, y = list(map(int, input().split()))\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\n\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"x, y=map(int, input().split())\\nA=set([1, 3, 5, 7, 8, 10, 12])\\nB=set([4, 6, 9, 11])\\nif x in A and y in A:\\n  print('Yes')\\nelif x in B and y in B:\\n  print('Yes')\\nelse:\\n  print('No')\", \"x,y=map(int,input().split())\\n \\nA=[1,3,5,7,8,10,12]\\nB=[4,6,9,11]\\n \\nif x==2 or y==2:\\n  print('No')\\nelif (x in A and y in A) or (x in B and y in B):\\n  print('Yes')\\nelse:\\n  print('No')\", \"x,y=map(int, input().split())  \\ng=[[1,3,5,7,8,10,12],[4,6,9,11]]\\nprint(\\\"Yes\\\" if any(x in g[i] and y in g[i] for i in range(2)) else \\\"No\\\")\", \"gr = [0,1,3,1,2,1,2,1,1,2,1,2,1]\\nx, y = map(int, input().split())\\nans = 'Yes' if gr[x] == gr[y] else 'No'\\nprint(ans)\", \"x,y = map(int,input().split())\\n\\ngrp1=[1,3,5,7,8,10,12]\\ngrp2=[4,6,9,11]\\n\\nif x in grp1 and y in grp1: print('Yes')\\nelif x in grp2 and y in grp2: print('Yes')\\nelse: print('No')\", \"a=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nx,y=map(int,input().split())\\nif (x in a and y in a) or (x in b and y in b):print('Yes')\\nelse:print('No')\", \"x,y=map(int,input().split())\\ngroup_A=[1,3,5,7,8,10,12]\\ngroup_B=[4,6,9,11]\\nif x in group_A and y in group_A :\\n  print(\\\"Yes\\\")\\nelif x in group_B and y in group_B :\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"L=[1,0,1,2,1,2,1,1,2,1,2,1]\\na,b=map(int,input().split())\\nif L[a-1]==L[b-1]:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"a = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\nx, y = map(int, input().split())\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=list(map(int,input().split()))\\nA={1,3,5,7,8,10,13}\\nB={4,6,9,11}\\nC={2}\\n\\nif (x in A and y in A) or (x in B and y in B) or (x in C and y in C):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"g = [-1, 0, 2, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]\\nx, y = map(int, input().split())\\nif g[x] == g[y]: print('Yes')\\nelse: print('No')\", \"x, y = list(map(int, input().split()))\\n\\nga = [4,6,9,11]\\ngb = [1,3,5,7,8,10,12]\\ngc = [2]\\n\\nxg = yg = \\\"\\\"\\ndef group(x):\\n  if x in ga:\\n    return \\\"ga\\\"\\n  if x in gb:\\n    return \\\"gb\\\"\\n  if x in gc:\\n    return \\\"gc\\\"\\nxg = group(x)\\nyg = group(y)\\nif xg == yg:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\\n\", \"x, y = map(int, input().split())\\n\\ng1 = [1, 3, 5, 7, 8, 10, 12]\\ng2 = [4, 6, 9, 11]\\n\\n\\nif x == 2 and y == 2:\\n    print(\\\"Yes\\\")\\nelif x in g1 and y in g1:\\n    print(\\\"Yes\\\")\\nelif x in g2 and y in g2:\\n    print(\\\"Yes\\\")\\nelse:\\n print(\\\"No\\\")\", \"a,b=map(int,input().split())\\ns=[1,3,5,7,8,10,12]\\nt=[4,6,9,11]\\nif a in s:\\n    a = 0\\nelif a in t:\\n    a = 1\\nelse:\\n    a = 2\\nif b in s:\\n    b = 0\\nelif b in t:\\n    b = 1\\nelse:\\n    b = 2\\nprint(\\\"Yes\\\" if a==b else \\\"No\\\")\", \"N = 12\\nParent = [I for I in range(N+1)]\\nRank = [0]*(N+1)\\ndef FindParent(X):\\n    if Parent[X]==X:\\n        return X\\n    else:\\n        Parent[X] = FindParent(Parent[X])\\n        return Parent[X]\\n\\ndef CheckParent(X,Y):\\n    return FindParent(X)==FindParent(Y)\\n\\ndef UniteParent(X,Y):\\n    X = FindParent(X)\\n    Y = FindParent(Y)\\n    if X==Y:\\n        return 0\\n    if Rank[X]<Rank[Y]:\\n        Parent[X] = Y\\n    else:\\n        Parent[Y] = X\\n        if Rank[X]==Rank[Y]:\\n            Rank[X] += 1\\n            \\nfor GA in [3,5,7,8,10,12]:\\n    UniteParent(1,GA)\\nfor GB in [6,9,11]:\\n    UniteParent(4,GB)\\nX,Y = (int(T) for T in input().split())\\nprint(['No','Yes'][CheckParent(X,Y)])\", \"import bisect, collections, copy, heapq, itertools, math, string, sys\\ninput = lambda: sys.stdin.readline().rstrip() \\nsys.setrecursionlimit(10**7)\\nINF = float('inf')\\ndef I(): return int(input())\\ndef F(): return float(input())\\ndef SS(): return input()\\ndef LI(): return [int(x) for x in input().split()]\\ndef LI_(): return [int(x)-1 for x in input().split()]\\ndef LF(): return [float(x) for x in input().split()]\\ndef LSS(): return input().split()\\n\\ndef resolve():\\n    x, y = LI()\\n    d = {1: 0, 2: 2, 3: 0, 4: 1, 5: 0, 6: 1, 7: 0, 8: 0, 9: 1, 10: 0, 11: 1, 12: 0}\\n\\n    if d[x] == d[y]:\\n        print('Yes')\\n    else:\\n        print('No')\\n\\ndef __starting_point():\\n    resolve()\\n\\n__starting_point()\", \"a = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\nc = [2]\\nx,y=map(int,input().split())\\nif x in a and y in a:\\n  print(\\\"Yes\\\")\\nelif x in b and y in b:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"x,y=map(int,input().split())\\ns1={1,3,5,7,8,10,12}\\ns2={4,6,9,11}\\nprint([\\\"No\\\",\\\"Yes\\\"][(x in s1 and y in s1) or (x in s2 and y in s2)]) \", \"x, y = map(int, input().split())\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\n\\nif (x in a and y in a) or (x in b and y in b) or (x in c and y in c):\\n    print('Yes')\\nelse:\\n    print('No')\", \"g = [0,1,3,1,2,1,2,1,1,2,1,2,1]\\nx, y = map(int,input().split())\\n\\nprint('Yes') if g[x] == g[y] else print('No')\", \"x,y=map(int,input().split())\\ndata=[1,3,1,2,1,2,1,1,2,1,2,1]\\nif data[x-1]==data[y-1]:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y=list(map(int,input().split()))\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=[2]\\nif x in a and y in a:\\n    print(\\\"Yes\\\")\\nelif x in b and y in b:\\n    print(\\\"Yes\\\")\\nelif x in c and y in c:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"a = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\nx,y = list(map(int,input().split()))\\nprint((\\\"Yes\\\" if (x in a and y in a) or (x in b and y in b) else \\\"No\\\"))\\n\", \"x, y = map(int, input().split())\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nif (x==y or (x in a and y in a) or (x in b and y in b)):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"a,b = map(int,input().split())\\nx = [1,3,5,7,8,10,12]\\ny = [4,6,9,11]\\nif a == 2 or b == 2:\\n    print(\\\"No\\\")\\nelse:\\n    if a in x and b in x:\\n        print(\\\"Yes\\\")\\n    elif a in y and b in y:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\", \"x,y = map(int,input().split())\\nA = [1,3,5,7,8,10,12]\\nB = [4,6,9,11]\\nC = [2]\\n\\nif x in A and y in A:\\n  check = True\\nelif x in B and y in B:\\n  check = True\\nelif x in C and y in C:\\n  check = True\\nelse:\\n  check = False\\n  \\nprint(\\\"Yes\\\" if check else \\\"No\\\")\", \"import sys, math\\nfrom itertools import combinations as c, product as p\\nfrom collections import deque\\nsys.setrecursionlimit(10**9)\\nINF = float('inf')\\nMOD = 10**9 + 7\\n#MOD = 998244353\\n\\n\\ndef si(): return input()\\ndef ii(): return int(input())\\ndef fi(): return float(input())\\ndef lstr(): return input().split()\\ndef lint(): return list(map(int, input().split()))\\ndef lintdec(): return list(map(lambda x:int(x) - 1, input().split()))\\ndef lnstr(n): return [input() for _ in range(n)]\\ndef lnint(n): return [int(input()) for _ in range(n)]\\ndef lint_list(n): return [lint() for _ in range(n)]\\n\\n\\n\\n############################################################\\nc = set(lint())\\na = set([1, 3, 5, 7, 8, 10, 12])\\nb = set([4, 6, 9, 11])\\n\\nif c & a == c or c & b == c:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x,y = list(map(int,input().split()))\\n\\na = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\n\\nif x == 2 or y == 2:\\n  print('No')\\nelif x in a and y in a:\\n  print('Yes')\\nelif x in b and y in b:\\n  print('Yes')\\nelse:\\n  print('No')\\n\", \"x, y = map(int, input().split())\\na = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc =[2]\\nif x in a and y in a:\\n  print(\\\"Yes\\\")\\nelif x in b and y in b:\\n  print(\\\"Yes\\\")\\nelif x in c and y in c:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"x, y = map(int, input().split())\\na = [4, 6, 9, 11]\\nb = 0\\nc = 0\\nif x == 2 or y == 2:\\n    print(\\\"No\\\")\\nelse:\\n    if x in a:\\n        b = 1\\n    if y in a:\\n        c = 1\\n    if (b + c) % 2 == 0:\\n        print(\\\"Yes\\\")\\n    else:\\n        print(\\\"No\\\")\", \"x, y = list(map(int, input().split()))\\n\\ngroup_1 = {1, 3, 5, 7, 8, 10, 12}\\ngroup_2 = {4, 6, 9, 11}\\n\\nif (x in group_1) and (y in group_1):\\n    print('Yes')\\nelif (x in group_2) and (y in group_2):\\n    print('Yes')\\nelse:\\n    print('No')\\n\", \"x,y=map(int,input().split())\\nG=\\\"121313113131\\\"\\nprint([\\\"No\\\",\\\"Yes\\\"][G[x-1]==G[y-1]])\", \"x, y = map(int, input().split())\\nd = {1:1, 3:1, 5:1, 7:1, 8:1, 10:1, 12:1, 4:2, 6:2, 9:2, 11:2, 2:3}\\nif d[x]==d[y]:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"s = \\\"0131212112121\\\"\\nx,y = map(int,input().split())\\nprint(\\\"Yes\\\" if s[x]==s[y] else \\\"No\\\")\", \"x,y = map(int,input().split())\\ng = [[1,3,5,7,8,10,12],[4,6,9,11],[2]]\\ns = 0\\nfor i in range(3):\\n    if x in g[i] and y in g[i]:\\n        print(\\\"Yes\\\")\\n        s = 1\\nif s == 0:\\n    print(\\\"No\\\")\", \"x,y = map(int, input().split())\\na = [1,3,5,7,8,10,12]\\nb = [4,6,9,11]\\nif (x in a and y in a) or (x in b and y in b):\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"print('YNeos'[len(set([0 if i==2 else [1,2][i in [4,6,9,11]] for i in list(map(int,input().split()))]))!=1::2])\", \"group = [0,2,0,1,0,1,0,0,1,0,1,0]\\nx,y = map(int, open(0).readline().split())\\nprint('Yes' if group[x-1] == group[y-1] else 'No')\", \"a, b = list(map(int, input().split()))\\ns = {1, 3, 5, 8, 7, 10, 12}\\nt = {4, 6, 9, 11}\\nu = {2}\\nif a in s and b in s:\\n    print(\\\"Yes\\\")\\nelif a in t and b in t:\\n    print(\\\"Yes\\\")\\nelif a in u and b in u:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\", \"x,y = list(map(int,input().split()))\\n\\ns = [1,3,5,7,8,10,12]\\ns1 = [4,6,9,11]\\ns2 = [2]\\n\\nif x in s:\\n    if y in s:\\n        print('Yes')\\n        return\\nelif x in s1:\\n    if y in s1:\\n        print('Yes')\\n        return\\nelif x in s2:\\n    if y in s2:\\n        print('Yes')\\n        return\\n\\nprint('No')\\n\", \"G = [set([1,3,5,7,8,10,12]), set([4,6,9,11]), set([2])]\\ndef check(x, y):\\n  for g in G:\\n    if x in g and y in g:\\n      return True\\n  return False\\nx, y = list(map(int, input().split()))\\nprint((\\\"Yes\\\" if check(x, y) else \\\"No\\\"))\\n\", \"lst = input().split()\\n\\nx = int(lst[0])\\ny = int(lst[1])\\n\\nA = [1, 3, 5, 7, 8, 10, 12]\\nB = [4, 6, 9, 11]\\nC = [2]\\n\\ndef judge(L):\\n   if (x in L) and (y in L):\\n      return True\\n   else:\\n      return False\\n\\nif judge(A) or judge(B) or judge(C):\\n   print('Yes')\\nelse:\\n   print('No')\", \"r = list(map(int,input().split()))\\na=[1,3,5,7,8,10,12]\\nb=[4,6,9,11]\\nc=[2]\\nif r[0]==2 or r[0]==2:\\n  print('No')\\nelif len(list(set(r) & set(a))) == 2:\\n  print('Yes')\\nelif len(list(set(r) & set(b))) == 2:\\n  print('Yes')\\nelse:\\n  print('No')\", \"lisa=[1,3,5,7,8,10,12]\\nlisb=[4,6,9,11]\\nlisc=[2]\\nx,y=map(int,input().split())\\nif (x in lisa)and(y in lisa):\\n    print(\\\"Yes\\\")\\nelif (x in lisb)and(y in lisb):\\n    print(\\\"Yes\\\")\\nelif (x in lisc)and(y in lisc):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\", \"x, y = map(int, input().split())\\n\\ng1 = [1, 3, 5, 7, 8, 10, 12]\\ng2 = [4, 6, 9, 11]\\n\\nprint(\\\"Yes\\\" if (x in g1 and y in g1) or (x in g2 and y in g2) else \\\"No\\\")\", \"a = [1, 3, 5, 7, 8, 10, 12]\\nb = [4, 6, 9, 11]\\nc = [2]\\nacount = 0\\nbcount = 0\\nccount = 0\\n\\nx, y = input().split()\\n\\nfor i in range(0, 7):\\n    if int(x) == a[i] or int(y) == a[i]:\\n        acount += 1\\n\\nfor i in range(0, 4):\\n    if int(x) == b[i] or int(y) == b[i]:\\n        bcount += 1\\n\\nif int(x) == c[0]:\\n    ccount += 1\\nif int(y) == c[0]:\\n    ccount += 1\\n\\n\\nif acount == 2 or bcount == 2 or ccount == 2:\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\\n\\n\", \"g = [[1, 3, 5, 7, 8, 10, 12], [4, 6, 9, 11], [2]]\\nx, y = map(int, input().split())\\nfor i in range(len(g)):\\n    if x in g[i]:\\n        xg = i\\n    if y in g[i]:\\n        yg = i\\nif xg == yg:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x, y = map(int, input().split())\\n\\ngr1=[1,3,5,7,8,10,12]\\ngr2=[4,6,9,11]\\ngr3=[2]\\n\\nif x in gr1 and y in gr1:\\n    print('Yes')\\nelif x in gr2 and y in gr2:\\n    print('Yes')\\nelif x in gr3 and y in gr3:\\n    print('Yes')\\nelse:\\n    print('No')\", \"x, y =map(int, input().split())\\nif x in {1,3,5,7,8,10,12}:\\n    x= 1\\nelif x in {4,6,9,11}:\\n    x =2\\nelse:\\n    x = 3\\nif y in {1,3,5,7,8,10,12}:\\n    y= 1\\nelif y in {4,6,9,11}:\\n    y =2\\nelse:\\n    y = 3\\nprint(\\\"Yes\\\" if x == y else \\\"No\\\")\", \"x,y=map(int,input().split())\\ng1 = {1,3,5,7,8,10,12}\\ng2 = {4,6,9,11}\\ng3 = {2}\\n\\ndef group(z):\\n  if z in g1:return 1\\n  elif z in g2:return 2\\n  else: return 3\\n  \\nif group(x)==group(y):print('Yes')\\nelse:print('No')\", \"'''\\nabc062 A - Grouping\\nhttps://atcoder.jp/contests/abc062/tasks/abc062_a\\n'''\\n\\ndirs = [{1, 3, 5, 7, 8, 10, 12}, {4, 6, 9, 11}, {2}]\\n\\ni = list(map(int, input().split()))\\n\\nfor dir in dirs:\\n    if i[0] in dir and i[1] in dir:\\n        print('Yes')\\n        return\\nelse:\\n    print('No')\\n\", \"a,b=input().split()\\na=int(a)\\nb=int(b)\\nl1=[1,3,5,7,8,10,12]\\nl2=[4,6,9,11]\\nif a in l1 and b in l1:\\n  print(\\\"Yes\\\")\\nelif a in l2 and b in l2:\\n  print(\\\"Yes\\\")\\nelse:\\n  print(\\\"No\\\")\", \"#k = int(input())\\n#s = input()\\n#a, b = map(int, input().split())\\n#s, t = map(str, input().split())\\n#l = list(map(int, input().split()))\\n#l = [list(map(int,input().split())) for i in range(n)]\\n#a = [list(input()) for _ in range(n)]\\n\\nx,y = list(map(int, input().split()))\\n\\ng1 = [1,3,5,7,8,10,12]\\ng2 = [4,6,9,11]\\ng3 = [2]\\n\\n\\nif (x in g1 and y in g1):\\n    print(\\\"Yes\\\")\\nelif (x in g2 and y in g2):\\n    print(\\\"Yes\\\")\\nelif (x in g3 and y in g3):\\n    print(\\\"Yes\\\")\\nelse:\\n    print(\\\"No\\\")\\n\\n\\n\"]",
        "difficulty": "introductory",
        "input": "2 4\n",
        "output": "No\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc062/tasks/abc062_a"
    },
    {
        "id": 523,
        "task_id": 4696,
        "test_case_id": 1,
        "question": "AtCoDeer the deer found two positive integers, a and b.\nDetermine whether the product of a and b is even or odd.\n\n-----Constraints-----\n - 1 ≤ a,b ≤ 10000\n - a and b are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\na b\n\n-----Output-----\nIf the product is odd, print Odd; if it is even, print Even.\n\n-----Sample Input-----\n3 4\n\n-----Sample Output-----\nEven\n\nAs 3 × 4 = 12 is even, print Even.",
        "solutions": "[\"a, b = map(int, input().split())\\nif a*b %2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nif a % 2 == 0:\\n  print('Even')\\nelif b % 2 == 0:\\n  print('Even')\\nelse:\\n  print('Odd')\", \"a,b=map(int, input().split())\\n\\nif a*b%2==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"# -*- coding: utf-8 -*-\\n \\na, b = map(int, input().split())\\n \\nmul = a * b\\n \\nresult = 'Even' if (mul % 2 == 0) else 'Odd'\\n  \\nprint(result)\", \"a, b = map(int, input().split())\\nprint([\\\"Even\\\", \\\"Odd\\\"][a * b % 2])\", \"a,b=(int(x) for x in input().split())\\n \\nif a*b%2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nprint('Odd' if a*b % 2 == 1 else 'Even')\", \"a, b = map(int,input().split())\\n\\nadd = (a * b)\\n\\nif add % 2 != 0:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a,b = list(map(int, input().split())) \\nc =a*b\\nif c%2==0:\\n  print('Even')\\nelse:\\n  print('Odd')\\n\", \"a,b=input().split()\\nif int(a)*int(b)%2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"import bisect,collections,copy,heapq,itertools,math,string\\nimport sys\\ndef I():\\n    #1 line 1 int\\n     return int(sys.stdin.readline().rstrip())\\ndef LI():\\n    #1 line n int\\n     return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S():\\n    #1 line 1 string\\n     return sys.stdin.readline().rstrip()\\ndef LS():\\n    #1 line n strings\\n     return list(sys.stdin.readline().rstrip().split())\\n\\na,b,=LI()\\n\\nif (a*b)%2==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nprint(\\\"Even\\\" if a * b % 2 == 0 else \\\"Odd\\\")\", \"a, b = list(map(int, input().split()))\\nif a * b % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\\n\", \"a,b = map(int,input().split())\\nc=a*b\\n\\nif c % 2 ==1:\\n    print('Odd')\\n\\nelse:\\n    print('Even')\", \"a, b = map(int, input().split())\\nif (a * b) % 2 == 0:\\n    print(\\\"Even\\\")\\nelif (a * b) % 2 != 0:\\n    print(\\\"Odd\\\")\", \"a,b = list(map(int,input().split()))\\nc = a * b\\nif c%2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nif (a*b)%2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a,b=list(map(int,input().split()))\\n\\nif(a*b)%2==0:\\n  print('Even')\\nelse:\\n  print('Odd')\\n\", \"a, b = map(int,input().split())\\nif a * b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"numbers = input().split(\\\" \\\")\\nif (int(numbers[0])*int(numbers[1])) % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"a, b = map(int, input().split())\\nc = a * b\\nif(c % 2):\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a,b = map(int,input().split())\\nprint([\\\"Odd\\\",\\\"Even\\\"][a*b%2==0])\", \"a, b = map(int, input().split())\\nif a * b % 2: print('Odd')\\nelse: print('Even')\", \"a, b = input().split(' ')\\n\\nc = int(a)*int(b)\\nif c % 2 == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a,b = map(int, input().split())\\nif a * b % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"x,y = map(int,input().split())\\n\\nseki = x * y\\n\\nif seki % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nif a*b%2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int,input().split())\\nif (a*b)%2==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nc = a * b\\nprint(\\\"Even\\\" if c % 2 == 0 else \\\"Odd\\\")\", \"a,b = map(int, input().split())\\n \\nif (a*b) % 2  == 0:\\n  print(\\\"Even\\\")\\n  \\nelse :\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nif (a*b)%2 == 0:\\n  print('Even')\\nelse:\\n  print('Odd')\", \"a, b = map(int, input().split())\\nif a * b % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a,b = list(map(int,input().split()))\\nprint((\\\"Odd\\\" if a*b%2!=0 else \\\"Even\\\"))\\n\", \"a, b = map(int, input().split())\\nc = (a*b)%2\\n\\nif c ==1:\\n    print('Odd')\\nelse:\\n    print('Even')\", \"a,b=map(int, input().split())\\nprint(\\\"Odd\\\" if a*b%2 else \\\"Even\\\")\", \"a,b=(int(xx) for xx in input().split())\\nif (a*b)%2==0:\\n    print('Even')\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"def mapt(fn, *args):\\n    return tuple(map(fn, *args))\\n\\n\\ndef Input():\\n    return mapt(int, input().split(\\\" \\\"))\\n\\n\\ndef main():\\n    a, b = Input()\\n    print(\\\"Even\\\" if (a*b)%2==0 else \\\"Odd\\\")\\n\\n\\nmain()\", \"a,b = map(int,input().split())\\nanswer = a * b\\n\\nif answer % 2 == 0 :\\n  print('Even')\\nelse : \\n  print('Odd')\", \"a,b = map(int,input().split())\\nc = (a * b) % 2\\nif c == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a,b = map(int,input().split())\\nmul = a*b\\nif mul%2==1:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a,b=map(int,input().split())\\n\\nif (a*b)%2==0:print('Even')\\nelse:print('Odd')\", \"a,b = list(map(int, input().split()))\\nprint('Odd' if a&1 and b&1 else 'Even')\", \"a, b = map(int, input().split())\\n\\nif a * b % 2 == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a,b = map(int,input().split())\\nif a % 2 == 1 and b % 2 == 1:\\n    print('Odd')\\nelse:\\n    print('Even')\", \"a, b = map(int, input().split())\\n\\nif a * b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nS = a*b\\n\\nif S % 2 == 1:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a,b = map(int,input().split())\\nc = a*b\\nif c % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"def isEven(a, b):\\n    if a % 2 == 0:\\n        return True\\n    if b % 2 == 0:\\n        return True\\n    return False\\n\\ni = input().split()\\na = int(i[0])\\nb = int(i[1])\\nif isEven(a, b):\\n    print('Even')\\nelse:\\n    print('Odd')\", \"# coding: utf-8\\n# Your code here!\\nnum=input().split()\\nnum2=int(num[0])*int(num[1])\\n\\nif num2%2==0:\\n\\tprint(\\\"Even\\\")\\nelse:\\n  \\tprint(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nprint('Even') if a*b % 2 == 0 else print('Odd')\", \"a, b = map(int, input().split())\\nprint(\\\"Even\\\" if a*b % 2 == 0 else \\\"Odd\\\")\", \"#!/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\nIS = lambda: int(input())\\nIA = lambda: [int(x) for x in input().split()]\\n\\na, b = IA()\\nprint((\\\"Odd\\\" if (a * b) % 2 else \\\"Even\\\"))\\n\", \"a, b = map(int, input().split())\\n\\nflag = (a*b %2 ==0)\\nif flag:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a,b=map(int,input().split())\\nprint('EOvdedn'[a*b%2::2])\", \"a,b=map(int,input().split(\\\" \\\"))\\nprint([\\\"Even\\\",\\\"Odd\\\"][(a*b)%2])\", \"a, b = map(int, input().split())\\nprint('Even' if (a*b % 2) == 0 else 'Odd')\", \"p = input().split()\\n\\nprint (\\\"Even\\\" if int(p[0]) * int(p[1]) % 2 == 0 else \\\"Odd\\\")\", \"def solve(a, b):\\n    if a * b % 2 == 0:\\n        print('Even')\\n    else:\\n        print('Odd')\\n\\n\\ndef __starting_point():\\n    a, b = list(map(int, input().split()))\\n    solve(a, b)\\n\\n__starting_point()\", \"a, b = map(int,input().split())\\nif a*b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"lst = input().split()\\n\\nif (int(lst[0]) * int(lst[1])) % 2 == 0:\\n   print('Even')\\nelse:\\n   print('Odd')\", \"a, b = map(int, input().split())\\n\\nif a%2 == 0 or b%2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nif a * b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"[a, b] = input().split()\\n\\nif (int(a) % 2 == 0) or (int(b) % 2 == 0):\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"a, b = map(int, input().split())\\nprint(\\\"Even\\\" if a * b % 2 == 0 else \\\"Odd\\\" )\", \"a, b = [int(i) for i in input().split()]\\n\\nprint(('Odd' if a * b % 2 == 1 else 'Even'))\\n\", \"a,b=map(int,input().split())\\nif a*b%2==0:\\n  print('Even')\\nelse:\\n  print('Odd')\", \"a, b = map(int, input().split(' '))\\n\\nmod_ab = (a*b)%2\\n\\nif(mod_ab==0) :\\n  print(\\\"Even\\\")\\nelse :\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nprint(\\\"Odd\\\" if a*b%2==1 else \\\"Even\\\")\", \"import numpy as np\\ns=list(map(int,input().split()))\\n\\np=np.prod(s)\\nif(p%2==0):\\n    print('Even')\\nelse:\\n    print('Odd')\", \"print(\\\"Odd\\\" if all(map(lambda x:int(x)%2, input().split())) else \\\"Even\\\")\", \"a,b = map(int,input().split())\\n\\nif a*b%2 == 0:\\n  print('Even')\\n  \\nelse:\\n  print('Odd')\", \"a, b = map(int, input().split())\\nif (a*b) % 2:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a, b = map(int, input().split())\\nc = (a * b) % 2\\n\\nif c == 0:\\n    print('Even')\\nelif c == 1:\\n    print('Odd')\", \"a,b = map(int, input().split())\\nif (a * b) %2 == 0:\\n    print('Even')\\nelif(a * b) %2 == 1:\\n    print('Odd')\", \"a, b = map(int, input().split())\\nprint(\\\"Odd\\\" if a * b % 2 == 1 else \\\"Even\\\")\", \"a,b = map(int, input().split())\\nif a*b%2 == 1:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"#85A\\na,b=map(int,input().split())\\nif a*b%2==0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a, b = map(int,input().split())\\nc = a * b\\nif c % 2 == 0 :\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nprint('Even' if a*b % 2 == 0 else 'Odd')\", \"a, b = list(map(int, input().split()))\\nif (a * b) % 2 == 0:\\n    print('Even')\\n\\nelse:\\n    print('Odd')\\n\", \"aa,bb=map(int,input().split())\\n\\nif aa * bb % 2 == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a, b = map(int,input().split())\\nif (a * b) % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"getints = lambda: list(map(int, input().split()))\\na, b = getints()\\nif a * b % 2:\\n    print('Odd')\\nelse:\\n    print('Even')\\n\", \"# \\u30b9\\u30da\\u30fc\\u30b9\\u533a\\u5207\\u308a\\u306e\\u6574\\u6570\\u306e\\u5165\\u529b\\nb, c = map(int, input().split())\\n \\nif b * c % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a,b = map(int,input().split())\\n\\nif (a*b)%2 == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a,b=map(int,input().split())\\nif 0==(a*b)%2:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"#!/usr/bin/env python3\\nimport sys\\nsys.setrecursionlimit(10**6)\\n\\na, b = list(map(int, input().split()))\\n\\nif a*b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"# coding: utf-8\\n# Your code here!\\n\\na, b = map(int, input().split())\\n\\nif a*b % 2 == 0 : \\n    print(\\\"Even\\\")\\nelse : \\n    print(\\\"Odd\\\")\", \"a,b = map(int,input().split())\\n\\nif a*b % 2 == 0:\\n  print('Even')\\nelse:\\n  print('Odd')\", \"x, y = map(int, input().split())\\n \\nl = (x*y) % 2\\nif l == 0:\\n\\tprint('Even')\\nelse:\\n \\tprint('Odd')\", \"a, b = map(int,input().split())\\nif a*b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nif (a * b) % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a,b=map(int,input().split())\\nif a*b%2==0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a,b = (int(x) for x in input().split())\\n\\nmulti = a * b\\n\\nif multi %2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"a, b = map(int, input().split())\\nif (a*b) % 2 ==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a,b = list(map(int,input().split()))\\nprint((\\\"Even\\\" if a*b%2 == 0 else \\\"Odd\\\"))\\n\\n\", \"a,b=map(int,input().split())\\nif a*b%2==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nif a % 2 == 1 and b % 2 == 1:\\n  print('Odd')\\nelse:\\n  print('Even')\", \"a, b = map(int, input().split())\\n\\nprint('Even') if a*b % 2 == 0 else print('Odd')\", \"a,b = map(int,input().split())\\nif (a * b) % 2 == 1:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\"]",
        "difficulty": "introductory",
        "input": "3 4\n",
        "output": "Even\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc086/tasks/abc086_a"
    },
    {
        "id": 524,
        "task_id": 4696,
        "test_case_id": 2,
        "question": "AtCoDeer the deer found two positive integers, a and b.\nDetermine whether the product of a and b is even or odd.\n\n-----Constraints-----\n - 1 ≤ a,b ≤ 10000\n - a and b are integers.\n\n-----Input-----\nInput is given from Standard Input in the following format:\na b\n\n-----Output-----\nIf the product is odd, print Odd; if it is even, print Even.\n\n-----Sample Input-----\n3 4\n\n-----Sample Output-----\nEven\n\nAs 3 × 4 = 12 is even, print Even.",
        "solutions": "[\"a, b = map(int, input().split())\\nif a*b %2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nif a % 2 == 0:\\n  print('Even')\\nelif b % 2 == 0:\\n  print('Even')\\nelse:\\n  print('Odd')\", \"a,b=map(int, input().split())\\n\\nif a*b%2==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"# -*- coding: utf-8 -*-\\n \\na, b = map(int, input().split())\\n \\nmul = a * b\\n \\nresult = 'Even' if (mul % 2 == 0) else 'Odd'\\n  \\nprint(result)\", \"a, b = map(int, input().split())\\nprint([\\\"Even\\\", \\\"Odd\\\"][a * b % 2])\", \"a,b=(int(x) for x in input().split())\\n \\nif a*b%2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nprint('Odd' if a*b % 2 == 1 else 'Even')\", \"a, b = map(int,input().split())\\n\\nadd = (a * b)\\n\\nif add % 2 != 0:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a,b = list(map(int, input().split())) \\nc =a*b\\nif c%2==0:\\n  print('Even')\\nelse:\\n  print('Odd')\\n\", \"a,b=input().split()\\nif int(a)*int(b)%2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"import bisect,collections,copy,heapq,itertools,math,string\\nimport sys\\ndef I():\\n    #1 line 1 int\\n     return int(sys.stdin.readline().rstrip())\\ndef LI():\\n    #1 line n int\\n     return list(map(int,sys.stdin.readline().rstrip().split()))\\ndef S():\\n    #1 line 1 string\\n     return sys.stdin.readline().rstrip()\\ndef LS():\\n    #1 line n strings\\n     return list(sys.stdin.readline().rstrip().split())\\n\\na,b,=LI()\\n\\nif (a*b)%2==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nprint(\\\"Even\\\" if a * b % 2 == 0 else \\\"Odd\\\")\", \"a, b = list(map(int, input().split()))\\nif a * b % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\\n\", \"a,b = map(int,input().split())\\nc=a*b\\n\\nif c % 2 ==1:\\n    print('Odd')\\n\\nelse:\\n    print('Even')\", \"a, b = map(int, input().split())\\nif (a * b) % 2 == 0:\\n    print(\\\"Even\\\")\\nelif (a * b) % 2 != 0:\\n    print(\\\"Odd\\\")\", \"a,b = list(map(int,input().split()))\\nc = a * b\\nif c%2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nif (a*b)%2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a,b=list(map(int,input().split()))\\n\\nif(a*b)%2==0:\\n  print('Even')\\nelse:\\n  print('Odd')\\n\", \"a, b = map(int,input().split())\\nif a * b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"numbers = input().split(\\\" \\\")\\nif (int(numbers[0])*int(numbers[1])) % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"a, b = map(int, input().split())\\nc = a * b\\nif(c % 2):\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a,b = map(int,input().split())\\nprint([\\\"Odd\\\",\\\"Even\\\"][a*b%2==0])\", \"a, b = map(int, input().split())\\nif a * b % 2: print('Odd')\\nelse: print('Even')\", \"a, b = input().split(' ')\\n\\nc = int(a)*int(b)\\nif c % 2 == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a,b = map(int, input().split())\\nif a * b % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"x,y = map(int,input().split())\\n\\nseki = x * y\\n\\nif seki % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nif a*b%2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int,input().split())\\nif (a*b)%2==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nc = a * b\\nprint(\\\"Even\\\" if c % 2 == 0 else \\\"Odd\\\")\", \"a,b = map(int, input().split())\\n \\nif (a*b) % 2  == 0:\\n  print(\\\"Even\\\")\\n  \\nelse :\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nif (a*b)%2 == 0:\\n  print('Even')\\nelse:\\n  print('Odd')\", \"a, b = map(int, input().split())\\nif a * b % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a,b = list(map(int,input().split()))\\nprint((\\\"Odd\\\" if a*b%2!=0 else \\\"Even\\\"))\\n\", \"a, b = map(int, input().split())\\nc = (a*b)%2\\n\\nif c ==1:\\n    print('Odd')\\nelse:\\n    print('Even')\", \"a,b=map(int, input().split())\\nprint(\\\"Odd\\\" if a*b%2 else \\\"Even\\\")\", \"a,b=(int(xx) for xx in input().split())\\nif (a*b)%2==0:\\n    print('Even')\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"def mapt(fn, *args):\\n    return tuple(map(fn, *args))\\n\\n\\ndef Input():\\n    return mapt(int, input().split(\\\" \\\"))\\n\\n\\ndef main():\\n    a, b = Input()\\n    print(\\\"Even\\\" if (a*b)%2==0 else \\\"Odd\\\")\\n\\n\\nmain()\", \"a,b = map(int,input().split())\\nanswer = a * b\\n\\nif answer % 2 == 0 :\\n  print('Even')\\nelse : \\n  print('Odd')\", \"a,b = map(int,input().split())\\nc = (a * b) % 2\\nif c == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a,b = map(int,input().split())\\nmul = a*b\\nif mul%2==1:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a,b=map(int,input().split())\\n\\nif (a*b)%2==0:print('Even')\\nelse:print('Odd')\", \"a,b = list(map(int, input().split()))\\nprint('Odd' if a&1 and b&1 else 'Even')\", \"a, b = map(int, input().split())\\n\\nif a * b % 2 == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a,b = map(int,input().split())\\nif a % 2 == 1 and b % 2 == 1:\\n    print('Odd')\\nelse:\\n    print('Even')\", \"a, b = map(int, input().split())\\n\\nif a * b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nS = a*b\\n\\nif S % 2 == 1:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a,b = map(int,input().split())\\nc = a*b\\nif c % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"def isEven(a, b):\\n    if a % 2 == 0:\\n        return True\\n    if b % 2 == 0:\\n        return True\\n    return False\\n\\ni = input().split()\\na = int(i[0])\\nb = int(i[1])\\nif isEven(a, b):\\n    print('Even')\\nelse:\\n    print('Odd')\", \"# coding: utf-8\\n# Your code here!\\nnum=input().split()\\nnum2=int(num[0])*int(num[1])\\n\\nif num2%2==0:\\n\\tprint(\\\"Even\\\")\\nelse:\\n  \\tprint(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nprint('Even') if a*b % 2 == 0 else print('Odd')\", \"a, b = map(int, input().split())\\nprint(\\\"Even\\\" if a*b % 2 == 0 else \\\"Odd\\\")\", \"#!/bin/env python3\\n# -*- coding: utf-8 -*-\\n\\nIS = lambda: int(input())\\nIA = lambda: [int(x) for x in input().split()]\\n\\na, b = IA()\\nprint((\\\"Odd\\\" if (a * b) % 2 else \\\"Even\\\"))\\n\", \"a, b = map(int, input().split())\\n\\nflag = (a*b %2 ==0)\\nif flag:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a,b=map(int,input().split())\\nprint('EOvdedn'[a*b%2::2])\", \"a,b=map(int,input().split(\\\" \\\"))\\nprint([\\\"Even\\\",\\\"Odd\\\"][(a*b)%2])\", \"a, b = map(int, input().split())\\nprint('Even' if (a*b % 2) == 0 else 'Odd')\", \"p = input().split()\\n\\nprint (\\\"Even\\\" if int(p[0]) * int(p[1]) % 2 == 0 else \\\"Odd\\\")\", \"def solve(a, b):\\n    if a * b % 2 == 0:\\n        print('Even')\\n    else:\\n        print('Odd')\\n\\n\\ndef __starting_point():\\n    a, b = list(map(int, input().split()))\\n    solve(a, b)\\n\\n__starting_point()\", \"a, b = map(int,input().split())\\nif a*b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"lst = input().split()\\n\\nif (int(lst[0]) * int(lst[1])) % 2 == 0:\\n   print('Even')\\nelse:\\n   print('Odd')\", \"a, b = map(int, input().split())\\n\\nif a%2 == 0 or b%2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nif a * b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"[a, b] = input().split()\\n\\nif (int(a) % 2 == 0) or (int(b) % 2 == 0):\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"a, b = map(int, input().split())\\nprint(\\\"Even\\\" if a * b % 2 == 0 else \\\"Odd\\\" )\", \"a, b = [int(i) for i in input().split()]\\n\\nprint(('Odd' if a * b % 2 == 1 else 'Even'))\\n\", \"a,b=map(int,input().split())\\nif a*b%2==0:\\n  print('Even')\\nelse:\\n  print('Odd')\", \"a, b = map(int, input().split(' '))\\n\\nmod_ab = (a*b)%2\\n\\nif(mod_ab==0) :\\n  print(\\\"Even\\\")\\nelse :\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nprint(\\\"Odd\\\" if a*b%2==1 else \\\"Even\\\")\", \"import numpy as np\\ns=list(map(int,input().split()))\\n\\np=np.prod(s)\\nif(p%2==0):\\n    print('Even')\\nelse:\\n    print('Odd')\", \"print(\\\"Odd\\\" if all(map(lambda x:int(x)%2, input().split())) else \\\"Even\\\")\", \"a,b = map(int,input().split())\\n\\nif a*b%2 == 0:\\n  print('Even')\\n  \\nelse:\\n  print('Odd')\", \"a, b = map(int, input().split())\\nif (a*b) % 2:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"a, b = map(int, input().split())\\nc = (a * b) % 2\\n\\nif c == 0:\\n    print('Even')\\nelif c == 1:\\n    print('Odd')\", \"a,b = map(int, input().split())\\nif (a * b) %2 == 0:\\n    print('Even')\\nelif(a * b) %2 == 1:\\n    print('Odd')\", \"a, b = map(int, input().split())\\nprint(\\\"Odd\\\" if a * b % 2 == 1 else \\\"Even\\\")\", \"a,b = map(int, input().split())\\nif a*b%2 == 1:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\", \"#85A\\na,b=map(int,input().split())\\nif a*b%2==0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a, b = map(int,input().split())\\nc = a * b\\nif c % 2 == 0 :\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\nprint('Even' if a*b % 2 == 0 else 'Odd')\", \"a, b = list(map(int, input().split()))\\nif (a * b) % 2 == 0:\\n    print('Even')\\n\\nelse:\\n    print('Odd')\\n\", \"aa,bb=map(int,input().split())\\n\\nif aa * bb % 2 == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a, b = map(int,input().split())\\nif (a * b) % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"getints = lambda: list(map(int, input().split()))\\na, b = getints()\\nif a * b % 2:\\n    print('Odd')\\nelse:\\n    print('Even')\\n\", \"# \\u30b9\\u30da\\u30fc\\u30b9\\u533a\\u5207\\u308a\\u306e\\u6574\\u6570\\u306e\\u5165\\u529b\\nb, c = map(int, input().split())\\n \\nif b * c % 2 == 0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a,b = map(int,input().split())\\n\\nif (a*b)%2 == 0:\\n    print('Even')\\nelse:\\n    print('Odd')\", \"a,b=map(int,input().split())\\nif 0==(a*b)%2:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"#!/usr/bin/env python3\\nimport sys\\nsys.setrecursionlimit(10**6)\\n\\na, b = list(map(int, input().split()))\\n\\nif a*b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"# coding: utf-8\\n# Your code here!\\n\\na, b = map(int, input().split())\\n\\nif a*b % 2 == 0 : \\n    print(\\\"Even\\\")\\nelse : \\n    print(\\\"Odd\\\")\", \"a,b = map(int,input().split())\\n\\nif a*b % 2 == 0:\\n  print('Even')\\nelse:\\n  print('Odd')\", \"x, y = map(int, input().split())\\n \\nl = (x*y) % 2\\nif l == 0:\\n\\tprint('Even')\\nelse:\\n \\tprint('Odd')\", \"a, b = map(int,input().split())\\nif a*b % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nif (a * b) % 2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a,b=map(int,input().split())\\nif a*b%2==0:\\n  print(\\\"Even\\\")\\nelse:\\n  print(\\\"Odd\\\")\", \"a,b = (int(x) for x in input().split())\\n\\nmulti = a * b\\n\\nif multi %2 == 0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\\n\", \"a, b = map(int, input().split())\\nif (a*b) % 2 ==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a,b = list(map(int,input().split()))\\nprint((\\\"Even\\\" if a*b%2 == 0 else \\\"Odd\\\"))\\n\\n\", \"a,b=map(int,input().split())\\nif a*b%2==0:\\n    print(\\\"Even\\\")\\nelse:\\n    print(\\\"Odd\\\")\", \"a, b = map(int, input().split())\\n\\nif a % 2 == 1 and b % 2 == 1:\\n  print('Odd')\\nelse:\\n  print('Even')\", \"a, b = map(int, input().split())\\n\\nprint('Even') if a*b % 2 == 0 else print('Odd')\", \"a,b = map(int,input().split())\\nif (a * b) % 2 == 1:\\n    print(\\\"Odd\\\")\\nelse:\\n    print(\\\"Even\\\")\"]",
        "difficulty": "introductory",
        "input": "1 21\n",
        "output": "Odd\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://atcoder.jp/contests/abc086/tasks/abc086_a"
    },
    {
        "id": 525,
        "task_id": 4891,
        "test_case_id": 1,
        "question": "Mirko has found an old chessboard and a set of pieces in his attic. Unfortunately, the set contains only white pieces, and apparently an incorrect number of them. A set of pieces should contain:\n - One king\n - One queen\n - Two rooks\n - Two bishops\n - Two knights\n - Eight pawns\n\nMirko would like to know how many pieces of each type he should add or remove to make a valid set.\n\n-----Input-----\nThe input consists of $6$ integers on a single line, each between $0$ and $10$ (inclusive). The numbers are, in order, the numbers of kings, queens, rooks, bishops, knights and pawns in the set Mirko found.\n\n-----Output-----\nOutput should consist of $6$ integers on a single line; the number of pieces of each type Mirko should add or remove. If a number is positive, Mirko needs to add that many pieces. If a number is negative, Mirko needs to remove pieces.\n\n-----Examples-----\nSample Input:\n0 1 2 2 2 7\nSample Output:\n1 0 0 0 0 1",
        "solutions": "",
        "difficulty": "introductory",
        "input": "0 1 2 2 2 7\n",
        "output": "1 0 0 0 0 1\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/bijele"
    },
    {
        "id": 526,
        "task_id": 4891,
        "test_case_id": 2,
        "question": "Mirko has found an old chessboard and a set of pieces in his attic. Unfortunately, the set contains only white pieces, and apparently an incorrect number of them. A set of pieces should contain:\n - One king\n - One queen\n - Two rooks\n - Two bishops\n - Two knights\n - Eight pawns\n\nMirko would like to know how many pieces of each type he should add or remove to make a valid set.\n\n-----Input-----\nThe input consists of $6$ integers on a single line, each between $0$ and $10$ (inclusive). The numbers are, in order, the numbers of kings, queens, rooks, bishops, knights and pawns in the set Mirko found.\n\n-----Output-----\nOutput should consist of $6$ integers on a single line; the number of pieces of each type Mirko should add or remove. If a number is positive, Mirko needs to add that many pieces. If a number is negative, Mirko needs to remove pieces.\n\n-----Examples-----\nSample Input:\n0 1 2 2 2 7\nSample Output:\n1 0 0 0 0 1",
        "solutions": "",
        "difficulty": "introductory",
        "input": "2 1 2 1 2 1\n",
        "output": "-1 0 0 1 0 7\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/bijele"
    },
    {
        "id": 527,
        "task_id": 4894,
        "test_case_id": 1,
        "question": "There are many types of languages, all used for different purposes. People communicate using natural languages like English and Spanish, program with formal languages like C++ and Perl, and compose music with musical notation. Let’s consider musical notation, which is typically a sequence of notes of specified pitches and durations. Computers can best represent these sequences using numbers and letters, such as\n\nC C D E C E D2 C C D E C2 B2 C C D E F E D C B g A B C2 C2\n\nwhich is a simple rendition of the song ‘Yankee Doodle’. The notes are chosen from a through g and A through G. A note without a number indicates it is held for a duration of one beat; the number $2$ following some of the notes indicate that note has a duration that is twice as long. It would be nice to take this notation and create something musicians are more used to reading, with notes and bars and staffs, etc. Write a program that does this.\n\n-----Input-----\nThe input for your program consists of two lines. The first line has an integer $1 \\le n \\le 100$ indicating the number of notes in the song. The second line contains $n$ notes. Each note consists of two parts: the pitch and the duration. The pitch is a letter a through g or A through G. Lowercase letters indicate the octave below uppercase letters, and we consider c to represent so-called ‘middle c’. The duration, which is optional, is a positive integer indicating a multiplier of the length of the default note. (If you are musical you’ll notice we’ve made many simplifying assumptions, such as leaving out many octaves, sharps, flats, rests, time signatures, etc.)\n\n-----Output-----\nFor each song, print a text-based representation on one staff. Each staff should have the following format: a $5$-line staff (for the treble clef), middle c, and one more line (for the top of the bass clef):\n\nG:           \nF: ----------------------------------------------------------\nE:           \nD: ----------------------------------------------------------\nC:           \nB: ----------------------------------------------------------\nA:           \ng: ----------------------------------------------------------\nf:           \ne: ----------------------------------------------------------\nd:           \nc:           \nb:           \na: ----------------------------------------------------------\n\nFor each song’s note, print a single asterisk on a line (or between lines) indicating its pitch. Use one asterisk for the default duration, two asterisks for notes twice as long, three asterisks for notes three times as long, etc. Leave a single separating column between each pair of consecutive notes. The staff lines should be only as long as necessary to complete the song. Notes that are between lines (i.e. b-d, f, A, C, E, G) should pad with spaces out to the end the staff lines.\n\n-----Examples-----\nSample Input:\n27\nC C D E C E D2 C C D E C2 B2 C C D E F E D C B g A B C2 C2\nSample Output:\nG:                                                           \nF: -------------------------------------*--------------------\nE:       *   *          *             *   *                  \nD: ----*-------**-----*-------------*-------*----------------\nC: * *     *      * *     **    * *           *         ** **\nB: --------------------------**-----------------*-----*------\nA:                                                  *        \ng: -----------------------------------------------*----------\nf:                                                           \ne: ----------------------------------------------------------\nd:                                                           \nc:                                                           \nb:                                                           \na: ----------------------------------------------------------",
        "solutions": "",
        "difficulty": "introductory",
        "input": "27\nC C D E C E D2 C C D E C2 B2 C C D E F E D C B g A B C2 C2\n",
        "output": "G:                                                           \nF: -------------------------------------*--------------------\nE:       *   *          *             *   *                  \nD: ----*-------**-----*-------------*-------*----------------\nC: * *     *      * *     **    * *           *         ** **\nB: --------------------------**-----------------*-----*------\nA:                                                  *        \ng: -----------------------------------------------*----------\nf:                                                           \ne: ----------------------------------------------------------\nd:                                                           \nc:                                                           \nb:                                                           \na: ----------------------------------------------------------\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/musicalnotation"
    },
    {
        "id": 528,
        "task_id": 4894,
        "test_case_id": 2,
        "question": "There are many types of languages, all used for different purposes. People communicate using natural languages like English and Spanish, program with formal languages like C++ and Perl, and compose music with musical notation. Let’s consider musical notation, which is typically a sequence of notes of specified pitches and durations. Computers can best represent these sequences using numbers and letters, such as\n\nC C D E C E D2 C C D E C2 B2 C C D E F E D C B g A B C2 C2\n\nwhich is a simple rendition of the song ‘Yankee Doodle’. The notes are chosen from a through g and A through G. A note without a number indicates it is held for a duration of one beat; the number $2$ following some of the notes indicate that note has a duration that is twice as long. It would be nice to take this notation and create something musicians are more used to reading, with notes and bars and staffs, etc. Write a program that does this.\n\n-----Input-----\nThe input for your program consists of two lines. The first line has an integer $1 \\le n \\le 100$ indicating the number of notes in the song. The second line contains $n$ notes. Each note consists of two parts: the pitch and the duration. The pitch is a letter a through g or A through G. Lowercase letters indicate the octave below uppercase letters, and we consider c to represent so-called ‘middle c’. The duration, which is optional, is a positive integer indicating a multiplier of the length of the default note. (If you are musical you’ll notice we’ve made many simplifying assumptions, such as leaving out many octaves, sharps, flats, rests, time signatures, etc.)\n\n-----Output-----\nFor each song, print a text-based representation on one staff. Each staff should have the following format: a $5$-line staff (for the treble clef), middle c, and one more line (for the top of the bass clef):\n\nG:           \nF: ----------------------------------------------------------\nE:           \nD: ----------------------------------------------------------\nC:           \nB: ----------------------------------------------------------\nA:           \ng: ----------------------------------------------------------\nf:           \ne: ----------------------------------------------------------\nd:           \nc:           \nb:           \na: ----------------------------------------------------------\n\nFor each song’s note, print a single asterisk on a line (or between lines) indicating its pitch. Use one asterisk for the default duration, two asterisks for notes twice as long, three asterisks for notes three times as long, etc. Leave a single separating column between each pair of consecutive notes. The staff lines should be only as long as necessary to complete the song. Notes that are between lines (i.e. b-d, f, A, C, E, G) should pad with spaces out to the end the staff lines.\n\n-----Examples-----\nSample Input:\n27\nC C D E C E D2 C C D E C2 B2 C C D E F E D C B g A B C2 C2\nSample Output:\nG:                                                           \nF: -------------------------------------*--------------------\nE:       *   *          *             *   *                  \nD: ----*-------**-----*-------------*-------*----------------\nC: * *     *      * *     **    * *           *         ** **\nB: --------------------------**-----------------*-----*------\nA:                                                  *        \ng: -----------------------------------------------*----------\nf:                                                           \ne: ----------------------------------------------------------\nd:                                                           \nc:                                                           \nb:                                                           \na: ----------------------------------------------------------",
        "solutions": "",
        "difficulty": "introductory",
        "input": "22\ne2 e d c2 c2 d2 d f e d c2 g2 g f e2 e2 e d c d e c3\n",
        "output": "G:                                                      \nF: -----------------------------------------------------\nE:                                                      \nD: -----------------------------------------------------\nC:                                                      \nB: -----------------------------------------------------\nA:                                                      \ng: ---------------------------**-*----------------------\nf:                   *             *                    \ne: **-*----------------*-------------**-**-*-------*----\nd:      *       ** *     *                   *   *      \nc:        ** **            **                  *     ***\nb:                                                      \na: -----------------------------------------------------\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/musicalnotation"
    },
    {
        "id": 529,
        "task_id": 4933,
        "test_case_id": 1,
        "question": "Mirko has chosen four integers which form an arithmetic progression. In other words, when the four numbers are sorted, then the difference between each pair of adjacent elements is constant.\n\nAs has become usual, Mirko lost one of the numbers and also is not sure whether the remaining three are in the correct (sorted) order.\n\nWrite a program that, given the three remaining numbers, finds the fourth number.\n\n-----Input-----\nThe input contains 3 integers between $-100$ and $100$ on a single line, separated by single spaces.\n\nNote: the input data will guarantee that a solution, although not necessarily unique, will always exist.\n\n-----Output-----\nOutput any number which could have been the fourth number in the sequence.\n\n-----Examples-----\nSample Input:\n4 6 8\nSample Output:\n10",
        "solutions": "",
        "difficulty": "introductory",
        "input": "4 6 8\n",
        "output": "10\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/cetiri"
    },
    {
        "id": 530,
        "task_id": 4933,
        "test_case_id": 2,
        "question": "Mirko has chosen four integers which form an arithmetic progression. In other words, when the four numbers are sorted, then the difference between each pair of adjacent elements is constant.\n\nAs has become usual, Mirko lost one of the numbers and also is not sure whether the remaining three are in the correct (sorted) order.\n\nWrite a program that, given the three remaining numbers, finds the fourth number.\n\n-----Input-----\nThe input contains 3 integers between $-100$ and $100$ on a single line, separated by single spaces.\n\nNote: the input data will guarantee that a solution, although not necessarily unique, will always exist.\n\n-----Output-----\nOutput any number which could have been the fourth number in the sequence.\n\n-----Examples-----\nSample Input:\n4 6 8\nSample Output:\n10",
        "solutions": "",
        "difficulty": "introductory",
        "input": "10 1 4\n",
        "output": "7\n",
        "halu_type": "External Source Hallucination",
        "fn_name": null,
        "starter_code": "",
        "url": "https://open.kattis.com/problems/cetiri"
    }
]